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In This Chapter

^ Reviewing important points on bonding

^ Breaking yourself in with some practice questions on bonding ^ Finding out what you did right. . . and not so right

Chapter 5 introduced you to chemical bonds, the attractive forces that bring atoms together to form compounds. Atoms come together to form different kinds of bonds and a multitude of different compounds. Yet, for all the complication, the basic rules of the game are pretty straightforward. Review them here and test your mastery of the material with the practice questions.

Brushing Up on Bonding Forget-Me-Nots

We’ve included a helpful summary of the points from Chapter 5 that you need to remember. So, do some bonding of your own with the following list:

Compounds Are collections of atoms held together by bonds.

• Ionic bonds Arise from electrostatic attraction between ions of opposite charge (between anions and cations).

• Covalent bonds Arise when atoms share electrons.

• Metallic bonding Involves a sea of electrons that moves freely through a lattice of metal cations.

Ionic bonds tend to form between a metal and a nonmetal. Covalent bonds tend to form between nonmetals.

Inorganic compounds are named in a systematic way (see the figure in Chapter 5). Naming and recognizing compounds will be much easier if you are familiar with the common polyatomic ions (see the table in Chapter 5).

Solid ionic compounds consist of a highly ordered lattice of ions. The strength of an ionic bond within a lattice is expressed by Lattice energy. Large, positive lattice energies correspond to strong ionic bonds.

Other factors being equal, ionic bonds tend to be stronger between ions with more charge, and between smaller ions.

Electrons within covalent bonds distribute with greater density in the region between the two atomic nuclei.

Usually, each atom of a covalent bond contributes one electron per bond. When one atom contributes both electrons, we say the bond is a Coordinate covalent bond.

The strength of covalent bonds is described by Bond enthalpy. Large, positive bond enthalpies correspond to strong covalent bonds.

Polar bonds Are marked by unequal sharing of electrons. Electronegativity Is the tendency of an atom to draw electrons to itself.

• Bonds between atoms with extreme differences in electronegativity are ionic.

• Bonds between atoms with significant differences in electronegativity are polar covalent.

• Bonds between atoms with insignificant differences in electronegativity are nonpolar covalent.

The polarity of a bond is described by the Bond dipole, U. = Qd, where Q is the magnitude of the separated charge and D Is the distance of separation.

Bond dipoles sum within molecules to produce Molecular dipoles. Dipole-dipole and ion-dipole interactions are major contributors to the properties of different compounds, especially boiling points and melting points.

Testing Your Knowledge

Try your hand at these practice questions on bonding. Do yourself a favor by not looking back in the text to get the questions correct on the first try. Do your best, and then check your answers afterward so that you can discover what you need to review.

1. Which of the following are compounds that might reasonably form from combining iron and oxygen?

(I) Fe2O3

(II) Fe3O2

(III) FeO

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) I and III only

2. Which of the following is least likely to be a stable compound?

(A) CF4

(B) S2O

(C) PCl3

(D) SiO3

(E) NO

3. Which of the following compounds is least likely to form?

(A) Na2Cr7O2

(B) KC2H3O2

(C) Li2CN

(D) Rb2C2O4

(E) HNO2

4. Which of the following is correctly named?

(A) CsCl; cesium (I) chloride

(B) Fe2O3; iron (II) oxide

(C) CBr4; carbon quatrobromide

(D) NO2; dioxygen mononitride

(E) MnO2; manganese (IV) oxide

5. Which empirical formula best fits the following percent composition? 50.00% carbon, 5.59% oxygen, 44.41% hydrogen

Questions 6 through 10 refer to the following types of bonds:

(A) Ionic bonds

(B) Polar covalent bonds

(C) Nonpolar covalent bonds

(D) Coordinate covalent bonds

(E) Metallic bonds

6. Form in compounds like N2 and O2

7. Tend to support electrical conductivity

8. Tend to form strong, brittle compounds

9. Tend to form from an atom containing a lone pair of electrons 10. Form in compounds like CO and H2S

Checking Your Work

You’ve done your best. Now check your work. Make sure to read the explanations thoroughly for any questions you got wrong — or for any you got right by guessing.

1. (E). Both Fe2O3 (iron (III) oxide) and FeO (iron (II) oxide) can form, the former from the Fe3+ cation and the latter from the Fe2+ cation. Fe3O2 is a bad choice because the overall charge of this compound is not neutral; even using Fe2+, there is an excess of positive charge because each oxygen can contribute only -2 charge.

2. (D). As shown, SiO3 is least likely to be stable. Although the SiO32- (silicate) anion exists, the compound shown in the question is neutral. In order to fill its valence shell and remain neutral, silicon requires four covalent bonds.

3. (C). Li2CN is least likely to occur because the "ion math" doesn’t work. Lithium forms cations with +1 charge (Li+) and the cyanide ion has -1 charge (CN-). So, a more likely version of this compound is LiCN.

4. (E). If a manganese ion with +4 charge is used (Mn4+), the compound can form; that ion is specified by the Roman numeral IV. As described in the answer for question 1, Fe2O3 is correct as long as the Fe3+ ion is used. But the Roman numeral II in the name specifies the Fe2+ ion. Answer A is incorrect because the alkali metal cesium forms only ions with +1 charge, so no Roman numeral is used in its name. The correct names for the compounds in choices C and D are carbon tetrabromide and nitrogen dioxide, respectively.

5. (C). Percent composition refers to percent weight. So, a 100.g sample of the mystery compound would contain 50.00g carbon, 44.41g oxygen, and 5.59g hydrogen. To convert these masses to relative numbers of each type of atom, divide each mass by the molar mass of that atom:

50.00g carbon / (12.01g mol-1) = 4.163 mol carbon 5.59g hydrogen / (1.01g mol-1) = 5.53 mol hydrogen 44.41g oxygen / (16.00g mol-1) = 2.776 mol oxygen

Next, take the smallest mol value of the set (2.776 mol in this case) and divide all the mol values by that number. You get: 1.5 mol carbon, 1 mol oxygen, and 2.0 mol hydrogen. You can’t build compounds with fractions of an atom, so multiply all results by the smallest number that will produce a set of whole numbers. In this case, multiplying all values by 2 does the trick, yielding: 3 mol carbon, 2 mol oxygen, and 4 mol hydrogen. Finally, assemble the atom symbols and the whole numbers into an empirical formula: C3H4O2.

6. (C). Covalent bonds between identical atoms are nonpolar because each atom has identical electronegativity.

7. (E). The sea of mobile electrons that is the defining feature of metallic bonding supports electrical conductivity; the mobile electrons can move in response to applied voltage.

8. (A). Ionic bonds are strong, but the extreme order of ionic bonding lends itself to fracturing.

9. (D). Coordinate covalent bonds form when one atom contributes both electrons to the bond; lone pairs are perfect for this task, because they include two electrons not otherwise involved in bonding.

10. (B). Polar covalent bonds form between the atoms in compounds like these because the atoms have significantly different electronegativities — but not so different that ionic bonds form instead.

In This Chapter

^ Finding your way around atoms and the periodic table

^ Figuring out ions and electron configuration

^ Illuminating the info you need on isotopes

^ Getting up to speed on decay

^ Understanding the excited state of electrons

For hundreds of years, scientists have operated under the idea that all matter is made up of smaller building blocks called Atoms. So small, in fact, that until the invention of the electron microscope, the only way to find out anything about these tiny, mysterious particles was to design a very clever experiment. These experiments allowed chemists to get around the fact that they couldn’t exactly corner a single atom in a back alley somewhere and study it alone — they had to study the properties of whole gangs of atoms and try to guess what individual ones might be like. Through some remarkable cleverness and some incredibly lucky shots in the dark, chemists now understand a great deal about the atom, and guess what? You need to, too! Because we don’t want to leave you hanging, in this chapter we introduce you to everything you need to know about atoms, their properties, and what they are made of.

Picking Apart Atoms and the Periodic Table

The following sections begin by giving you the basics on how atoms are structured so that you can not only get to know their components, but also, you can easily figure out how atoms help to classify elements. Even better, we give you the ultimate road map for the periodic table, showing you how the periodic table can give you some valuable info that helps you predict certain properties of elements.

Getting a gander at what makes up an atom

For now, picture an atom as a microscopic building block. Atoms come in all shapes and sizes, and you can build larger structures out of them. However, like building blocks, atoms are extremely hard to break. In fact, there is so much energy stored inside an atom that breaking one in half is the process that drives a nuclear explosion.

All substances consist of the 120 unique varieties of atoms, each of which is made up of a combination of three types of Subatomic particles:

Protons: Protons have equal and opposite charges to electrons and have very nearly the same mass as neutrons.

Electrons: Electrons have equal and opposite charges to protons, and electrons are much lighter than protons and neutrons.

^ Neutrons: Neutrons are neutral and have the same mass as protons. We summarize the must-know information about the three subatomic particles in Table 3-1.

Atoms always have an equal number of protons and electrons, which makes them overall electrically neutral. Many atoms, however, actually prefer to have an unbalanced number of protons and electrons, which leaves them with an overall charge. We discuss these charged atoms, called Ions, Even further in the section "Exercising Electrons: Ions and Electron Configuration," later in this chapter.

The atom can still safely be called the smallest possible unit of an element because after you break an atom of an element into its subatomic particles, it loses the basic properties that make that element unique.

So what does all of this mean for the structure of an atom? What does an atom actually look like? It took scientists a very long time to figure it out through clever experimentation and tricky math, and over time a succession of models grew closer and closer to an accurate description:

^ The Thompson model, Also called the "Plum Pudding" model, pictured discrete, negatively charged electrons evenly distributed through a positively charged medium that composed the rest of the atom. The electrons were like plums in a positive pudding.

Iir The Rutherford model Modified the Thompson model by making clear that most of the volume of the atom is empty space, with a large amount of charge concentrated at the center of the atom.

^ The Bohr model Built on the Rutherford model by describing the compact, central charge as a nucleus composed of distinct proton and neutron particles. The positive charge of the nucleus derived from the protons. Bohr envisioned electrons as discrete particles that orbited the nucleus along distinct paths, like planets in orbit around the sun.

I The Quantum Mechanical model Modified the Bohr model, pointing out that electrons do not orbit the nucleus like planets around the sun. Instead, they occupy their orbitals in a cloudlike manner; one can only describe their location in terms of probability, with some "dense" regions having a very high probability of having an electron and other regions having lower probability.

Classifying elements with mass and atomic numbers

Two very important numbers associated with an atom are the Atomic number And the Mass number. Chemists tend to memorize these numbers like sports fans memorize baseball stats, but clever chemistry students do not need to resort to memorization when they have the all-important periodic table at their disposal. Here are the basics about atomic numbers and mass numbers:

I The atomic number is the number of protons in the nucleus of an atom. Atomic numbers identify elements, because the number of protons is what gives an element its unique identity. Changing the number of protons (and therefore the atomic number) changes the identity of the element. Atomic numbers are listed as a subscript (on the bottom) to the left side of an element’s chemical symbol.

Notice that the atoms of the periodic table are lined up according to their atomic number. Atomic numbers increase by one each time you move to the right in the periodic table, continuing their march, row by row, from the top of the table to the bottom.

I The mass number is the sum of the protons and neutrons in the nucleus of an atom. Subtracting the atomic number from the mass number gives you the number of neutrons in the nucleus of an atom. Different atoms of the same element can have different numbers of neutrons, and we call those different atoms Isotopes. Mass numbers are listed as a superscript (on the top) to the left side of an element’s chemical symbol.

The mass number gives the mass of an individual atom in atomic mass units, amu, where 1 amu = 1.66 x 10-27 kg.

Why, you may wonder, don’t we care about electrons? Remember that an electron has only Hs36 of the mass of a proton or neutron. So, though electrons are incredibly important from the standpoint of charge, they make little contribution to mass. Atomic masses in amu are never whole numbers for a variety of reasons, including the fact that most elements exist in nature as a combination of different isotopes. The percent of each isotope relative to the whole is called its Natural abundance. The nonwhole number atomic masses you see listed on the periodic table are the average of all isotopes of a given element, in which each isotope is weighted by its natural abundance within the average.

In order to specify the atomic and mass numbers of an element, chemists will typically write that element in the form

AX

Where Z is the atomic number, A is the mass number, and X is the chemical symbol for that element.

Grouping elements within the periodic table

The whole purpose of the periodic table, aside from providing interior decoration for chemistry classrooms, is to organize elements to help predict and explain their properties. Notice in Figure 3-1 that the atoms of the periodic table are lined up according to their atomic numbers, as if their teacher has just taken a roll call to make sure they are all in their proper places. Here are some characterisitics of how the periodic table is organized:

I Atomic numbers increase by one each time you move to the right in the periodic table and when they run out of space in one row, they move down one and continue increasing to the right again.

