In This Chapter

^ Picturing the particles that make up liquids and solids

^ Predicting what happens when you change temperature and pressure

^ Seeing what happens when you mix particles to form solutions

Hen asked, young children often report that solids, liquids, and gases are made up of different kinds of matter. This (mistaken) idea, not usually shared by older people, is understandable given the striking differences in the properties of these three states. But the AP chemistry exam leaves no room for charming misconceptions. In this chapter, we discuss how the properties of the condensed states — liquids and solids — emerge from the interactions between particles, and how these properties can change as temperature and pressure change. We also explore the kinds of interactions that occur between particles within homogenous mixtures called Solutions. Like the properties of pure substances, the properties of solutions depend on the interactions of the particles that make them up.

Restricting Motion: Kinetic Molecular Theory of Liquids and Solids

Kinetic theory (as described in greater detail in Chapter 9) explains the properties of matter in terms of the energetic motions of its particles. Well, not All Of the motions. Really, kinetic theory usually limits itself to a simplified version of matter, one in which infinitely small particles do nothing but zip around quickly and bump into one another or into the sides of a container. This description isn’t ever literally true, but is sometimes a very good approximation of reality, especially for gases in large volumes.

Adding energy to a sample increases its temperature and increases the kinetic energy of the particles, which means that they move about more quickly and bump into things more vigorously. Removing energy from a sample (cooling it) has the opposite effect.

When atoms or molecules have less kinetic energy, or when that energy competes with other effects (like high pressure or strong attractive forces), the matter ceases to be in the diffuse, gaseous state and comes together into one of the Condensed states:

Liquid: The particles within a liquid are much closer together than those in a gas. As a result, applying pressure to a liquid does very little to change the volume. The particles still have an appreciable amount of kinetic energy associated with them, so they may undergo various kinds of twisting, stretching, and vibrating motions. In addition, the particles can slide past one another (translate) fairly easily, so liquids are fluid, though less fluid than gases. Fluid matter assumes the shape of anything that contains it, as shown in Figure 11-1. The particles of a liquid have Short-range order, Meaning that they tend to exhibit some degree of organization over short distances.

^ Solid: The state of matter with the least amount of obvious motion is the solid. In a solid, the particles are packed together quite tightly and undergo almost no long-range translation. Therefore, solids are not fluid. Matter in the solid state still vibrates in place or undergoes other types of motion, depending on its temperature (in other words, on its kinetic energy). The particles of a solid have Long-range order, Meaning that they tend to exhibit organization over long distances. However, matter at a certain temperature must contain a specific amount of energy, regardless of its state. Temperature has no meaning without motion energy.

R

Fluid

Condensed

Gas

Liquid

Increasing order among particles

Solid

Decreasing average kinetic energy

The temperatures and pressures at which different types of matter switch between states depend on the unique properties of the atoms or molecules within that matter. But be careful! It is easy to get fooled by trying to compare different substances at different temperatures. Typically, particles that are very attracted to one another and have easily stackable shapes tend to be in condensed states (at a fixed temperature). Particles with no mutual attraction (or that have mutual repulsion) and with not-so-easily stackable shapes tend toward the gaseous state. Think of a football game between fiercely rival schools. When fans of either school sit in their own section of the stands, the crowd is orderly, sitting nicely in rows. Put rival fans into the same section of the stands, however, and they’ll repel each other with great energy. But be sure you are comparing fans with the same amount of energy. Water as ice has less energy than as a liquid because it has a lower temperature. Technically if you could have a mole of water vapor, a mole of liquid water, and a mole of solid water (ice) all at the same temperature, the water molecules would all have the same kinetic energy!

Getting a Firm Grip on Solids

Solids all have less-apparent motion than their liquid or gaseous counterparts, but that doesn’t mean all solids are alike. The forces between particles within solids as well as the degree of order in the packing of particles within solids vary greatly, giving each solid different properties. The sections that follow shed some light on both the forces that affect solids as well as the packing order that helps to determine a solid’s properties.

Different types of solids and their properties

The properties of a solid depend heavily on the forces between the particles within it. The easiest property to compare is the melting point — that temperature at which the kinetic energy overcomes the strong forces of attraction holding the particles vibrating tightly in a solid.

IU Several different forces determine different melting points of a solid:

• Ionic solids Are held together by an array of very strong ionic bonds (see Chapter 5 for more about these bonds), and, therefore, tend to have high melting points — it takes a great deal of energy to pull apart the particles.

• Molecular solids Consist of packed molecules that are less strongly attractive to each other, so molecular solids tend to have lower melting points.