I The rows are called Periods.

The columns are called Groups.

The elements within any group have very similar properties. The properties of the elements emerge mostly from their different numbers of protons and electrons, and from the arrangement of their electrons. As you move across any period, you pass over a series of elements whose properties change in a predictable way. Here are the groups you can find on the periodic table:

I Group IA (alkali metals): Starting on the far left of the periodic table is group IA

(notice the group label atop each column), also known as the alkali metals. These elements, the most metallic of all elements, are very reactive, and are never found naturally in a pure state, but always in a bonded state.

Group IIA (alkaline earth metals): Just like the alkali metals, the alkaline earth metals are highly reactive, and not found free in nature.

I Group B. . . mostly (transition metals): The large central block of the periodic table is occupied by the transition metals. Transition metals have properties that vary from extremely metallic, at the left side, to far less metallic, on the right side. The rightmost boundary of the transition metals is shaped like a staircase, shown in bold in the figure, and the staircase separates the elements further:

• Metals: Elements to the left of the staircase (except hydrogen) are metals. Metals tend to be solid, shiny, malleable (easily shaped), and ductile (easily drawn out into wire). Metals also conduct electricity and heat and easily give up electrons.

• Nonmetals: Elements to the right of the staircase are nonmetals, which have properties opposite to those of metals: They also tend to be solids, but are generally dull, hard, and do not conduct electricity.

• Metalloids Or Semi-metals: Elements bordering the staircase are called metalloids or semi-metals because they have properties between metals and nonmetals: They are somewhat ductile and a little shiny and can conduct electricity, but not as well as a metal.

I Group VIIIA (noble gases): The most extreme nonmetals are the noble gases which are inert, or extremely unreactive.

Group VIIA (halogens): One column to the left of the noble gases, is another key family of nonmetals, the halogens. In nature, the reactive halogens tend to bond with metals to form salts, like sodium chloride, NaCl.

Be aware that some periodic tables use a different system for labeling the groups, in which each column is simply numbered from 1 to 18, left to right.

Rummaging through reactivity in the periodic table

The properties of elements change as a function of the numbers of protons and electrons in the element. Increasing numbers of protons increases the positive charge of the nucleus, which contributes to Electronegativity, The pull exerted by the nucleus of one atom on electrons in a bond with a second atom. Increasing numbers of electrons changes the reactivity of the element in predictable ways, based on how those electrons fill up successive energy levels.

DpfREft The outermost electrons (in the highest energy level, which is discussed later) are called

Valence electrons. Valence electrons are the ones most important in determining whether an element is reactive or unreactive and are the electrons involved in bonding. Because much of chemistry is about the making and breaking of bonds, valence electrons are the most important particles for chemistry. The details of how electrons fill up the various energy levels are covered later in this chapter, in the section "Exercising Electrons: Ions and Electron Configuration." For now, understand that atoms are most stable when their valence shells (or clouds) are completely filled with electrons.

Chemistry happens as a result of atoms attempting to fill the valence shells. Alkali metals are especially reactive because they need only give up one electron to have a completely filled valence shell. Halogens are especially reactive because they need only acquire one electron to have a completely filled valence shell. The elements within a group tend to have the same number of valence electrons, and for that reason tend to have similar chemical properties. Elements in the A groups have the same number of valence electrons as the roman numeral of their group. For example, magnesium in Group IIA has two valence electrons.

Rounding up the atomic radius in the periodic table

In addition to reactivity, another property that varies across the table is atomic radius, or the geometric size (not the mass) of the atoms. As you move down a column or to the right along a row on the periodic table, elements have both more protons and more electrons. As you move down the table the added electrons occupy discretely higher energy levels. So, atomic radius tends to decrease as you move to the right because the increasing positive charge of the nuclei pulls inwardly on the electrons of that energy level. As you move down the table, atomic radius tends to increase because, even though you are adding positively charged protons to the nucleus, you are now adding electrons to higher and higher energy levels, which are farther and farther from the nucleus and therefore feel a much lower attraction to the nucleus.

PERIODIC TABLE OF THE ELEMENTS

1

IA

18 0

§ Note: Elements 113, 115, and 117 are not known at this time, but are included in the table to show their expected positions.

Exercising Electrons: Ions and Electron Configuration

The outermost shell of an element, which is the highest energy level, is the Valence shell. Elements are so insistent about having filled valence shells that they’ll actively gain or lose valence electrons to do so. Atoms that gain or lose electrons in this way are called Ions. When atoms become ions, they lose the one-to-one balance between their protons and electrons, and therefore acquire an overall charge.

IU Atoms that lose electrons (like metals) acquire positive charge, becoming Cations, Such as Na+ or Mg2+. You can remember this with the simple phrase "cats have paws (pos +)," so cations are positively charged.

I Atoms that gain electrons (like nonmetals) acquire negative charge, becoming Anions, Such as Cl – or O2-.

In the following sections we show you how to figure out which elements gain or lose electrons as well as how to diagram and write out electron configurations.

Knowing which elements gain or lose electrons

You can discover what kind of ion many elements will form simply by looking at their position on the periodic table. With the exception of row one (hydrogen and helium), all elements are most stable with a full shell of eight valence electrons, known as an Octet. Atoms tend to take the shortest path to a complete octet, whether that means ditching a few electrons to achieve a full octet at a lower energy level, or grabbing extra electrons to complete the octet at their current energy level. In general, metals tend to lose electrons, and nonmetals tend to gain electrons. However, a partner atom is usually required for these processes to happen.

You can predict just how many electrons an atom will gain or lose to become an ion (but things do get unpredictable in the transition metal region and then get more predictable with the nonmetals). Elements tend to lose or gain as many electrons as necessary to have valence shells resembling the elements in Group VIIIA, the noble gases:

Group IA (alkali metal) elements lose one electron. I Group IIA (alkaline earth metal) elements lose two electrons. I Group VIIA (halogen) elements gain one electron. I Group VIA elements tend to gain two electrons. I Group VA elements tend to gain three electrons.

Figuring out electron configuration

An awful lot of detail goes into determining just how many electrons an atom has and just which energy levels those electrons occupy. Several different schemes exist for annotating all of this important information, but the Electron configuration Is a type of shorthand that captures much of the pertinent information. Each electron gets a symbol code that indicates the type of energy and shape (called an electron orbital) that it will have in the atom.

Here’s how electron configuration works:

Each numbered row of the periodic table corresponds to a different Principal energy level, With higher numbers indicating higher energy. Remember higher energy means farther from the nucleus.

Within each energy level, electrons can occupy different Subshells (or clouds). Different types of subshells have slightly different energy levels.

Each subshell has a certain number of Orbitals.

• Each orbital can hold up to two electrons, but electrons won’t double up within an orbital unless no other open orbitals exists within the same subshell.

• Electrons fill up orbitals from the lowest energies to the highest, to try to keep everything in the lowest energy state, like everything else in chemistry.

The four types of subshells or clouds, named S, p, d, And f fill with electrons in the following ways:

Row 1 consists of a single 1s subshell. A single electron in this subshell corresponds to the electron configuration of hydrogen, written as 1s1. The superscript written after the symbol for the subshell indicates how many electrons occupy that subshell. Filling the subshell with two electrons, 1s2, corresponds to the electron configuration of helium. Each higher principal energy level contains its own S Subshell (2s, 3s, and so on), and these subshells are the first to fill within those levels.

In addition to S Subshells, principal energy levels 2 and higher contain P Subshells. There are three P Orbitals at each level, accommodating a maximum of six electrons. Because the three P Orbitals (also known as Px, py, And pz) have equal energy in an isolated atom they are each filled with a single electron before any receives a second electron. The elements in rows 2 and 3 on the periodic table contain only S And P Subshells. The P Subshells of each energy level are filled only after the S Subshell is filled.

Rows 4 and higher on the periodic table include D Orbitals, of which there are five at each principal energy level, accommodating a maximum of 10 electrons. D Subshell electrons are a major feature of the transition metals. These are also equal in energy unless the atom is involved in bonding.

Rows 5 and higher include F Orbitals, numbering seven at each level, accommodating a maximum of 14 electrons. F Subshell electrons are a hallmark of the Lanthanides And the Actinides, The two rows of elements detached from the rest of the periodic table, and set aside at the bottom.

After you get to row 4, the exact order in which you fill the energy levels can get a bit confusing. To keep things straight, it’s useful to refer to the Aufbau filling diagram, shown in Figure 3-2. Start at the bottom of the diagram and work your way up from the lowest arrows to the highest. For example, always start by filling 1 S, Then fill 2S, Then 2P, Then 3S, Then 4S, Then 3D, And so on.

Figure 3-2:

The Aufbau filling diagram.

Noting exceptions to the Aufbau fitting diagram

Sadly, there are a few exceptions to the tidy picture presented by the Aufbau filling diagram. Copper, chromium, and palladium are notable examples. These exceptional electron configurations arise from situations where electrons get transferred from their proper, Aufbau-filled subshells to create half-filled or fully filled sets of D Subshells; these half – and fully filled states are slightly more stable than the states produced by strict Aufbau-based filling.

Two conditions typically lead to exceptional electron configurations:

U Successive orbital energies must lie close together, as is the case with 3d and 4s orbitals, for example.

U Shifting electrons between these energetically similar orbitals must result in a half-filled or fully filled set of identical orbitals, an energetically happy state of affairs.

Here are a few examples:

U Strictly by the rules, chromium should have the following electron configuration: [Ar]3d*4s2.

U Because shifting a single electron from 4s to the energetically similar 3d level half-fills the 3D Set, the actual configuration of chromium is [Ar]3D54S1.

U For similar reasons, the configuration of copper is not the expected [Ar]3d°4s2, but instead is [Ar]3D104S1.

Writing out electron configuration

To come up with a written electron configuration you

1. Determine how many electrons the atom in question actually has.

2. You assign those electrons to subshells, one electron at a time, from the lowest energy subshells to the highest.

In a given type of subshell (like a 2p or 3d subshell, for example) you only place two electrons within the same subshell when there is no other choice. For example, only at oxygen (1s22s22p4) would electrons begin to double up in the 2p subshells.

3. Write out the configuration based on the assignment of electrons.

From lowest subshell to highest, you write the subshell and add the number of electrons assigned to it in superscript, like oxygen, 1 S22S22P4.

For example, suppose you want to find the electron configuration of carbon:

1. Determine the amount of electrons. Carbon has six electrons, the same as the number of its protons as described by its atomic number, and it’s in row 2 of the periodic table.

2. Assign electrons to subshells.

First, the S Subshell of level 1 is filled. Then, the S Subshell of level 2 is filled.

These subshells each accept two electrons, leaving two more with which to fill the P Subshells of level 2.

Each of the remaining electrons would occupy a separate P Subshell.

3. Write out the configuration: 1s22s22p2.

Ions have different electron configurations than their parent atoms because ions are created by gaining or losing electrons. Atoms tend to gain or lose electrons so they can achieve full valence octets, like those of the noble gases. Guess what? Many of the resulting ions have precisely the same electron configurations as those noble gases. So, by forming the Br-anion, bromine achieves the same electron configuration as the noble gas, krypton. This is called being Isoelectronic. You can use this concept to condense electron configurations, which can get a bit long to write. For example, [Ne]3s23p3 is the condensed configuration for phosphorous. The expanded electron configuration for phosphorous is 1s22s22p63s23p3. The condensed form simply means that the atom’s electron configuration is just like that of neon (Ne), with additional electrons filled into subshells 3S And 3P As annotated. Warning: Don’t try to get too creative and write something like [Be]2p4 for oxygen. Only noble gases Can be used for the base element in the condensed form! On the AP test be careful — if the problem asks for the complete formula, the condensed version does not receive credit.

Locating electrons with quantum numbers

Chemists use a set of four numbers called collectively the Quantum numbers To describe the state of any particular electron within an electron configuration of an atom. No two electrons in the same atom can share the same set of quantum numbers. In other words, there is no such thing as identical electron twins. They Must Differ from one another in at least one of their quantum numbers. Note that chemists invented this scheme to describe electrons in an atom. There are not "slots" to fill in the atom.

U The Principal quantum number, Which indicates the principal energy level of an electron, is denoted with the variable N And can be any integer number greater than or equal to 1. Electrons that share the same principal quantum number are said to be in the same Shell.

U The Azimuthal quantum number, L, which denotes the subshell which an electron occupies, has only four values: 0, 1, 2, or 3 corresponding to S, p, d, And F Subshells respectively. Any particular N Value, or Shell, Has subshells ranging from L = 0 to L = n-1. The third shell, for example, has subshells with L Values 0, 1, and 2. In other words, the third shell has S, p, And D Subshells.