• Some solids consist of many particles that are covalently bonded to one another in an extensive array. These Covalent solids Tend to be exceptionally strong due to the strength of their extensive covalent network. One example of a covalent solid is diamond. Covalent solids have Very High melting points. Ever try to melt a diamond? (Chapter 5 has details about covalent bonds.)

I Metallic solids Are made up of closely packed metal atoms. These atoms bond to one another more strongly than the particles of most molecular solids, but less strongly than the particles of covalent solids. Because metal atoms so easily give up valence electrons, the atoms within the lattice of a metallic solid seem to exist in a shared "sea" of mobile electrons. The positively charged metal nuclei are held together by their attraction to this negatively charged sea. Metallic solids can be be soft or relatively hard, are ductile and malleable, and are good conductors of heat and electricity. The orderly array of atoms in many metals can allow "sheets" of atoms to slide over one another easily, hence the ease with which metals can be made into wires (ductility) Or beaten into thin foils (malleability).

Packing order in solids

The degree of order in the packing of particles within a solid can vary tremendously. How ordered the particles are within a solid determines how well defined its melting point is. If the particles are well ordered, then the whole sample tends to melt at the same temperature, but if different regions of the sample have different degrees of order, then those regions melt at different temperatures.

I Most solids are highly ordered, packing into neat, repeating patterns called Crystals. The smallest packing unit, the one that repeats over and over to form the Crystalline solid, Is called the Unit cell. Crystalline solids tend to have well-defined melting points.

The particles in crystalline solids tend to organize themselves into arrangements that make the most of the attractive forces between them. Usually, this means packing the particles as closely together as possible.

IU Amorphous solids Are those solids that lack an ordered packing structure. Glass and plastic are examples of amorphous solids. Amorphous solids tend to melt over a broad range of temperatures because some parts of the structures are more easily pulled apart than others.

When cooling a liquid through a phase transition into a solid, the rate of cooling can have a significant impact on the properties of the solid. The particles may need time to move into the extreme order with which they are packed together in crystalline solids. So, substances that are capable of forming crystalline solids may nevertheless freeze into amporphous solids if they are cooled rapidly. The particles may become trapped in disordered packing arrangements. Sometimes this adds considerable strength to a substance, so steels may be "hardened" by heating and sudden cooling.

A collection of different types of forces is very important in determining liquid-solid phase behavior. These forces are more important for the liquid-solid phase than in gases because liquids and solids are condensed states; the molecules within these states are in very close proximity.

In molecular solids, dipole-dipole forces, London dispersion forces, and hydrogen bonds play prominent roles (see Figure 11-2). At the same time, these forces are relatively weak compared to those that dominate in other kinds of solids. Because of the weakness of these forces, molecular solids are relatively soft and tend to have much lower melting points than other solids. In the list below, we describe how these forces work.

Forces at work in condensed states

The forces at work between the particles in a solid (or liquid) largely determine the properties of the substance. For the AP exam, you should definitely know each of the kinds of forces at work in solids and liquids, and be able to predict which forces are most important within a sample of a given compound. These forces include relatively weaker forces (dipole-dipole, London dispersion, and hydrogen bonding) and relatively stronger forces (ionic and covalent bonds).

Here are the intermolecular forces you should know:

IU Dipole-dipole forces (see Figure 11-2) take place between molecules with permanent dipoles (separated regions of opposite charge). Oppositely charged parts of different molecules attract and regions with same type of charge repel. These forces tend to order the molecules.

IU London dispersion forces (shown in Figure 11-2) take place when the positively charged nucleus of one atom attracts the electron cloud of another atom while the electron clouds of both atoms mutually repel one another. In other words, the two atoms induce dipoles in each other, and these Induced dipoles (temporary dipoles created by the nearness of electron clouds) attract one another. It is more easy to redistribute the electrons of some molecules into an induced dipole than it is with others. In other words, some molecules are more Polarizable (capable of having their electrons redistributed) than others. Polarizable molecules tend to take part more strongly in London dispersion forces.

IU Hydrogen bonds Are specific kinds of dipole-dipole attractions that take place between a hydrogen atom in a polar bond and a lone pair of electrons on an electronegative atom (see Chapter 5 for a refresher on electronegativity). Because it participates in a polar bond, the hydrogen has a partial positive charge, 8+. Because it is electronegative, the atom that contributes the lone pair has a partial negative charge, 8-. These partial charges attract. Hydrogen atoms that bond with fluorine, oxygen, and nitrogen are particularly prone to engage in hydrogen bonds. When these interactions take place Between molecules, They significantly increase melting and freezing points. Water hydrogen bonds avidly to itself and to other molecules, as shown in Figure 11-2.