U The Magnetic quantum number, Ml, builds off of the azimuthal quantum number and describes the three-dimensional geometry of each subshell. The magnetic quantum number describes the number of Orbitals In each subshell, and each orbital can be occupied by at most two electrons. The magnetic quantum number has values ranging from -l To L For each subshell. In other words, a P Subshell (which has an azimuthal quantum number of L = 1) has ml values of -1, 0, and 1, while a D Subshell with an azimuthal quantum number of L = 2 has mL Values of -2, -1, 0, 1, and 2. This rule means that a P Subshell has three orbitals in which electrons may exist, while a D Subshell has five.

U The spin quantum number, S, Has only two values: —2 and K. Each orbital shares the same N, l, And mL Numbers by definition and, because no two electrons can share the same set of quantum numbers, the spin quantum number must be where the two electrons in an orbital differ. Two electrons can be in one orbital as long as one has a spin of —2 and the other has a spin of K. Counting up the ml and S Quantum numbers leads you directly to the number of total electrons that can fit in each subshell. If an S Orbital has an L Value of 0, for example, this means that it has a single mL Value of 0. Because two electrons (one with each type of spin) can fit in this mL = 0 lobe, an S Orbital will always fit two and only two electrons no matter what its principle quantum number is. Similarly, a P Subshell has three mL Values (-1, 0, and 1) and each of those can have two electrons of opposing spin so a P Subshell can have up to six electrons.

Isolating Info on Isotopes

Isotopes Are atoms of the same element, but they have different atomic masses, which must translate to different numbers of neutrons. If that’s all there is to them, then why do chemists get so titillated by isotopes? A neutron is, after all, a Neutral Particle, so you wouldn’t think adding one would change much about an atom. Indeed, much of the time, adding a neutron does not alter the properties of an element significantly, but merely makes it slightly heavier.

Occasionally, however, adding another sinister little neutron can push an atom over to the dark side of radioactivity. If an atom has just the right number of neutrons, it becomes unstable, or radioactive, which means that it will break down into another element at a predicable rate. These radioactive isotopes are called radioisotopes for short. The more unstable the added neutron makes the atom, the faster it tends to decay into another.

Although the word "radioactivity" conjures up images of three-headed frogs and fish with ten eyes, the truth is that it doesn’t deserve its bad rep. Many radioactive elements are harmless. Some radioactive isotopes are very useful, such as those used in medical imaging.

Regardless of how you feel about radioactivity, we give you some useful calculations related to radioisotopes and istopes that you definitely need to check out in the sections that follow.

Calculating the remainder of a radioisotope

Science and medicine are stuffed with useful, friendly applications for radioisotopes. Many of these applications center on the predictable decay rates of various radioisotopes. These predictable rates are characterized by Half lives. The half life of a radioisotope is simply the amount of time it takes for exactly half of a sample of that isotope to decay into daughter nuclei. For example, if a scientist knows that a sample originally contained 42mg of a certain radioisotope and measures 21mg of that isotope in the sample four days later, then the half life of that radioisotope is four days. The half lives of radioisotopes range from seconds to billions of years.

Radioactive dating Is the process scientists use to date samples based on the amount of radioisotope remaining. The most famous form of radioactive dating is carbon-14 dating, which has been used to date human remains and other organic artifacts. However, radio-isotopes have also been used to date the Earth, the solar system, and even the universe.

Table 3-2 lists some of the more useful radioisotopes, along with their half lives and decay modes, which are described in detail later in the chapter.

Consider the element carbon, for example, which has three naturally occurring isotopes. carbon-12 (or carbon with six protons and six neutrons), written as:

Is boring old run-of-the-mill carbon, and it accounts for 99 percent of all of the carbon out there. carbon-13 (or carbon with six protons and Seven Neutrons), written as:

Is a slightly more exotic, though equally dull, isotope, which makes up most of the remaining 1 percent of carbon atoms. Taking on an extra neutron makes carbon-13 slightly heavier than carbon-12, but does little else to change it. However, even this minor change has some very real scientific consequences. Scientists compare the ratio of carbon-12 to carbon-13 in meteorites to help them determine where that meteorite came from. These ratios have been especially useful for identifying Martian meteorites. Earth is significantly more massive than Mars, and therefore, has a stronger magnetic field, allowing it to hold onto its atmosphere. Mars, on the other hand, is too small to hold onto the upper part of its atmosphere. carbon-12 is lighter than carbon-13, so it floats up to the upper atmosphere of Mars, where the solar wind comes along like the big bad wolf and blows it away. This leaves Mars with a higher percentage of carbon-13 than you would find on Earth. So, minerals on Mars that take carbon from the atmosphere and turn it into rock end up with a little more carbon-13 and a little less carbon-12 than similar minerals on earth. When a meteor from Mars lands on Earth, scientists can verify its origin by testing the ratio of carbon-12 to carbon-13.

Carbon-14, the most exotic and interesting isotope of carbon, has been very important in the process of radioactive dating. Carbon is one of the building blocks of organic matter, including the human body. Only one out of every trillion or so carbon atoms is the carbon-14 (or carbon with six protons and eghtneutrons) radioiso-tope, which looks like

You have many, many trillions of trillions of trillions of carbon atoms in your body, which means that you contain trillions of atoms of radioactive carbon! Now before you go checking the mirror to see if you have sprouted a third eye, rest assured that this radioactive carbon will not harm you in any way. In fact, it is what allows scientists to determine the age of fossils.

As an example, take Matilda the Mammoth, who met her untimely end 4,500 years ago. While Matilda was alive, the carbon in her body was constantly being replenished, so she was always made of about 99 percent carbon-12, 1 percent carbon-13, and 0.0000000001 percent carbon-14. However, when poor Matilda kicked the bucket, the biological processes that were replacing the carbon in her body came to an abrupt end. With their supply of carbon-14 cut off, Matilda’s bones slowly lost their carbon-14 as it broke down through radioactive decay into nitrogen. Paleontologists digging up Matilda 4,500 years later will run straight to their friendly neighborhood chemist, Dr. Isotopian, and ask him to tell them how much carbon-14 is left in Matilda. Because carbon-14 breaks down at a very predictable rate, Dr. Isotopian is able to guess to within a few hundred years exactly how long ago Matilda kicked the bucket.

To calculate the remaining amount of a radioisotope, use the following formula where A0 Is the amount of the radioisotope that existed originally, T Is the amount of time the sample has had to decay and T Is the half life:

A = A0 x(0.5F

Calculating the average mass of an element

That number beneath each element in the periodic table is calculated using percentages such as the carbon abundances mentioned earlier, which allow scientists to give an Average Atomic mass for the isotope. Certain elements, such as chlorine, have several commonly occurring isotopes, so their average atomic masses are rarely close to whole integers. Many elements, however, such as carbon, have one very commonly occurring isotope and several rare isotopes, resulting in an average atomic mass that is very close to the mass of the most common isotope.

To calculate an average atomic mass you

1. Make a list of the masses of each isotope, noting the percentage, in decimal form, at which each isotope is found in nature, a quantity called the Relative abundance Of the isotope.

2. Multiply the mass and the relative abundance together.

3. Add up the results of each calculation in step 2 to get the average atomic mass.

On the AP chemistry exam, you will be expected to know how to calculate this weighted average or to determine at which isotope is the most common based on that weighted average.

The most commonly occurring isotope Often Has a mass number closest to the average atomic mass. Be careful when the average atomic mass differs from the nearest whole number by more than about 0.1, however. Such numbers can lead you to false conclusions regarding the most abundant isotope. Chlorine, for example, has an average atomic mass of 35.5amu. This may lead you to conclude that the isotopes

7 Cl

36 Cl

Both have roughly 50 percent abundances because the average atomic mass is almost exactly halfway between 35 and 36. In reality, however

35 Cl

17

Exists with roughly 75 percent abundance, while

3177 Cl

17

Exists with roughly 25 percent abundance.

Is about as common as a Chemistry teacher without chalk on the butt of his pants.

Running into Radioactivity

Atomic numbers are like name tags, identifying elements by telling you the number of protons in the nucleus of that element. Adding or removing a proton to the nucleus of an atom changes its atomic number (and thus its identity), and atoms are very fond of their identities, so adding or removing protons from an atom is usually impossible.

However, you Can Change atomic numbers:

U Certain large elements can be split in half, and certain small elements can be smashed together in processes called Nuclear fission And Nuclear fusion, Respectively. This splitting or joining of atoms releases a tremendous amount of energy and is not something that you should try at home, even if you do have a nuclear reactor in your basement.

U The only other way for an atom to change its atomic number (and therefore its identity) is to "decay" into something else through a radioactive process, and this happens about as often as chemists remember to brush their hair in the mornings. There are three key ways in which an element can decay, and these are described following.

Many elements in the periodic table have unstable versions called Radioisotopes. These radioisotopes decay into other, generally more stable elements at periodic intervals in a process called Radioactive decay. There are many radioisotopes in existence; however not all radioisotopes are created equal. Radioisotopes break down through three separate decay processes. Yep, you guessed it: We’re gonna tell you all about ‘em.

Alpha decay

The first decay process, called Alpha decay, Involves the emission of an alpha particle by the nucleus of an unstable atom. Emitting an alpha particle, which is nothing more exotic than the nucleus of a helium atom (two protons and two neutrons), causes the atomic number of the daughter nucleus to decrease by two and the mass number to decrease by four. The following pattern shows the decay of the parent nucleus X into a daughter nucleus Y and an alpha particle.

AX — AB-42Y + 2He

Beta decay

The second type of decay, called Beta decay, Comes in three forms:

U Beta plus decay: A proton in the nucleus is converted into a neutron, a positron (e+), and a tiny weakly interacting particle called a neutrino (u), resulting in the atomic number decreasing by one. The mass number, however, Does not change, Even though the actual mass does change very slightly. A proton becoming a neutron, after all, should have absolutely no effect on the mass number because both protons and neutrons are Nucleons, Or particles contained in the nucleus, and converting one to the other does not change the overall number of particles in the nucleus.

Beta plus decay follows the form of the equation below, with the atomic number being decreased by one and the mass number remaining the same.

BX

AY

U Beta minus decay: A neutron is converted into a proton, emitting in this case an electron and an antineutrino (u). Again, the mass number remains the same throughout the decay because the number of nucleons remains the same; however the atomic number Increases By one. In case you haven’t guessed, this is the reverse of beta plus decay.

Beta minus decay follows the form of the equation below, with the atomic number being increased by one and the mass number remaining the same.

AX— *Y+E-+v

U Electron capture: The final form of beta decay occurs when an inner electron is captured by an atomic proton, converting it into a neutron and emitting a neutrino in the process.

Electron capture follows the form of the equation below, with the atomic number being decreased by one and the mass number remaining the same.

BX

AY

B-1

BB9

All three of these processes involve the emission or capture of an electron or a positron and result in a change in the atomic number of the daughter atom.

Gamma decay

The last form of decay, termed Gamma decay, Involves the emission of a high-energy form of light, called a gamma ray, by an excited nucleus. Although it does not change the atomic number or the mass number of the daughter nucleus, gamma decay often accompanies alpha or beta decay and it is a means for the nucleus of a daughter atom to reach its lowest possible energy state. The general form of gamma decay is shown below, where

Represents the excited state of the parent nucleus, and the greek letter gamma (y) represents the gamma ray.

The forces that hold atomic nuclei together are extremely powerful, and the energy required to join two light nuclei together or split one heavy nucleus in two is tremendous. The only place where nuclear reactions happen in nature is in the very center of stars like our sun, where extreme temperatures cause atoms of hydrogen, helium, and other light elements to smash together and join into one. This extremely energetic process, called Nuclear fusion, Is what ultimately causes the sun to shine and provides the outward pressure required to support the sun against gravitational collapse.

Nuclear fission, on the other hand, occurs only rarely in nature. At a site in central Africa called Oklo a natural nuclear reactor has been found to have occurred many, many, years ago. Humans first harnessed the tremendous power released when splitting an atom through fission during the United States’s Manhattan Project, which led to the development of the first atomic bomb. Fission has since been used for more benign purposes in nuclear power plants, which produce energy much more efficiently and cleanly than traditional fossil fuel-burning power plants.

Special circumstances can drive electrons to configurations other than their ideal Ground state (or lowest energy) configurations. You will need to know the causes and consequences of electrons being driven from their ground states and the equations that will allow you to qualitatively analyze those transitions, all of which are laid out for you in this chapter.