In addition to the relatively weak forces described above, ionic and covalent bonds (discussed in detail in Chapter 5) are strong forces that greatly affect the melting point of a compound:

In ionic solids, Ionic bonds (electrostatic interactions) provide a major source of attraction between particles. These types of solids tend to be hard but brittle (the ionic lattice can crack) and have very high melting points. Lattice energy Is a measure of the strength of the interactions between ions in the lattice of an ionic solid. The larger the lattice energy, the stronger the ion-ion interactions.

^ In covalent solids, particles are bound to each other within strong networks of Covalent bonds. These solids are often exceptionally hard and have very high melting points.

Figure 11-2:

Inter-molecular intera ctions include

(a) dipole-dipole interactions,

(b) London dispersion

Forces, and

(c) hydrogen Attraction- 8- S+ 8-8+

Bonds. Repulsion…..

Moving Through States with Phase Diagrams

The previous sections described how microscopic interactions between particles can lead to large-scale differences in the properties of a sample, especially by causing the sample to be in different states (solid, liquid, or gas). This section describes some tools you can use to track the state of a sample as it moves through different regions of temperature, pressure, or added heat energy.

Phases and phase diagrams

M&l Each state (solid, liquid, gas) is called a Phase. When matter moves from one phase to another due to changes in temperature and/or pressure, that matter is said to undergo a Phase transition. The way a particular substance moves through states as temperature and pressure vary is summarized by a Phase diagram. Phase diagrams usually display pressure on the vertical axis and temperature on the horizontal axis. Lines drawn within the temperature-pressure field of the diagram represent the equilibrium boundaries between phases. A representative phase diagram is shown in Figure 11-3. Refer back to this figure as you read through the section.

Moving from liquid to gas is called Boiling, And the temperature at which boiling occurs is called the Boiling point. The normal boiling point is when this transition occurs at 1 atmosphere of pressure. Moving from solid to liquid is called Melting, And the temperature at which melting occurs is called the Melting point. The melting point temperature is the same as the Freezing point Temperature, but freezing implies matter moving from liquid to solid phase. The melting point a substance has at 1atm pressure is called the Normal melting point. Just as freezing and melting points are the same, condensation points and boiling points are the same temperature. For this reason published tables are of freezing points and boiling points.

Temperature

At the surface of a liquid, molecules can enter the gas phase more easily than elsewhere within the liquid because the motions of those molecules aren’t as constrained by the molecules around them. So, these surface molecules can enter the gas phase at temperatures below the liquid’s characteristic boiling point. This low-temperature phase change is called Evaporation And is very sensitive to pressure. Low pressures allow for greater evaporation, while high pressures encourage molecules to re-enter the liquid phase in a process called Condensation. The pressure of the gas over the surface of a liquid is called the Vapor pressure. It is important not to confuse this with atmospheric pressure due to other gases in the air. For example a sample of liquid water at 20°C has a vapor pressure of 0.023atm while the atmosphere has a pressure of l. Oatm. Understandably, liquids with low boiling points tend to have high vapor pressures; particles in liquids with low boiling points are weakly attracted to each other. At the surface of a liquid, weakly interacting particles have more of a chance to escape into vapor phase, thereby increasing the vapor pressure. See how kinetic theory helps make sense of things?

In addition to having high vapor pressure and low boiling points, substances with weakly interacting molecules tend to have low surface tension and low cohesion. Surface tension Is a measure of the amount of energy it takes to spread out a substance over a larger surface; the weaker the interactions between molecules, the easier this is to do. Cohesion Is the tendency of the molecules of a substance to attract one another. Adhesion Is the tendency of those molecules to bond to the molecules of another substance. Substances that are both adhesive and cohesive display Capillary action, The ability to pull themselves through narrow tubes.

At the right combination of pressure and temperature, matter can move directly from solid to a gas or vapor. This type of phase change is called Sublimation, And is the kind of phase change responsible for the white mist that emanates from dry ice, the common name for solid carbon dioxide. Movement in the opposite direction, from gas directly into solid phase, is called Deposition.

For any given type of matter there is a unique combination of pressure and temperature at the nexus of all three states. This pressure-temperature combination is called the Triple point. At the triple point, all three phases coexist. In the case of good old H2O, going to the triple point produces ice-water vapor. Take a moment to bask in the weirdness.