Electrons can be driven to higher energy levels than they would otherwise occupy by absorbing energy in the form of heat, light, or electric current. An electron can only absorb an amount of energy exactly equivalent to the difference in energy between the state it is already occupying and another nearby energy state. Electrons in these higher-than-expected energy levels are said to be in an Excited state. Excited electrons quickly release amounts of energy equivalent to the difference between their excited state and a lower energy state by emitting a Photon, Or particle of light, with an equivalent energy. The Wavelength (which in the realm of visible light is equivalent to color) of this photon characterizes the energy difference between the excited and lower energy state. It is only by measuring these that chemists know about the energy structure of atoms. There isn’t any way to learn about the inside of an atom by just looking at a ground state, stable one.

A B

X*

A B

Getting Electrons Excited

Excited state

An electron that should be in the 3s subshell, for example, may be kicked up into the 4f Sub-shell, where it wants to remain just about as badly as you want to remain on the couch during your Great Aunt Maybell’s slideshow of her summer at the lake. In order to get back to the 3s subshell where it belongs, it must emit an amount of energy exactly equal to the energy difference between the 4f And the 3s subshells. This energy difference corresponds to a very specific wavelength, or color, of light because of the relationship between the energy and wavelength of a photon of light.

Converting energies to Wavelengths

Max Planck developed the equation

E = hf-

To show the relationship between the wavelength and the energy of a photon. However, this equation can also be written as E = hu

This alternative equation is based on another convenient relationship between the properties of light, specifically the relationship between wavelength and frequency:

C = Au

Here’s an explanation of the variables in those two equations: Energy (E) Is expressed in Joules (J).

H Is a constant called Planck’s constant equal to 6.63 x 10-34 m2 x kg/s.

Frequency (u) is expressed in reciprocal seconds (1/s or s-1) also known as Hertz (1 Hz = 1 s-1).

C is the speed of light, Specifically 3.0 x 108 m/s. Wavelength (A) is expressed in meters.

Niels Bohr, in order to complete his model of the atom, used Planck’s ideas to explain why the orbits of electrons in the hydrogen atom are Quantized, Or occur only at certain distances from the nucleus. Planck had proposed that the energy of light particles (photons) Came in Quanta, Or discrete values. Bohr found that the energy levels of the electron orbits were also quantized and followed the formula

E n

-2.178 x 10-

Joules

Where n is the principal quantum number. You will be expected to recognize and use this formula for predicting energy levels in the hydrogen atom on the AP exam, but make sure that you note that it applies to the Hydrogen atom alone And will give you an incorrect answer if you apply it to any other element.

Emission spectra

Although it sounds like the next blockbluster sci-fi movie, Planck’s formula E= hU also helps explain the phenomenon of atomic Emission spectra, Which are characterized by bright lines of light of very specific colors. Chemists had realized long before Bohr and Planck came along that if you used a prism or spectrograph to disperse the light emitted when a pure solid element is burned or a pure gaseous element has an electronic current passed through it, then every individual element would emit a characteristic sequence of bright-colored lines called its Spectrum. No two excited elements emitted identical spectra, so spectra became a definitive method for identifying elements.

An element’s characteristic spectrum contains lines of specific colors because every element has its own unique set of allowed energies and therefore its own unique set of energy transitions. Because excited electrons must emit photons in order to reach the ground state and photon energies correspond directly to wavelengths, or colors, the appearance of every atomic spectrum is unique in the color and brightness of each line. The brighter a spectral line is, the more likely that transition is to occur. Most elements have hundreds of allowed transitions and emit light from infrared to X-ray wavelengths. The specific wavelength of light emitted when an electron drops to a lower energy level can be found by taking the energy difference between the excited and ground states and translating it into a wavelength using Planck’s formula and substituting this energy change (A) for E as in

AE = M

A

In This Chapter

^ Moving from molecular formulas to Lewis structures

^ Overlapping orbitals to make molecular shapes

^ Understanding how shape contributes to polarity and isomers

Olecular shapes help determine how molecules interact with each other and within themselves. For example, molecules that stack nicely on one another are more likely to form solids. And two molecules that can fit together so their reactive bits lie closer together in space are more likely to react with one another. In this chapter, we describe how to get a sense of the shape of a molecule, starting with only its molecular formula. Then, we explore a few ways that molecular shape can impact molecular properties.

Drawing Dots and Lines with Lewis

Valence electrons are critical for bonding. If that sentence confuses you, then you need to amble through Chapter 5 before moving further into this chapter. Because valence electrons are the ones important for bonding, chemists use Lewis electron dot structures: Symbols that represent valence electrons as dots surrounding an atom’s chemical symbol.

You should be able to draw and interpret electron dot structures for atoms so that you understand how the dots relate to the valence shell electrons possessed by an atom. By keeping track of how filled or unfilled an atom’s valence shell is, you can predict whether it is likely to bond with other atoms in an attempt to fill its valence shell.

Drawing electron dot structures

Figure 7-1 shows the electron dot structures for elements in the periodic table’s first two rows. Electrons in an atom’s valence shell are represented by dots surrounding the symbol for the element. Completely filled shells are surrounded by eight (8) dots (or two dots, in the lone case of helium). Valence shells progressively fill moving from left to right in the table. This pattern repeats itself with each successive row of the periodic table, as each row corresponds to adding a new outermost valence shell. Because atoms are most stable (think "happiest") when their valence shells are full, they tend to seek full-shell states in one of two ways. Atoms may gain or lose electrons (forming anions or cations, respectively) to end up with filled shells. Or, atoms may covalently bond with each other so that each atom can lay claim to the electrons within the bond.

To draw the electron dot structure of any element

1. Write the element’s name.

2. Count the number of electrons in that element’s valence shell.

3. Draw that number of dots around the chemical symbol for the element. As a general rule, space the dots evenly around the element’s symbol.

Figure 7-1:

Electron dot structures

For elements in the first

Two rows of

The periodic table.

IA

IIA

•Be*

IIIA IVA VA VIA VIIA VIIIA

He!

• • • •

•ES« ‘OIIM! 101 IF* INeL

H

Li

Constructing Lewis structures

Just as electron dot structures show the number of valence electrons that surround individual atoms, Lewis structures use dots and lines to show the distribution of electrons around all the atoms within a compound. Lewis structures are great tools for figuring out which molecules are reasonable (filling up all the atomic valence shells) and which molecules aren’t so reasonable (leaving some valence shells unhappily unfilled).

If you know the molecule’s formula you can figure out the correct Lewis structure for that molecule. The following example gives you the steps you need to work out a Lewis structure. This example uses formaldehyde, CH2O. You can follow along with Figure 7-2:

1. Add up all the valence electrons for all the atoms in the molecule.

These are the electrons you can use to build the structure. Account for any extra or missing electrons in the case of ions. For example, if you know your molecule has +2 charge, remember to subtract two from the total number of valence electrons. In the case of formaldehyde, C has four valence electrons, each H has one valence electron, and O has six valence electrons. The total number of valence electrons is 12.

2. Pick a "central" atom to serve as the anchor of your Lewis structure.

The central atom is usually one that can form the most bonds, which is often the atom with the most empty valence orbital slots to fill. In larger molecules, some trial-and-error may be involved in this step, but in smaller molecules, some choices are obviously better than others. For example, carbon is a better choice than hydrogen to be the central atom because carbon tends to form four bonds, whereas hydrogen tends to form only one bond. In the case of formaldehyde, carbon is the obvious first choice because it can form four bonds, while oxygen can form only two, and each hydrogen can form only one.

3. Connect the other, "outer" atoms to your central atom using single bonds only.

Each single bond counts for two electrons. In the case of formaldehyde, attach the single oxygen and each of the two hydrogen atoms to the central carbon atom.

4. Fill the valence shells of your outer atoms. Then put any remaining electrons on the central atom.

In our example, carbon and oxygen should each have eight electrons in their valence shells; each hydrogen atom should have two. However, by the time we fill the valence shells of our outer atoms (oxygen and the two hydrogens), we have used up our allotment of 12 electrons.

5. Check whether the central atom now has a full valence shell.

If the central atom has a full valence shell, then your Lewis structure is drawn properly — it’s formally correct even though it may not correspond to a real structure. If the central atom still has an incompletely filled valence shell, then use electron dots (nonbonding electrons) from outer atoms to create double and/or triple bonds to the central atom until the central atom’s valence shell is filled. Remember, each added bond requires two electrons. In the case of our formaldehyde molecule, we must create a double bond between carbon and one of the outer atoms. Oxygen is the only choice for a double-bond partner, because each hydrogen can accommodate only two electrons in its shell. So, we use two of the electrons assigned to oxygen to create a second bond with carbon.

1. C(4 e-) + H(1 e-) + H(1 e-) + 0(6 e-) = 12e -

2. Carbon is the central atom; it can form more bonds (4) than 0, H.

Figure 7-2:

Putting together a Lewis structure.

HCH

C

HH

Getting bonds straight with line structures

Atoms involved in covalent bonds share electrons such that each atom ends up with a completely filled valence shell, as described more fully in Chapter 5. The simplest and best studied covalent bond is the one formed between two hydrogen atoms (dihydrogen). Separately, each atom has only one electron with which to fill its 1s orbital. By forming a covalent bond, each atom lays claim to two electrons within the molecule of dihydrogen. Covalent bonds can be represented in different ways, as shown for dihydrogen in Figure 7-3.

Figure 7-3:

Three representations of the formation of a covalent bond in dihydrogen.

3.

0

4.

Lewis structures for compounds more complicated than dihydrogen can get pretty busy-looking. Most Lewis structures get rid of the dizzying effect of swarms of electron dots by representing shared electron pairs —that is, covalent bonds — as lines. Each two-dot electron pair that is shared between two atoms is rewritten as a nice, clean line connecting the atom symbols. Only nonbonding electrons (lone pairs) are left as dots. Whether a Lewis structure for a compound uses electron dot pairs or lines to represent bonds, those dots or lines refer to preceisely the same entities: covalent bonds.

Atoms can share more than a single pair of electrons. When atoms share two pairs of electrons, they are said to form a Double bond, And when they share three pairs of electrons they are said to form a Triple bond. Examples of double and triple bonds are shown with Lewis structures using both electron dots and lines in Figure 7-4.

Figure 7-4:

The formation of double bonds in carbon dioxide and triple bonds in dinitrogen.

Rummaging through resonance structures

Sometimes a given set of atoms can covalently bond with each other in multiple ways to form a compound. In these cases, you can draw several possible valid Lewis structures for the compound. This situation leads to something called Resonance. Each of the possible Lewis structures is called a Resonance structure. The actual structure of the compound is a Resonance hybrid, A sort of average of all the resonance structures. Resonance is particularly common in molecules where much bonding occurs in a side-by-side manner with P-orbital electrons from adjacent atoms. These kinds of bonds are called n bonds (see "Overlapping Orbitals to Form Valence Bonds " for more on that type of bond).

When resonance structures involve n bonds, electrons in the bonds can become "delocal-ized," forming an extended orbital that bonds more than two atoms. The benzene molecule, shown in Figure 7-5, is a classic example of resonance and electron delocalization.

A)

H i

C

HCH H

H i

HCH

C

CC HCH

H

Figure 7-5:

The resonance structures (a)resonance hybrid (b) and electron delocaliza-tion of benzene(c).

B)

C)

Adjacent P Orbitals

H i

I: !l

CC HCH

H

Delocalization among n bonds

I—I

I—I

I—I

I—I

Overlapping Orbitals to Form Valence Bonds

When we say that covalent bonds "share" valence electrons (if you’re asking yourself, "What in the world are covalent bonds?" see Chapter 5 for more info), what do we really mean? We mean that shared electron pairs now flit about within overlapping atomic orbitals (if your head is orbiting right now trying to figure out what atomic orbitals are, check out Chapter 3).

From a molecular formula you can figure out a Lewis structure. From the Lewis structure and by using valence bond theory and VSEPR theory you can often get a pretty good idea of the shape of a molecule, which is a major factor in determining other properties, like polarity, phase behavior, and the tendency to interact or react with other molecules. Going from a Lewis structure to a molecular shape requires a little know-how, however. In the next few sections, we give you the skills you need.

We realize the word "theory" sounds stuffy and perhaps intimidating, but, hey, we didn’t pick it. However, we take the stuffiness out of the valence bond theory as well as the VSEPR theory in the following sections so that you can predict the shape of molecules.

Getting a grasp on valence bond theory

According to valence bond theory, two atoms approach each other as they form a covalent bond, overlapping their electron shells, until they reach a minimum energy (see Figure 7-6). The positively charged nuclei draw closer together as each is attracted to the negative charge of the electrons between them. After a point, drawing any closer together would crowd their positively charged nuclei too closely for comfort. The positive charges begin to repel at such short distances. So, the length of the covalent bond is the result of a balancing act between attractive and repulsive forces.

Figure 7-6:

Two hydrogen atoms overlapping to form a covalent bond.

HH (too c lose)

(\\ …….. (too far)

Energy minimum at 74 x 10-12m

Distance between hydrogen nuclei

Different kinds of bonds result from the different ways the orbitals can overlap in space. The kind of symmetry the resulting bond has with the Bond axis, (an imaginary line that connects the centers of the bonded atoms) determines what kind of bond is formed:

Sigma bond: When orbitals overlap in a way that is Completely Symmetrical with the bond axis, a o bond (sigma bond) is formed. Sigma bonds form when S Or P Orbitals overlap in a head-on manner. Single bonds are usually sigma bonds.

I Pi bond: When orbitals overlap in a way that is symmetrical with the bond axis In only one plane, A n bond (pi bond) is formed. Pi bonds form when adjacent P Orbitals overlap above and below the bond axis.

Sigma bonds are stronger than pi bonds because the electrons within sigma bonds lie entirely between the two atomic nuclei, simultaneously attracted to both. A double bond is one sigma bond and one pi bond, and a triple bond is one sigma bond and two pi bonds.

+

0

Figure 7-7 shows you an example of a sigma bond forming from two S Orbitals and the formation of a pi bond from two adjacent P Orbitals.

Figure 7-7:

Formation of sigma and pi bonds.

Ss

+

Pp

S:

Shaping up with the VSEPR theory

Sigma and pi bonds form by overlapping the valence orbitals of atoms (see "Getting a grasp on valence bond theory" for more on sigma and pi bonds), so the overall shape of a molecule depends largely on the geometric arrangement of valence orbitals around each atom. That’s where VSEPR theory comes into play. Now don’t worry: We’ll start with the hard part: VSEPR stands for Valence shell electron pair repulsion. Okay, now it gets easier. VSEPR is simply a model that helps predict and explain why molecules have the shapes they do.

Only use VSEPR theory on the "p-block" elements. These elements are the ones in Groups IIIA, IVA, VA, VIA, VIIA, and VIIIA (except helium) on the right side of the periodic table. For the most part, this restriction means that you use VSEPR theory to predict geometry around nonmetal atoms.

In the following sections, we break down the basics of VSEPR theory so you can understand and predict the shape of molecules.

Predicting shapes with VSEPR theory

Simply by combining the principle that valence electron pairs (lone or bonds) want to get as far apart as they can (thus "repulsion" in the acronym VSEPR) with the fact that lone pairs repel more strongly than do bonding pairs, you can predict an impressive array of molecular shapes. The total number of valence electron pairs determines the overall geometry around a central atom. The distribution of these pairs between bonding and nonbonding orbitals adjusts that geometry. So VSEPR theory can predict several shapes that appear over and over in real-life molecules. These shapes, shown in Figure 7-8, resemble those observed in real-life molecules.

—

K

# of e pairs

E pair geometry

Bonding pairs

Lone pairs

Molecular

Shape

2 pairs

Linear

B A B Linear

4 pairs

Tetrahedral

40 A

B

B B Tetrahedral

Figure 7-8:

Molecular

Shapes predicted by VSEPR theory.

31 A

Trigonal pyramidal

B *

Bent

2

0

Making molecular shapes with hybridization

VSEPR theory is pretty good at making predictions about what shapes will emerge from a set of mostly equivalent valence shell electron pairs. But wait — what about the difference between valence electrons in S Orbitals versus those in P Orbitals? These electrons don’t seem equivalent. That’s when hybridization jumps in. Hybridization Refers to the mixing of atomic orbitals into new, hybrid orbitals. Valence electron pairs occupy equivalent hybrid orbitals.

Check out the electron configuration of carbon in Figure 7-9. Carbon contains a filled 1s orbital, but this is an inner-shell orbital, so it doesn’t impact the geometry of bonding. However, the valence shell of carbon contains one filled 2s orbital, two half-filled 2p orbitals, and one empty P Orbital. Not the picture of equality, so the valence orbitals must form new shapes or hybridize.

.fcjABEfl Different combinations of orbitals produce different hybrids. One S Orbital mixes with two P Orbitals to create three identical Sp2 Hybrids. One S Orbital mixes with one P Orbital to create HJUl ) two identical Sp Hybrids. Centers with sp3, sp2, and Sp Hybridization tend to possess tetra-hedral, trigonal planar, and linear shapes, respectively.

Figure 7-9:

The electron configuration of carbon.

Tl tl t t

1s

2s

2p

C

Doing the math to predict molecular shapes

The shapes of real molecules emerge from the geometry of valence orbitals — the orbitals that bond to other atoms. Here’s how to predict this geometry:

1. Count the number of lone pairs and bonding partners an atom actually has within a molecule. You can do this by looking at the Lewis structure.

In formaldehyde (H2C = O), for example, carbon bonds with two hydrogen atoms and double bonds with one oxygen atom. So, carbon effectively has three valence orbitals.

2. Next, inspect the electron configuration, looking for the mixture of orbital types (like s and P) That the valence electrons occupy.

Carbon has four valence electrons in 2s22p2 configuration. Two valence electrons occupy an S Orbital, and one electron occupies each of two identical P Orbitals. The S Orbital isn’t equivalent to the P Orbitals. So, we mix the S Orbital with the two P Orbitals to create three identical Sp2 Hybrid orbitals, as shown in Figure 7-11.

Note that the total number of orbitals doesn’t change; in the example, formaldehyde has three valence orbitals before mixing and still has three valence orbitals after mixing. VSEPR theory predicts that electrons in three identical orbitals mutually repel to create a trigonal planar geometry like the one shown in Figure 7-8, which is the shape of the formaldehyde molecule.

Elements in periods 3 and below of the periodic table can engage in Hypervalency, Meaning that they can possess more than eight electrons in their valence shell. Hypervalency complicates things a bit, but the basic principles of VSEPR theory still apply — electron pairs distribute themselves as far apart as possible around the hypervaent atom. Depending on the distribution of bonding and nonbonding electron pairs, hypervalent atoms participate in "expanded octet" geometries like octahedral, square planar and T-shaped, as shown in Figure 7-10.

Figure 7-10:

"Expanded octet" geometries.

Xe

90°

■ CI-F

87.5°

Octahedral

Square planar

F

T-shaped

Figure 7-11:

Formation ofthree ^

Equivalent

Sp2 Orbitals from one SOrbital and two

POrbitals.

O

/…

Pp

Hybridization

§-\ /o"\ /°i

Polarity and Isomers

You can often get a pretty good idea of the shape of a molecule (if you can’t, see the section earlier in this chapter, "Overlapping Orbitals to Form Valence Bonds"). Knowing the shape of a molecule helps you to understand the molecule’s other properties, like polarity, phase behavior, and the tendency to interact or react with other molecules. These are exactly the kinds of things that chemists and the rest of us actually Care About, whether we know it or not. For example, life on Earth depends largely upon the unique polarity and shape of the water molecule. The tasty combination of oil and vinegar in a raspberry vinaigrette depends on the phase behavior of the oil and vinegar components.

F

F

F

S

F

F

F

F

+

+

S

Polarity

The shape of a molecule and its polarity have a fairly simple relationship; the polarity of a molecule emerges from the polarities of the bonds within that molecule. As described in Chapter 5, differences in the electronegativity of atoms create polarity in bonds (which causes those bonds to be polar bonds) between those atoms. Each polar bond possesses a Bond dipole, Which is represented by this symbol: |i. Depending of the shape of the molecule, individual bond dipoles may or may not lead to an overall molecular dipole, a polarity in the molecule as a whole.

You can calculate a bond dipole by multiplying the amount of charge separated along that bond (Q) by the distance of the separation, d. Because the SI units of charge and distance are Coulombs (C) and meters (m), this calculation yields units of Coulomb-meters. A Coulomb-meter is a ridiculously big unit compared to the size of bond dipole, so bond dipoles are typically reported in Debyes (D), where 1 D = 3.336 x 10-30 Cm.

You won’t be asked to calculate a bond dipole on the AP exam, but knowing how bond dipoles are calculated helps you to understand how they add up within a molecule.

You won’t be asked to calculate a bond dipole on the AP exam, but knowing how bond dipoles are calculated helps you to understand how they add up within a molecule.

The precise way in which individual bond dipoles contribute to the overall Molecular dipole Depends on the shape of the molecule. Dipoles add as Vectors. Basically, this means

If two equivalent bond dipoles point in opposite directions, they cancel each other out. IU If the two bond dipoles point in the same direction, they add.

I If two bond dipoles point at a diagonal to one another, the horizontal and vertical components of the dipoles add (or cancel) separately.

The molecular dipoles of carbon dioxide and water demonstrate vector addition of bond dipoles nicely, as shown in Figure 7-12:

I Each molecule consists of a central atom bonded to two identical partners.

• In the case of carbon dioxide, carbon double-bonds to two oxygens to produce a linear molecule (thanks to Sp Hybridization!). The two C-O bond dipoles of carbon dioxide cancel each other out, so the molecular dipole is zero.

• In the case of water, a single oxygen atom single-bonds to two hydrogens that leaves the oxygen with two lone pairs.

I The bond pairs and the lone pairs (which are Sp3 Hybridized) lead to a nearly tetra-hedral orbital geometry and result in a bent shape of the molecule as you trace from hydrogen to oxygen to hydrogen.

I The two C-O bond dipoles of carbon dioxide cancel each other out, so the molecular dipole is zero.

I Only the horizontal components of the two H-O bond dipoles of water cancel each other out.

I The vertical components of those bond dipoles add, making the molecular dipole of water the sum of those components.

Because carbon dioxide has no molecular dipole, it interacts very weakly with itself and therefore is a gas at room temperature. Because water has a significant molecular dipole, it acts as a good solvent for other polar compounds.

+ +

A)

U(CO,)= A, + u, = 0

B)

Figure 7-12:

Vector addition of bond dipoles to produce molecular dipoles.

C)

Isomers

Molecular shapes can contribute to chemical diversity (an abundance of compounds with differing properties) through the creation of Isomers. Isomers are compounds made up of the same atoms but put together in different arrangements. Isomers with the same molecular formula may freeze or boil at different temperatures, may undergo different kinds of reactions, and may have important differences in situations where exact shape is critically important. Distinguishing between isomers is especially important in organic chemistry and biochemistry (see Chapter 25 for more detail on these) because these branches of chemistry involve many large molecules built with many individual bonds. With many bonds, there are many opportunities for isomerism. It turns out that big organic molecules can be very selective, reacting specifically with one isomer but not with others.

The following list gives you an overview of the different kinds of isomers, and how each is related to the others:

Structural isomers Have the same set of atoms, but the atoms are connected differently.

Stereoisomers Have the same bonds, but different three-dimensional arrangements of atoms. Among stereoisomers, you have

• Geometric isomers: Geometric isomers can occur when atoms are restricted from rotating freely about their bonds, such as in the case of a double bond or when bulky groups of atoms bump into each other. In these cases, atoms or groups of atoms can get trapped on one side or the other of the bond, creating geometrically distinct versions of the molecule.

• Optical isomers: Optical isomers (also called Enantiomers) Are mirror images of one another, but ones you can’t superimpose — in the same way you can’t match your left hand with your right hand when both palms face in the same direction. Molecules that have this handedness are called Chiral.

In This Chapter

► Taking or embracing electrons

► Naming compounds

► Getting a glimpse of ionic bonds

► Cozying up to covalent bonds

► Arming yourself with info on polarity and electonegativity

Chemistry textbooks would be much thinner if it weren’t for bonding. As appealing as thinner textbooks may be, they’d come at the cost of other appealing things, such as cars, chocolate (Heaven help us!), and being alive. Bonds of different types between different elements and in different arrangements underlie the stunning diversity and complexity of matter. Although that complexity may sound daunting, we make taking a look at bonding a breeze by breaking down just how bonding builds things up.

Bringing Atoms Together: Bonding Basics

Sometimes atoms hang out together. Sometimes they form close friendships, sometimes only loose alliances. Close mutual attractions between atoms, ones strong enough to hold them persistently together, are called Bonds. Isn’t that sweet?

Why do atoms buddy up and bond with one another? In short, pairs of atoms seek stability. In particular, atoms prefer to dwell in states with more stable electron configurations. (Chapter 3 describes what makes for a stable electron configuration in case you need to check it out. . . and you do for the exam.) Atoms just tend to be most stable when their valence shells are completely filled with electrons so each atom does its best to fill its Valence shell, Its outermost shell.

Just like the different types of bonds you form in life — bonds between buddies, sisters and brothers, your children, your coworkers (okay, maybe that’s a stretch) — atoms form different types of bonds as well, and we’ll give you the skinny on those types of bonds in the following sections.