Other weird phases include the following:

Plasma Is a gaslike state in which electrons pop off gaseous atoms to produce a mixture of free electrons and cations (which are atoms or molecules with positive charge). For most types of matter, achieving the plasma state requires very high temperatures, very low pressures, or both. Matter at the surface of the sun, for example, exists as plasma.

^ Supercritical fluids (SCF) exist under high temperature-high pressure conditions. For a given type of matter, there is a unique combination of temperature and pressure called the Critical point. At temperatures and pressures higher than those at this point, the phase boundary between liquid and gas disappears, and the matter exists as a kind of liquidy gas or gassy liquid. Supercritical fluids can diffuse through solids like gases do, but can also dissolve things like liquids do. SCFs are being used in some areas as extraction agents in dry cleaning.

Changing phase and temperature along heating curves

Starting from the solid phase, you can add heat energy to a sample, causing it to progress through liquid and vapor phases. If you measure the temperature of the sample as you do this, you’ll find that it has a staircase pattern. This pattern is called a Heating curve, And results from the fact that it takes energy simply to move particles from solid to liquid and from liquid to vapor (moving in the opposite direction releases energy). When a substance is at its melting point or freezing point, added heat energy goes toward disrupting attractive forces between the molecules instead of increasing the temperature (the average kinetic energy) of the molecules. Like phase diagrams, the exact shape of a heating curve varies from one substance to another. The heating curve for water is shown in Figure 11-4. Heating curves usually assume a constant rate of energy input.

Figure 11-4:

A heating curve for water.

125 100 75 50 25 0

-25

Heat Added

Dissolving With Distinction: Solubility and Types of Solutions

Compounds can form mixtures. When compounds mix completely, right down to the level of individual molecules, we call the mixture a Solution. Each type of compound in a solution is called a Component. The component of which there is the most is usually called the Solvent. The other components are called Solutes. Although most people think "liquid" when they think of solutions, a solution can be a solid, liquid, or gas. The only criterion is that the components are completely intermixed. We explain what you need to know in this section. By far the most important solutions (99% on the AP exam) are those where water is the solvent. Master those before worrying about other solutions.

Forces in solvation

For gases, forming a solution is a straightforward process. Gases simply diffuse into a common volume (see Chapter 9 for more about diffusion). Things are a bit more complicated for condensed states like liquids and solids. In liquids and solids, molecules or ions are crammed so closely together that Intermolecular forces (forces between molecules) are very important. Examples of these kinds of forces include dipole-dipole, hydrogen bonding, and London dispersion forces as discussed previously. In addition, ion-dipole forces can be important in solutions, as shown for water in Figure 11-5.

Figure 11-5:

Water molecules participate in ion-dipole intera ctions with a cation.

V

O 8-

O

8-

+

©

8-

O

8-

O

Introducing a solute into a solvent initiates a tournament of forces. Attractive forces between solute and solvent compete with attractive solute-solute and solvent-solvent forces, as depicted in Figure 11-6. A solution forms only to the extent that solute-solvent forces dominate over the others. The process in which solvent molecules compete and win in the tournament of forces is called Solvation Or, in the specific case where water is the solvent, Hydration. Solvated solutes are surrounded by solvent molecules. When solute ions or molecules become separated from one another and surrounded in this way, we say they are Dissolved.

Imagine that the members of a ridiculously popular band exit their hotel to be greeted by an assembled throng of fans and the media. The band members attempt to cling to each other, but are soon overwhelmed by the crowd’s ceaseless, repeated attempts to get closer. Soon, each member of the band is surrounded by his own attending shell of reporters and hyperventilating fans. So it is with dissolution.

Figure 11-6:

An ionic compound dissolves in water.

The tournament of forces plays out differently among different combinations of components. In mixtures where solute and solvent are strongly attracted to one another, more solute can be dissolved. One factor that always tends to favor solvation is Entropy, A kind of disorder or "randomness" within a system. Dissolved solutes are less ordered than undissolved solutes. Beyond a certain point, however, adding more solute to a solution doesn’t result in a greater amount of solvation. At this point, the solution is in dynamic equilibrium; the rate at which solute becomes solvated equals the rate at which dissolved solute Crystallizes, Or falls out of solution. A solution in this state is Saturated. By contrast, an Unsaturated Solution is one that can accommodate more solute. A Supersaturated Solution is a temporary one in which more solute is dissolved than is necessary to make a saturated solution. A supersaturated solution is unstable; solute molecules may crash out of solution given the slightest perturbation. The situation is like that of Wile E. Coyote, who runs off a cliff and remains suspended in the air until he looks down — at which point he inevitably falls.