Attracting the opposite: Ionic bonds

Ionic bonds Form between oppositely charged ions. Ions Themselves form when an atom either gains or loses valence electrons in pursuit of filling its valence shell. Positively charged ions are electrostatically attracted to negatively charged ions, so the two nestle together to form an ionic bond. In a sense, atoms transfer whole electrons to create ions and form these bonds (more on cations and anions in Chapter 3). Sometimes, an ion consists of more than one kind of atom. These multiatom ions are called Polyatomic ions, Which have won many awards for their extreme inconvenience to chemistry students. Table 5-1 lists the most

Common polyatomic ions, grouped by ionic charge. They’ll pop up frequently. They’ll annoy you until you simply buckle down and memorize them. You can find out more about ionic bonds later in the chapter in the section, "Eyeing Ionic Bonds."

Sharing electrons: CoValent bonds

Covalent bonds Form between atoms that share electrons, rather than transfer them. These shared electrons are in orbits that surround both bonded atoms. Sharing may or may not be equal, depending on which atom "wants" the electrons more. The chemical term for electron greed is Electronegativity. Differences in electronegativity between atoms largely determine what kind of bond forms between them. As described more completely in the section, "Getting a grip on electronegativity," differences in electronegativity determine whether a bond is ionic or covalent.

Keeping it solid with metals: Metallic bonding

Okay, we’re not referring to being groupies with a heavy metal band. You can do that after the AP exam. Instead, Metallic bonding Occurs within metallic solids (big surprise, we know). Metallic bonding helps to explain the unique properties of metals:

The Electron-sea model Of metallic bonding describes metallic solids as lattices of metal cations immersed within a fluid "sea" of mobile electrons. Although the electrons are constrained to the cation lattice, they can move freely within it. This model provides a satisfying intuitive explanation for metals’ electrical conductivity because the electrons within the lattice aren’t constrained to orbitals around individual atoms, but are in delocalized orbitals.

For example, a sample of solid copper holds itself together with metallic bonds. The electrons in this sample don’t clearly "belong" to any particular copper atom, but can move through the sample. So, if you draw out the sample into a wire, you can use the mobile electrons to conduct electric current.

So what do you get when you bond? In life, you get families and friends. In chemistry, you get compounds. Chemical Compounds Are the consequence of bonding. A compound consists of bonded atoms, and has properties that are different from a simple mixture of the identical, nonbonded atoms. In other words, the structure of a compound confers properties to that compound. The relationship between structures and properties is a major theme of chemistry. That theme revolves around the concept of the chemical bond. In the next section we begin to deal with the basics of compounds, especially how to recognize and interpret their names and formulas.

Naming Names: Nomenclature, Formulas, and Percent Composition

Okay, so our parents always told us not to call people names, but in chemistry, there are exceptions (and we don’t mean your chemistry teacher). There are more known chemical compounds than there are residents of New York City so something must be done to keep these compounds straight. In the early days of chemistry, far fewer compounds were known, so chemists assigned those compounds Common names, Like "ammonia." Calling a compound by its common name is essentially like calling it "Reggie." Eventually, it became clear that common names, while charming, made a mess of things because these names told you nothing about the compound. So, modern chemists prefer Systematic names, Ones assigned by certain rules, which tell you a great deal about a compound. The process of using rules to assign names to compounds is called chemical Nomenclature.

In the next sections you’ll learn to move easily back and forth between the chemical formula for a compound (H2O) and its systematic name (dihydrogen oxide). For common compounds, there is always the possibility of a charmingly messy common name (water). Finally, you’ll learn to crunch the numbers of percent composition, one of the common ways chemists begin to define an unknown compound.

Knitting names to formulas: Nomenclature

Different naming rules apply to inorganic compounds (ones not based on multi-carbon structures) versus organic compounds (ones that Are Based on multi-carbon structures). The system presented in this chapter applies to inorganic compounds; organic compound nomenclature is described in Chapter 25.

The main idea behind systematic naming is that the poor, addled chemist, drowning in compounds, can move easily between the name of a compound and that compound’s Formula.

Formulas can be one of two types:

Empirical: An empirical formula lists the kinds of atoms in a compound and gives the ratio of atoms to each other — not necessarily their actual numbers.

Molecular: A molecular formula also lists the kinds of atoms in a compound, but gives the actual number of each kind of atom within one molecule of that compound. The compounds nitrogen monoxide and dinitrogen tetroxide make clear the difference between empirical and molecular formulas; just check out Table 5-2.

KBEft When you write out the molecular formula, if the number of atoms within a molecule of the compound is one (1), you don’t write the numeral one (1), as it’s implied. Nitrogen monoxide only has one atom within each molecule of that compound so you write its molecular formula simply as NO.

A great number of chemical compounds are binary compounds, ones that are built of only two kinds of elements. Binary compounds can be either ionic (held together by ionic bonds) or molecular (held together by covalent bonds). Ionic compounds have only empirical formulas because they are not composed of distinct molecules. Molecular compounds have both empirical and molecular formulas.

Naming binary compounds

Many chemical substances are binary compounds, consisting of only two kinds of elements. The generic formula for a binary compound is XAYB, where X and Y are the different elements, and A and B are the relative (and sometimes actual) amounts of each element within one representative unit of the compound. A representative unit might be a molecule or it might be a Formula unit, The smallest repeating unit of an ionic compound.

Figure 5-1 provides a visual summary of the method for assigning systematic names to inorganic compounds, but we also give you the steps for naming a binary compound below.

Is X hydrogen? Yes^^ no

X. Y„ is An acid

A B

Is X a metal? Yes no

Can X have variable charge? Yes no

XAYB is a Molecular compound,

AB

Prefixes are required

Figure 5-1:

Flowchart for assigning systematic names to inorganic compounds.

XAYB is an Ionic compound,

Roman numerals are required

XAYB is an

Ionic compound

Is Y a polyatomic ion?

Yes

Ending depends on anion

No

Ending is -ide

To name a binary compound, ask yourself these questions:

1. Is X hydrogen? Compounds that contain hydrogen cations (H+) often fall into a class of compounds called Acids. Sadly, many common acids are still saddled with common names. Table 5-3 summarizes many of these names. Although these are common names (and are therefore inconvenient), some patterns exist that help make sense of things:

• Acids composed with monoatomic (single-atom) anions use the prefix Hydro – And the suffix -ic.

• Acids composed with polyatomic anions with names ending in -ate Use the suffix -ic.

• Acids composed with polyatomic anions with names ending in -ite Use the suffix -ous.

• If a polyatomic anion includes the prefix Per- Or Hypo-, That prefix transfers to the acid name.

• Be careful. If a compound like HCl is in a gaseous state, it is Not Called hydrochloric acid.

2. Is X a nonmetal or a metal? If X is a nonmetal, you’re dealing with a molecular compound. As such, you’ll need to use prefixes to describe the number of each type of element, X and Y. Table 5-4 summarizes the prefixes you’ll most commonly encounter. If X is a metal, then you’re dealing with an ionic compound — proceed to step 3.

The name of a molecular compound usually lists the element furthest to the left within the periodic table as the first. If both elements occur in the same column, the lower one is usually listed first. The second element in the name of the compound receives the suffix -ide.

Prefixes are always given on both elements unless there is only one of the first element; in that case, the "mono" prefix is dropped.

Nitrogen monoxide (NO) and dinitrogen tetroxide (N2O4) are examples of molecular compounds named according to these rules.

3. Is X a metal that can form cations of different charges? Although alkali metals and alkaline earth metals reliably form only one kind of cation, metals in the center of the periodic table (especially the transition metals) can sometimes form different charges of cations. If a compound contains one of these metals, you must specify the charge of the cation within the compound name. To do so, use Roman numerals within parentheses after the name of the metal; the Roman numeral corresponds to the size of the positive charge. For example, the element iron, Fe, frequently occurs as either a +2 cation or a

+3 cation. The Roman numeral system describes Fe2+ as iron (II) and Fe3+ as iron (III).

Unlike the case with molecular compounds, ionic compound names do not include prefixes to describe the number of each kind of atom within the ionic compound. Why not? Because ionic compounds always occur in the combination of ions that results in zero overall charge. Because ionic compounds have zero overall charge, you can use the charges of the individual ions to determine the formula of the ionic compound — and vice versa. Binary ionic compounds add the suffix -ide To the name of the second element.

Here are some examples of binary ionic compound formulas and names: •Na+ and Cl – combine to form NaCl, known as sodium chloride. •Fe2+ and O2- combine to form FeO, known as iron (II) oxide. •Fe3+ and O2- combine to form Fe2O3, known as iron (III) oxide.

4. Is Y a polyatomic ion? If Y is a polyatomic ion, you have permission to be momentarily annoyed. After the moment has passed, either recall the name of the polyatomic ion from memory (as you’ll have to do on the AP Chemistry exam), or refer to a handy table like Table 5-1.

For example, if Y is SO42 , then you’re dealing with the polyatomic ion called Sulfate. If your compound is Na2SO4, then the name is Sodium sulfate.

Calculating percent composition

Formulas and names emphasize the numbers of different kinds of AtomS within a compound. Percent composition Emphasizes the Mass Of different kinds of atoms within a compound. Naming by percent composition simply means that you make a list of each kind of atom in a compound accompanied by the percent of the compound’s total mass contributed by that kind of atom.

To calculate percent composition you

1. Determine the mass for each mole of the compound. Do this by counting the number of each kind of element within the compound, finding the elements’ atomic masses from the periodic table, and then adding up the individual masses of all the elements.

2. Determine the mass for each mole of each atom. Again, find the elements’ atomic masses on the periodic table.

3. Multiply the mass of the atom by however many of that atom the compound contains.

4. Divide the mass contributed by an individual element by the total mass of the compound.

5. Multiply the result of step 4 by 100%.

6. Repeat steps 2 through 5 for each element type in the compound.

7. Write out the percent composition by listing each element type alongside that element’s percent mass.

Consider the compound water, H2O.

Each mole (6.022 x 1023) of water molecules has mass 18.02g.

Each mole of water molecules contains one mole of oxygen atoms and two moles of hydrogen atoms.

Each mole of oxygen atoms has mass 16.00g. Each mole of hydrogen atoms has mass 1.008g.

So, you calculate the percent composition of water

Oxygen: (16.00g mol-1 / 18.02g mol-1) x 100.0% = 88.79% Hydrogen: [(2 x 1.008g mol-1) / 18.02g mol-1] x 100.0% = 11.21% More briefly, the percent composition is O 88.79%, H 11.21%.

So, by sheer number of atoms, water is mostly hydrogen. But by mass — in other words, by percent composition — water is overwhelmingly oxygen.

Eyeing Ionic Bonds

Ionic bonds form between cations (positively charged ions) and anions (negatively charged ions). The strength of an ionic bond derives from electrostatic attraction between ions of opposite charge. Ionic compounds form extended, three-dimensional lattices, such as the one shown in Figure 5-2. The exact geometrical arrangement of ions in an ionic lattice results from an interplay of factors, all conspiring to maximize the favorable (as in attractive) interactions between the ions.

Figure 5-2:

A lattice of Na+ and Cl-ions within the ionic compound sodium chloride, NaCl.

The NaCl lattice shown in Figure 5-2 consists of repeating, two-atom units of Na+ and Cl-. You can imagine that each sodium atom has donated an electron to a neighboring chlorine atom. Thinking about ionic bonding in this way makes clear why ionic compounds typically form between a metal and a nonmetal. Metals tend to lose valence electrons easily. Nonmetals tend to gain extra valence electrons avidly. Ions scratch each other’s backs.

The strength of ionic bonds within an ionic compound is expressed by Lattice energy. Lattice energy represents the amount of energy required to completely separate the component ions of one mole of an ionic compound into gaseous ions. Larger positive lattice energies correspond to stronger ionic bonds.

Electrostatic attraction increases not only with the magnitude of opposing charges, but also as the distance between those charges decreases. In other words, greater quantity of charge attracts more strongly than less quantity of charge, and closer charges attract more strongly than distant charges. The overall charge of an ion effectively acts as a point charge at the atom’s center. The centers of bigger-sized atoms can’t nestle as closely together as those of smaller-sized atoms. As a result, ionic bonds tend to be stronger between ions with greater magnitude of charge and between ions of smaller size. So, the strongest ionic bonds are between two small, highly charged ions.

Considering Covalent Bonds

Unlike ionic bonds, where atoms either lose or gain electrons, covalent bonds are a a kinder, gentler bond. Covalent bonds form when atoms share valence electrons. Atoms do this kind of thing because it helps them to fill their valence shells. Covalent bonds tend to form between atoms that do not completely give up electrons. In other words, covalent bonds tend to form between nonmetals.