To dissolve or not to dissolve: Solubility

The concentration of solute (the amount of solute relative to the amount of solvent or the total amount of solution) required to make a saturated solution is the Solubility Of that solute. Solubility varies with the conditions of the solution. The same solute may have different solubility in different solvents, and at different temperatures, and so on.

When one liquid is added to another, the extent to which they intermix is called Miscibility. Typically, liquids that have similar properties mix well — they are Miscible. Liquids with dissimilar properties often don’t mix well — they are Immiscible. This pattern is summarized by the phrase, "like dissolves like." Alternately, you may understand lack of miscibility in terms of the Italian Salad Dressing Principle. Inspect a bottle of Italian salad dressing that has been sitting in your refrigerator. Observe the following: The dressing consists of two distinct layers, an oily layer and a watery layer. Before using, you must shake the bottle to temporarily mix the layers. Eventually, they will separate again because water is polar and oil is nonpolar.

(See Chapter 5 if the distinction between polar and nonpolar is lost on you.) Polar and non-polar liquids mix poorly, though occasionally with positive gastronomic consequences.

Similarity or difference in polarity between components is often a good predictor of solubility, regardless of whether those components are liquid, solid, or gas. This rule is often described as "like dissolves like." Why is polarity such a good predictor? Because polarity is central to the tournament of forces that underlies solubility. So, solids held together by ionic bonds (the most polar type of bond) or polar covalent bonds tend to dissolve well in polar solvents, like water. For a refresher on ionic and covalent bonding, visit Chapter 5.

Heat effects on solubility

Increasing temperature magnifies the effects of entropy on a system. Because the entropy of a solute is usually increased when it dissolves, increasing temperature usually increases solubility — for solid and liquid solutes, anyway. Another way to understand the effect of temperature on solubility is to think about heat as a reactant in the dissolution reaction:

Solid solute + solvent + heat — Dissolved solute

Heat is usually absorbed when a solute dissolves. Increasing temperature corresponds to added heat. So, by increasing temperature you supply a needed reactant in the dissolution reaction. (In those rare cases where dissolution releases heat, increasing temperature can decrease solubility.) NaCl is an example where the solubility changes very little with temperature change.

Gaseous solutes behave differently than do solid or liquid solutes with respect to temperature. Increasing the temperature tends to decrease the solubility of gas in liquid. To understand this pattern, recall the concept of vapor pressure from earlier in the chapter. Increasing temperature increases vapor pressure because added heat increases the kinetic energy of the particles in solution. With added energy, these particles stand a greater chance of breaking free from the intermolecular forces that hold them in solution. A classic, real-life example of temperature’s effect on gas solubility is carbonated soda. Which goes flat (loses its dissolved carbon dioxide gas) more quickly: warm soda or cold soda?

Pressure effects on gas solubility

The comparison of gas solubility in liquids with the concept of vapor pressure highlights another important pattern: Increasing pressure increases the solubility of a gas in liquid. Just as high pressures make it more difficult for surface-dwelling liquid molecules to escape into vapor phase, high pressures inhibit the escape of gases dissolved in solvent, as highlighted by Figure 11-7. The relationship between pressure and gas solubility is summarized by Henry’s law:

SA = k x PA

Where SA is the solubility of A, PA is the partial pressure of A in the vapor over the solution, and K Is Henry’s constant. The value of Henry’s constant depends on the gas, solvent, and temperature, and is accurate for small concentrations of solute. A particularly useful form of Henry’s law relates the change in solubility (S) That accompanies a change in pressure (P) Between two different states:

S1 / P1 = S2 / P2

According to this relationship, tripling the pressure triples the gas solubility, for example.

Figure 11-7:

Pressure alters the

Equilibrium of vapor

Molecules at a liquid interface.

O o o

Lid

Measuring solute concentration

It seems that different solutes dissolve to different extents in different solvents in different conditions. How can anybody keep track of all these differences? Chemists do so by measuring Concentration. Qualitatively, a solution with a large amount of solute is said to be Concentrated. A solution with only a small amount of solute is said to be Dilute. As you may suspect, simply describing a solution as concentrated or dilute is usually about as useful as calling it "pretty" or naming it "Fifi." We need numbers. Two important ways to measure concentration are Molarity And Percent solution.