Sharing electrons… or not

The attractive force of a covalent bond arises from the attraction of the shared electrons to the positively charged nuclei of the bonded atoms. Within bonds, electrons don’t act as truly distinct particles, but are distributed into "clouds" of varying density. The shared electrons of a covalent bond distribute with higher density in the region directly between nuclei, as shown in Figure 5-3.

Each single covalent bond houses two shared electrons. In a standard covalent bond, each bonded atom contributes one electron. So, each atom gains one electron (that of its bonding partner) in the bargain.

Sometimes one atom donates both electrons to a covalent bond, with the other atom contributing no electrons. This kind of bond is called a Coordinate covalent bond. Atoms with Lone pairs Of electrons often engage in coordinate covalent bonding. A Lone pair Consists of two electrons that are not used in bonding paired within the same orbital.

Even though covalent bonding usually occurs between nonmetals, metals can engage in coordinate covalent bonding. Usually, the metal receives electrons from an electron donor called a Ligand.

Figure 5-3:

Distribution of electron density

Within the + +

Electron cloud of a

Covalent bond.

Getting to know structural formulas

Atoms can share more than a single pair of electrons. When atoms share two pairs of electrons, they form a double bond, and when they share three pairs of electrons they form a triple bond. A solid line drawn between element symbols serves as shorthand in structural formulas to indicate that atoms are covalently bonded. So, the covalently bonded atoms of water, carbon dioxide, and dinitrogen can be indicated as shown in Table 5-5.

Rules for determining the number of covalent bonds between atoms and for estimating the geometric arrangement of covalently bonded atoms are described in Chapter 7.

Measuring the strength of covalent bonds

Bond enthalpy Describes the strength of covalent bonds. The bond enthalpy (AH) Is an estimate of the amount of energy required to break the bond. In the case of diatomic molecules with single covalent bonds (such as Cl2), the bond enthalpy is a very good estimate. In the case of polyatomic molecules (such as CH4, which contains four distinct C-H bonds), the bond enthalpy is an Average bond enthalpy, An estimate averaged over the four bonds of the molecule.

Larger bond enthalpies correspond to stronger covalent bonds. Typically, atoms held together with more bonds and/or with stronger bonds approach each other more closely than do atoms held together with fewer and/or with weaker bonds.

Bond enthalpies are easily measured, so chemists frequently use them to help determine the strength of bonds and to estimate bond distances. On the AP exam, you might be asked to make the same kinds of estimates from a set of bond enthalpy data.

Separating Charge: Polarity and Electronegativity

Polarity Refers to an uneven distribution of charge. In chemical bonds, polarity arises from a difference in Electronegativity Between bonded atoms. More electronegative atoms draw greater electron density toward themselves. You might think that atoms with more protons (more positively charged nuclei) are always more electronegative, but this isn’t the case. Why? The electronegativity of an atom derives from the positive charge of its nucleus And From the extent to which that positive charge is offset or "shielded" by the successive layers of electron density that surround that nucleus. Because atoms with many protons also tend to have a greater number of electron shells, the large positive charge of these atoms’ nuclei is partially offset by the negatively charged electron shells.

Getting a grip on electronegativity

Within a given row of the periodic table, electronegativity tends to increase from left to right. Within a given column of the table, electronegativity tends to increase from bottom to top. These trends are only overall patterns because electronegativity is influenced by more subtle factors. The electronegativities of the elements are shown in Figure 5-4.

Figure 5-4:

Electronegativities of the elements.

If-*~

OO

CO

The greater the difference in electronegativity between bonded atoms, the more polar is the bond between those atoms. Covalent bonds that are very polar more closely resemble ionic bonds than do covalent bonds that are less polar. In fact, no real physical distinction exists between ionic and covalent bonds — ionic bonds are simply so polar that it becomes useful to imagine that one atom has emerged entirely victorious from the tug-of-war between competing nuclei for electron density.

Although different sources use slightly different numbers to make the split between polar and nonpolar, usually, differences in electronegativity are interpreted with the following categories:

A difference in electronegativity between bonded atoms of less than about 0.3 leads to a description of the bond as "nonpolar."

A difference in electronegativity ranging from 0.3 to about 1.7 leads to a description of "polar."

A difference in electronegativity greater than about 1.7 leads to the description "ionic."

Digging into dipoles

Within a polar covalent bond, electrons are distributed unevenly between the two atoms. The more electronegative atom is surrounded by greater electron density and assumes a Partial negative charge. The less electronegative atom draws correspondingly less electron density and assumes a Partial positive charge. Partial negative and partial positive charges are indicated by the symbols 5- and 8+, respectively. Separation of charge along the line connecting two bonded atoms (the Bond axis) Creates a Bond dipole. Bond dipoles are often indicated in one of two different ways, as shown in Figure 5-5:

Figure 5-5:

Two different depictions of a

Bond dipole in the HCl molecule.

8+ 8-H — Cl

H->

H — Cl

The size of a bond dipole is measured quantitatively by the Dipole moment, U.. A dipole moment measures the polarity of a bond by taking into account two key factors:

IU How much charge is separated along the bond axis IU How far apart the charge is separated

Polar bonds have a larger dipole moment than nonpolar bonds. Dipole moments are vector quantities, which means that they have both size and direction. Within a molecule, different bonds may point in different directions, and these differences can be important.

Individual bonds’ dipoles sum over all the bonds of a molecule, resulting in a Molecular dipole. In addition to the Permanent dipoles Created by polar bonds, Instantaneous dipoles Can flicker into and out of existence within nonpolar bonds and molecules. Both kinds of dipoles play important roles in the interactions between molecules. Permanent dipoles lead to Dipole-dipole interactions And to Hydrogen bonds. Instantaneous dipoles lead to attractive London forces.

In addition to ion-ion interactions, these are the forces that must be overcome in order to turn a liquid into a gas or a solid into a liquid. Different compounds have different boiling points and different melting points because they engage in different collections of interactions. Here is a summary of the intermolecular forces that contribute to boiling and melting points, and examples of compounds in which each kind of force dominates.

Force Compound

Ion-ion NaCl

Hydrogen bonding H2O

Dipole-dipole H2CO

London forces CH4

Melting point Boiling point

1074 K 1738 K

273 K 373 K

156 K 254 K

91 K 112 K

In This Chapter

► Understanding the ins and outs of atomic structure

► Practicing atomic and nuclear chemistry problems

► Applying your knowledge to test questions

► Getting some answers and explanations

The concepts reviewed in Chapter 3 are the most basic in all of chemistry, and they are also some of the most important and testable concepts on the AP chemistry exam. A strong understanding of the most fundamental aspects of modern chemistry is essential to your success on the exam, and the concepts presented in Chapter 3 provide the foundation for the rest of introductory chemistry. Questions that appear regularly in both multiple-choice and free-response questions involve

Periodic table trends Nuclear chemistry

The structure of the atom and nucleus

Many AP questions that do not ask directly about atomic structure nonetheless assume that you have a solid understanding of its concepts.

In this chapter, we highlight the most important points of Chapter 3 for you, and then allow you to try your hand at AP chemistry-style test questions about atomic structure. Keep your eye out for these question types and others that build off of them in the practice tests (Chapters 29 and 30) at the end of the book as well.

Reinforcing the Foundation for Atomic Structure

For the AP exam, you should be familiar with the concepts of atomic structure as well as how to use and manipulate any equations and/or constants related to atomic structure. In this section we review these important concepts covering atomic structure so that you’re prepared for some AP-style exam questions we give you later in this chapter.

Make sure that you thoroughly understand all of the basic components of the atom and how scientists arrived at their understanding of the modern atom. Burn the following major points into your brain before the exam:

Atomic structure came to be understood gradually through the work of Thompson, Rutherford and Bohr:

• Thompson’s model, called the Plum pudding Model of the atom, consisted of blobs of negative charge in a soup of positive charge.

• Rutherford shot bullets (alpha particles) at tissue paper (gold foil) and had to dodge them every once in a while as they came bouncing back at him. He thereby discovered that the majority of the mass and one of the types of charge (the positively charged protons) of the atom were concentrated at its very center in the nucleus.

• Bohr said that the negative charges in an atom (the electrons) orbited the positively charged nucleus like the planets orbit the sun.

• Later models see the electrons in atoms as cloudlike and not as particles that orbit like planets around the sun.

Proton number is what determines the identity of an atom and is equivalent to its atomic number.

If you add the number of neutrons to the number of protons in an atom, you will get its mass number, equivalent to the number of massive particles in its nucleus (nucleons, Or protons and neutrons).

All neutral atoms have equal numbers of positive and negative charges.

Atoms with more electrons than protons have excess negative charge and are called Anions.

^ Atoms with too few electrons and excess positive charge are called Cations. i Atoms can decay via three processes:

• Alpha decay Involves the emission of a helium nucleus, resulting in a daughter atom with a decrease of two in the atomic number and four in the mass number.

• Beta decay Happens through three separate methods, all of which result in an atomic number change of one.

• Gamma decay Is simply the emission of a high-energy particle of light by an excited atom and does not result in any changes in the important numbers defining an atom.

^ Nuclear fusion Involves the joining of two light elements into one heavier element.

^ Nuclear fission Involves the splitting of an enormous atom into two smaller atomic pieces.

^ Electron configurations Show the locations of the electrons in an atom, organized by shells and subshells:

• Electrons always occupy these shells and subshells from lowest energy to highest, often according to the Aufbau diagram.

• Atoms of elements in the copper and chromium families, however, are prone to "steal" an electron from their neighboring S Orbitals in order to achieve a half full or completely full D Orbital, which is the more stable state. These elements have Exceptional electron configurations, Which differ slightly from those predicted by the Aufbau diagram.

• Unruly electrons can jump to higher energy levels by absorbing energy, which they must then emit in order to reach the Ground state. They release this energy in the form of particles of light called Photons, Which have very specific Wavelengths.

Testing Your Knowledge

Now that you’ve absorbed everything you need to know about atoms, try answering some questions. Remember that you can look back at the formulas, variables, and constants, listed on the Cheat Sheet at the front of this book, but try not to look back at the rest of the text until after you check your answers.

The best way that you can practice is by going through the questions provided in this chapter in one sitting and then checking them at the end to identify which areas you still need to review.

Questions 1 through 4 refer to atoms of the following elements.

1. In the ground state, has two electrons in one (and only one) of the P Orbitals.

2. Has the largest atomic radius.

3. Has the largest value of the first ionization energy.

4. Has the smallest second ionization energy.

5. The half-life of 3H is about 12 years. How much of a 4mg sample will remain after 36 years?

(A) 0.25mg

(B) 0.5mg

(C) 1mg

(D) 2mg

(E) 4mg

6. All of the following statements about the oxygen family of elements are true Except:

(A) The electron configuration of the valence shell of the atom is ns2np4.

(B) It contains all nonmetals.

(C) The atomic radii decrease with decreasing atomic number.

(D) Electronegativity increases with decreasing atomic number.

7. Which of the following is the correct electron configuration for molybdenum?

(A) 1s22s22p63s23p64s23d104p65s24d*

(B) [Kr] 5s24d4

(C) 1s22s22p63s23p64s23d104p65s14d5

(D) [Kr] 5S14D4

8. Which of the following sequence of decays might lead to the creation of

234 Pa

91

From

238 U

92

(A) Alpha then gamma decay

(B) Alpha then beta decay

(C) Alpha decay only

(D) Beta decay only

9(a). There are three common isotopes of naturally occuring magnesium as indicated in the table

Using the information above, calculate the average atomic mass of magnesium.

9(b). A major line in the emission spectrum of magnesium corresponds to a wavelength of

518.3nm. Calculate the energy in Joules of the transition resulting in the emission of that spectral line.

The table below shows the first three ionization energies for two mystery elements.

First Ionization Second Ionization Third Ionization Energy (kJ mol’1) Energy (kJ mol’1) Energy (kJ mol’1)

Element 1 520 7300 11820

Element 2 900 1760 14850

10(a). Elements 1 and 2 are both in the second period. What are their identities? Explain your reasoning.

10(b). Write the full electron configuration for element 1 after it has been ionized once. What other element shares the same electron configuration in its neutral state?

Checking Your Work

You’ve done your best. Now check your work. Make sure to read the explanations thoroughly for any questions you got wrong — or for any you got right by guessing.

1. (D). There are three P Subshell orbitals, and an atom that has been forced to double up on electrons in one and only one P Orbital must have four electrons in its P Subshell. The electron configuration of oxygen is 1 S22S22P4, So it fits the bill.

2. (A). Atomic radius decreases as you move to the right across a period, therefore the element in the list with the lowest atomic number (in other words, the farthest to the left), will have the largest atomic radius.