Molarity relates the amount of solute to the volume of the solution:

Molarity (M )= molessolute liters solution

In order to calculate molarity, you may have to use conversion factors to move between units. For example, if you are given the mass of a solute in grams, use the molar mass of that solute to convert the given mass into moles. If you are given the volume of solution in cm3 or some other unit, you’ll need to convert that volume into liters.

The units of molarity are always mol L-1. These units are often abbreviated as M And referred to as "molar." Thus, 0.25M KOH(aq) is described as "Point two-five molar potassium hydroxide" and contains 0.25 moles of KOH per liter of solution. Note that this does Not Mean that there are 0.25 moles KOH per liter of Solvent (water, in this case) — only the final volume of the solution (solute plus solvent) is important in molarity. Why? Because often volumes just don’t add up when two substances are mixed. (It is kinetic theory again!) Molar concentrations of a substance are often denoted by brackets, as in [KOH] = 0.25. Like other units, the unit of molarity can be modified by standard prefixes, as in millimolar (mM, 10-3 mol L-1) and micromolar (uJM, 10-6 mol L-1).

One important quantity that is measured in units of molarity is the Solubility product constant, Ksp. The solubility product is useful for measuring the dynamic equilibrium of ionic compounds in any given solvent. Once a saturated solution of the compound has been made, further addition of that compound has no effect on the concentration of dissolved solute. The concentrations of the component ions of the compound therefore remain constant and

Reflect the characteristic solubility of the compound in that solvent. The Ksp measures this solubility. For the the ionic compound XAYB,

Ksp = [X]A x [Y]B

Percent solution Is another common way to express concentration. The precise units of percent solution typically depend on the phase of each component. For solids dissolved in liquids, mass percent is usually used:

Mass % = 100% x-masssolute.

Total mass solution

This kind of measurement is sometimes called a mass-mass percent solution because one mass is divided by another. Very dilute concentrations (as in the concentration of a contaminant in drinking water) are sometimes expressed as a special mass percent called Parts per million (ppm) Or Parts per billion (ppb). In these metrics, the mass of the solute is divided by the total mass of the solution, and the resulting fraction is multiplied by 106 (ppm) or by 109 (ppb).

Clearly, it’s important to pay attention to units when working with concentration. Only by observing which units are attached to a measurement can you determine whether you are working with molarity, mass percent, or with mass-mass, mass-volume, or volume-volume percent solution.

Real-life chemists in real-life labs don’t make every solution from scratch. Instead, they make concentrated Stock solutions (starting solutions) and then make Dilutions (solutions in which solvent is added to stock solution) of those stocks as necessary for a given experiment.

To make a dilution, you simply add a small quantity of a concentrated stock solution to an amount of pure solvent. The resulting solution contains the amount of solute originally taken from the stock solution, but disperses that solute throughout a greater volume. So, the final concentration is lower; the final solution is less concentrated and more dilute.

But how do you know how much of the stock solution to use, and how much of the pure solvent to use? It depends on the concentration of the stock and on the concentration and volume of the final solution you want. You can answer these kinds of pressing questions by using the dilution equation, which relates concentration (C) And volume (V) Between initial and final states:

C1 x V1 = C2 x V2

This equation can be used with any units of concentration, provided the same units are used throughout the calculation. Because molarity is such a common way to express concentration, the dilution equation is sometimes expressed in the following way, where M1 and M2 refer to the initial and final molarity, respectively:

M1 x V1 = M2 x V2

Dissolving with Perfection: Ideal Solutions and Colligative Properties

If you’ve read the rest of this chapter, you may consider yourself a recently minted expert in solubility and molarity, ready to write off solutions as another chemistry topic mastered. Don’t. You, as a chemist worth your salt, must be aware of another piece to the puzzle: Colligative properties. Colligative properties are the properties of a solution compared to a

Pure solvent that change as a function of the number of solute particles in solution, regardless of what kind of particles. The presence of extra particles in a formerly pure solvent has a significant impact on some of that solvent’s characteristic properties, such as vapor pressure, freezing point, and boiling point.

Understanding ideal solutions

Understanding how solute particles affect the properties of a solution requires you to know first whether you’re dealing with an "ideal solution." An Ideal solution Is one in which properties change proportionally (that is, in a linear way) with the amount of added solute. Thankfully, only ideal solutions are on the AP test!

Two kinds of solutions tend to approach ideal behavior:

Very dilute solutions

Solutions in which solute-solvent interactions are about the same strength as solvent-solvent and solute-solute interactions

Ideal solutions obey Raoult’s law. Raoult’s law states that the vapor pressure over the surface of an ideal solution should be the sum of the vapor pressures of the pure components multi-pled by their mole fraction in the solution. In other words, each solution component should contribute exactly its fair share to the total vapor pressure, no more, no less. For a two-component solution

Ptotal = PA X XA + PB X XB

Where Ptotal is the total vapor pressure over the solution, PA And PB Are the vapor pressures of pure samples of components A and B, and - A and - B are the mole fractions of components A and B in the solution.

Mole fraction Is the ratio of the number of moles of one component in a solution to the QfBER Number of moles of all the components in the solution.

In general, the mole fractions of a two-component solution are expressed as

X A = ——— and XB = ———

At"I-1-T"I B „ i „

N A + nB nA + n B

Where nA is the number of moles of component A (like a solute) and nB is the number of moles of component B (like a solvent).

Raoult’s law makes a prediction: If you add a nonvolatile solute (one that contributes no vapor pressure of its own) to a solvent, the vapor pressure of the resulting solution should be lower than the vapor pressure of the pure solvent. If you’ve got a solution that seems to obey Raoult’s law, then you’ve got a solution for which you can make useful predictions about colligative properties.

Using molality to predict colligative properties

To correctly account for the effects of solute particles on some colligative properties, you need a new way to measure solution concentration: Molality. No, that’s not a typo. Molality is different from molarity.

Like the difference in their names, the difference between molarity and molality is subtle. Whereas molarity measures the moles of solute per liter of solution, molality measures the Moles of solute particles per kilogram of solvent:

,, , w / \ moles solute particles

Molality (M ) = ——–

V ‘ kilogram solvent

Notice that the numerator of the fraction for calculating molality includes "solute particles" and not just "solute." What’s the difference? When one mole of the ionic compound NaCl dissolves into one liter of aqueous solution, it produces 1 molar sodium chloride, 1M NaCl(aq). But when NaCl dissolves, it becomes one mole of Na+ cation and one mole of Cl – anion — two moles of solute particles. So, when one mole of NaCl dissolves into one kilogram of water, it produces 2 molal sodium chloride, 2m NaCl(aq).

Calculating molality is no more or less difficult than calculating molarity, so you may be asking yourself, "Why all the fuss?" Is it even worth adding another quantity and another variable to memorize? Yes! Although molarity is exceptionally convenient for calculating concentrations and working out how to make dilutions in the most efficient way, molality is useful for predicting important colligative properties, including the boiling point of a solution. When solute particles are added to a solvent, the boiling point of the resulting solution tends to increase relative to the boiling point of the pure solvent. This phenomenon is called Boiling point elevation. The more solute you add, the greater you elevate the boiling point.

Boiling point elevation is directly proportional to the molality of a solution, but chemists have found that some solvents are more susceptible to this change than others. The formula for the change in the boiling point (TB) of a solution therefore contains a proportionality constant, Kb (not to be confused with an equilibrium constant!). The Kb is determined by experiment and in practice you usually look it up in a table such as Table 11-1. The formula for the boiling point elevation is

A7b = Kb x M

Note the use of the Greek letter delta (A) in the formula to indicate that you are calculating a Change In boiling point, not the boiling point itself. You’ll need to add this number to the boiling point of the pure solvent to get the boiling point of the solution. The units of KB are given in degrees Celsius per molality (°C m"1).

Boiling point elevations are a result of the attraction between solvent and solute particles in a solution. Adding solute particles increases these intermolecular attractions because there are more particles around to attract one another. Solvent particles must therefore achieve a greater kinetic energy to overcome this extra attractive force and boil off the surface. Greater kinetic energy means a higher temperature, and therefore a higher boiling point. An alternative explanation is that there are simply fewer solvent molecules on the surface to escape as some surface locations are occupied by solute particles.

The second of the important colligative properties you can calculate by using molality is the freezing point (TF) of a solution. When solute particles are added to a solvent, the freezing point of the solution tends to decrease relative to that of the pure solvent. This phenomenon is called Freezing point depression. The more solute you add, the more you decrease the freezing point. This is the reason, for example, that you sprinkle salt on icy sidewalks. The salt mixes with the ice and lowers its freezing point. If this new freezing point is lower than the outside temperature, the ice melts, eliminating the spectacular wipeouts so common on salt-free sidewalks. The colder it is outside, the more salt is needed to melt the ice and lower the freezing point to below the ambient temperature.

Like boiling point elevation, freezing point depression is directly proportional to the molality of the solution. So, the formula for freezing point depression contains a constant of proportionality, KF, that depends on the solvent in question. The formula for freezing point depression is

Tf = Kf x M

To calculate the new freezing point of a compound, you must Subtract The change in freezing point from the freezing point of the pure solvent. Table 11-2 lists several common KF values.