3. (E). The element with the largest value of the first ionization energy should be the one that is least likely to give up an electron. Halogens are the most likely candidates for high first ion-ization energies because they are the closest to achieving noble gas configurations through gaining electrons. Fluorine is the only halogen in the group.

4. (A). The element with the lowest second ionization energy should be one that is eager to give up its second electron. This corresponds to elements in the alkaline earth metal column, which need to be ionized twice in order to achieve noble gas configurations.

5. (B). Thirty-six years is equivalent to three half lives for 3H. This means that the amount of radioactive material in the sample will have decreased by half three times. This leaves 2mg at 12 years, 1mg at 24 years, and 0.5mg at 36 years.

6. (B). The first statement is true because elements in the oxygen family always have full S Subshells and four electrons in their P Subshells by virtue of sharing the same horizontal location in the periodic table. B is not true. Several of the oxygen family’s elements fall below the "staircase" marking the division between nonmetals and metals on the periodic table, indicating that they are metals or semimetals. C is a deceptively tricky statement because, while the atomic radius of elements in the same Family Do indeed decrease with decreasing atomic number, elements in the same period have precisely the opposite relationship, so you must be careful to keep them straight. D is also true because electronegativity increases to the right in a period and toward the top of a family.

7. (C). One might expect molybdenum to have the electron configuration shown in A and B (which are equivalent). However, molybdenum, being of the chromium family, falls under the umbrella of exceptional electron configurations. Its 4d orbital will abscond with an electron, which would normally belong to the 5S Orbital in order to make it more stable. This leaves you with the electron configuration 1 S22S22P63S23P64S23D104P65S14D5, Which can also be written as [Kr]5S14D5.

8. (B). The net result in the decay of

Is a decrease of four in mass number and a decrease of one in atomic number. Because neither beta nor gamma decay result in a decrease in mass number, an alpha decay must occur, which would leave you with

To then increase the atomic number by one from the initial alpha decay,

Must undergo a beta decay.

238

92

U

To

29314

91

Pa

9(a). 24.3amu. Multiply each mass by its percent abundance in decimal form, giving you

(24.0 x 0.79) + (25.0 x.010) + (26.0 x 0.11) = 24.32amu

9(b). 3.84 x 10-19J. This problem is a direct application of the equation E = Hv, and C = Xv. Plugging the speed of light as well as the given wavelength into the second equation and solving for frequency gives you

V = c = 3.0 x 10 Ms— = 5.79 x 1014 Hz X 518.3 x 10 9 M

Take this frequency value and plug it in turn into the first equation to give you the energy value of the spectral line in question:

E = hxu= 6.63x 10 34Jsx5.79x 1019Hz = 3.84x 10 14J

10(a). Element 1 is lithium and Element 2 is berylium. It requires roughly 14 times more energy to remove the second electron from element 1 than it did to remove the first, implying that the first electron was given up relatively easily and that the atom is very reluctant to give up another. This is consistent with the alkali metals, which only need to lose one electron to achieve a noble gas configuration. Once any element achieves noble gas configuration, it is reluctant to lose it by giving up another electron, explaining the large jump to the second ion-ization energy. Because you are told that these elements are in the second period, element 1 must be lithium. As for Element 2, it requires only twice as much energy to remove the second electron as was required to remove the first, but then it requires eight times more energy to remove the third. This implies that the first and second electrons are considerably easier to remove than the third, which is consistent with an alkaline earth metal. In this case, that metal must be berylium, which is the only alkaline earth metal in the second period.

10(b). 1 S2, Helium. The general electron configuration of lithium is 1 S22S1. When lithium is ionized, however, it loses an electron, achieving the electron configuration of the noble gas helium, whose electron configuration is simply 1 S2.

In This Chapter

^ Hitting the high points

^ Shaping up your skill with some practice questions

^ Discovering the answers and explanations to your questions

Chapter 7 was packed with ideas, starting with the way valence electrons distribute themselves around individual atoms, building up through the way atoms connect themselves into molecules with particular shapes and finishing with the way molecular shapes help determine the properties of different compounds. In other words, Chapter 7 was a lot to take in one bite. Here is where you chew. In the following sections we review the highlights of Chapter 7, give you practice problems to help sear important concepts into your brain, and give you full explanations for the answers to help you swallow what you’ve chewed.

Shaping Up the High Points

Before you attempt any questions in this chapter, you should review the following sections of important points from Chapter 7.

Electron dot structures and Lewis structures

Electron dot structures And Lewis structures Use dots and/or lines to represent valence electrons and/or lines to represent valence electron pairs.

Basic steps to follow when drawing a Lewis structure are

1. Add up all the valence electrons for all the atoms in the molecule.

2. Pick a "central" atom to serve as the anchor of your Lewis structure.

3. Connect the other, "outer" atoms to your central atom using single bonds only.

4. Fill the valence shells of your outer atoms. Then put any remaining electrons on the central atom.

5. Check whether the central atom now has a full valence shell.

Compounds that can engage in multiple, valid Lewis structures participate in Resonance, Based on an old idea that the molecules might actually be in equilibrium between the multiple structures. Although we now know that not to be the case, the term has stuck. Individual Resonance structures Contribute to an overall, averaged structure called a Resonance hybrid. Adjacent p-orbital electrons are commonly involved in resonance, in which they participate within delocalized N Bonds.

Valence bond theory

Valence bond theory Describes covalent bonds in terms of overlap between atomic orbitals:

IU Orbitals that overlap in a manner completely symmetric to the bond axis form Sigma bonds.

I Orbitals that overlap in a manner that is symmetric to the bond axis in only one plane form Pi bonds.

VSEPR theory

VSEPR theory Explains molecular shapes in terms of mutual repulsion between electron pairs (both bonding and nonbonding pairs) around a central atom:

IU Lone (nonbonding) pairs repel more strongly than bonding pairs.

IU Valence electrons in different kinds orbitals (like S And P Orbitals) Hybridize Into mixed, equivalent orbitals. The total number of hybridized orbitals is the same as the original number of unmixed orbitals.

I One S Orbital mixes with one P Orbital to create two identical Sp Hybrids.

Sp Hybridized centers will have linear geometry. IU One S Orbital mixes with two P Orbitals to create three identical Sp2 Hybrids.

Sp2 Hybridized centers will have trigonal planar geometry. IU One S Orbital mixes with three P Orbitals to create four identical Sp3 Hybrids.

Sp3 Hybridized centers will have tetrahedral geometry.

Bond dipoles

Individual Bond dipoles Arise from differences in electronegativity in bonded atoms. Except for homonuclear diatomic molecules (like O2, H2, and so on), all atom-atom bonds will have a at least a small bond dipole. Within a molecule, bond dipoles may or may not contribute to an overall Molecular dipole Depending on geometry:

I Bond dipoles add as vectors within molecules, building on each other or canceling each other out depending on geometry.

IU Dipole moment (□,) = amount of separated charge (Q) x distance separated (d); the equation looks like this: u, = Qd

Isomers

Isomers Are compounds made up of the same atoms, but are put together in the following different arrangements:

IU Structural isomers Have different bonds.

IU Stereoisomers Have the same bonds, but different three-dimensional arrangements of atoms.

• Geometric isomers Can occur when atoms are restricted from rotating freely about their bonds.

• Optical isomers (also called Enantiomers) Are nonsuperimposable mirror images of one another and are therefore Chiral.

Testing Your Knowledge

Now that you know your sp2′s from your sp3′s, and have your VSEPR in shape, give these practice questions a try.

1. Which of the following correctly lists the molecules in order of increasing polarity?

(A) H2O, H2S, HF, H2

(B) H2, HF, H2S, H2O

(C) H2, H2S, HF, H2O

(D) H2, H2S, H2O, HF

(E) H2S, H2O, HF, H2

2. Which of the following molecules has bond angles closest to 109.5°?

(A) BF3

(B) SiS2

(C) CCl4

(D) H2O

(E) CO2

3. Identify the incorrect set of resonance structures.

A.

-1 • • +1 . • -1 IO — N — O!

-1 • • +1 • •

! O — N — O • • | • •

I O I

"-1

• • +1 . • -1

O — N — O!

• • | • •

I O I -1 • •

B.

H

C.

H

H H H

H — C — O I

M m

H

H

HH H

‘.OL I..

HCO

D.

+1

‘, O — O — O!

+1

I O — O — O I

-1 • • • •

I O — C = O

• • I • •

‘.OL

* *-1

-1 • • • • • .-1

I O — C — O I

OCO

Mm | • •

‘.OL

* *-1

4. Group IVA elements tend to hybridize in which of the following ways?

5. Within formaldehyde, CH2O, carbon possesses which of the following traits?

I. Sp2 Hybridization

II. Three equivalent sigma bonds

III. Trigonal planar bonding geometry

(A) I only

(B) II only

(C) III only

(D) I and III only

(E) I, II and III

O

H

H

-1

O

-1

-1

E.

-1

O

Questions 6 through 10 refer to the following list of geometries:

6. Characteristic of four electron pairs, two bonding and two nonbonding

7. Typical of Sp Hybridization

8. Accounts for the nonpolarity of SiF4

9. Nitrate anion 10. PCl5

Questions 11 through 14 refer to the following molecule, and the accompanying set of choices:

O

11. Exhibit(s) Sp2 Hybridization

12. Exhibit(s) Sp3 Hybridization

13. Has a lone pair

14. Has a pi bond

Checking Your Work

Don’t play the angles. Clear up any lingering confusion by checking your answers, making sure you understand the explanations for any questions you got wrong — or the ones that you got right by guessing.

1. (D). H2 is the least polar because its sole covalent bond occurs between atoms that are identical, and which therefore have identical electronegativity. H2S and H2O are close, but H2O is slightly more polar because oxygen is slightly more electronegative than sulfur. The "bent" geometry of both H2S and H2O is key to the presence of a molecular dipole in each

Case — a linear shape would lead to canceling of the bond dipoles, resulting in nonpolar molecules. The sole covalent (nearly ionic) bond in HF is the most polar of them all.

2. (C). Bond angles of 109.5° signify a perfect tetrahedron. Many molecules approach this ideal, but perfect tetrahedral geometry typically requires that the central atom (carbon, in this case) possess four identical bonding partners (chlorines, in this case).

3. (E). The last set of resonance structures, for CO32- anion, are incorrect. Each of the structures includes an oxygen atom with an excess of valence electrons. The oxygen atom double-bonded to carbon in each structure should have only two lone pairs, not three.

4. (C). Group IVA atoms tend to engage in four covalent bonds. Because of hybridization, these bonds involve four identical Sp3 Orbitals.

5. (D). In formaldehyde, the central carbon indeed exhibits Sp2 Hybridization. This hybridization leads to a trigonal planar (though not perfectly so) molecular shape. However, the three sigma bonds are not identical, for two reasons. First, C-O bonds differ in polarity from C-H bonds. Second, the C-O bond axis includes a pi bond; double-bonding between carbon and oxygen brings those two atoms closer together than does a single bond.

6. (B). In water, for example, the two lone pairs of oxygen and the two O-H bonds lead to just such a bent shape.

7. (A). In an Sp Hybridized atom, there are only two bond axes. The electrons in these axes mutually repel to achieve the maximum separation afforded by linear geometry.

8. (D). Because of its perfect tetrahedral geometry, silicon tetrafluoride is nonpolar, despite the fact that each silicon-fluorine bond is polar.

9. (C). Nitrate displays resonance between three Sp2 Hybridized resonance structures. The hybrid structure therefore has a trigonal planar shape consistent with Sp2 Hybridization.

10. (E). This compound may have thrown you. The central phosphorous of PCl5 is "hyperva-lent," meaning that it engages in more than the three covalent bonds you’d expect from its position on the periodic table. But even if the hypervalency freaked you out, take heart: the basic principles of VSEPR still apply. Whatever the reasons for pentavalent phosphorous, the fact remains that the electrons within the five bond axes mutually repel, seeking the shape with maximum separation. That shape is trigonal bipyramidal.

11. (C). Carbon III engages in a double bond (with carbon) and in two single bonds (with hydrogen and nitrogen). This arrangement leads to three bonding axes and Sp2 Hybridization.

12. (D). Carbon I engages in four separate single bonds, one with another carbon and three with hydrogens. Four separate single bonds around a central carbon are a hallmark of Sp3 Hybridization. Nitrogen II may at first appear to be Sp2 Hybridized, because it engages in only three bonds — but the nitrogen also contains a lone pair, and is thus Sp3 Hybridized.

13. (B). Carbons I and III keep their four valence electrons occupied within various combinations of covalent bonds. Because it has one more valence electron than carbon, Nitrogen II engages in only three covalent bonds, reserving two electrons as a nonbonding "lone pair."

14. (C). Double bonds, like the carbon-carbon double bond in which Carbon III participates, include both sigma and pi bonds.