Freezing point depressions are the result of solute particles interrupting the crystalline order of a frozen solid. In order to reach a solid, frozen state, the solution must achieve an even lower average kinetic energy. Lower kinetic energy means lower temperature, and therefore a lower freezing point.

In summary, adding solute particles to a solvent increases the stability of the liquid phase. Boiling point elevation and freezing point depression mean that greater changes in energy are required to shift the solution out of liquid phase into solid or vapor phase. This effect can be seen in a phase diagram that overlays the behavior of a solution with that of the pure solvent, as shown in Figure 11-8.

By carefully measuring boiling point elevations and freezing point depressions, you can determine the molar mass of a mystery compound that is added to a known quantity of solvent. To pull off this trick you must know the total mass of the pile of mystery solute that has been dissolved, the mass of solvent into which the compound was dissolved, and either the change in the freezing or boiling point or the new freezing or boiling point itself. From this information you then follow this set of simple steps to determine the molecular mass:

1. If you know the boiling point of the solution, calculate the ATJ, By subtracting the boiling point of the pure solvent from that value. If you know the freezing point of the solution, subtract the freezing point of the pure solvent to that value to get the ATF.

2. Look up the Kb Or Kf Of the solvent (in a place like Table 11-1 or 11-2).

3. Solve for the molality of the solution using the equation for A7B Or ATF.

4. Calculate the number of moles of solute in the solution by multiplying the molality calculated in Step 3 by the mass of solvent, in kilograms.

5. Divide the mass of the pile of mystery solute that has been dissolved by the number of moles calculated in Step 4. The result of this calculation is the molar mass (number of grams per mole) of the mystery compound. From this value, you can often make an educated guess about the identity of the compound.

Osmotic pressure Is another property of a solution that depends on the number of solute particles. To understand osmotic pressure, it helps to understand Osmosis, The movement of solvent molecules through a semipermeable barrier (one which lets some things pass, but not others) from areas of low solute concentration to areas of high solute concentration. Osmosis is a result of the more general process of Diffusion, The net movement of a substance from where it is more concentrated to where it is less concentrated. In solutions with higher solute concentration, solvent is less concentrated. In solutions with lower solute concentration, solvent is more concentrated. So, given the opportunity, solvent diffuses toward solutions with higher solute concentration.

If solvent and a solution made with that solvent are separated by a semipermeable membrane in a setup like the one shown in Figure 11-9, solvent molecules will move by osmosis into the solute-containing chamber. This movement of solute will alter the surface height within each chamber until the difference in height causes enough pressure to prevent a further net movement of solvent into the solute-containing chamber. This pressure difference is equal to the osmotic pressure, n, of the solution. Osmotic pressure depends on the moles of solute particles per unit volume of solution; that is, in contrast to boiling points and freezing points, osmotic pressure depends on molarity, not molality:

N = I N Soiae I Rt = MRT

{ VSoUion J

Where Nsolute Is the moles of solute particles, Vsolutoon Is the volume of solution, M Is molarity of particles, R Is the gas constant and T Is temperature.

■ Semipermeable membrane

Pressure

Figure 11-9:

Osmosis across a semipermeable membrane.

O O O

O o o

Solvent

O

O

O °Q

©o Qo

O ___.

Osmosis

Solute

Osmosis and osmotic pressure are important in biology because cell membranes are semi-permeable, allowing transport of solvent water molecules while restricting transport of many solutes. So, if a cell finds itself in a Hypertonic Environment (one with higher solute concentration than that of the cell), osmosis may cause the cell to shrivel as water diffuses outward. If the cell finds itself in a Hypotonic Environment (one with lower solute concentration than that of the cell), osmosis may cause the cell to swell (or explode!) as water diffuses inward. So, even if you yawn at osmotic pressure, the cells that compose you consider it a life-or-death kind of thing.

Dissolving with Reality: Nonideal Solutions

Many solutions come very close to ideal behavior. But some solutions deviate pretty significantly from ideal behavior. And for sensitive applications, sometimes even very close isn’t close enough. Situations like these force us to deal with Nonideal solutions, Ones that don’t obey Raoult’s law or Henry’s law, and whose properties aren’t proportional to the amount of added solute.

Nonideal solutions occur when solute concentrations are very high and/or when solute-solvent interactions are significantly more attractive or repulsive than solute-solute interactions and solvent-solvent interactions.

When solute-solvent interactions are especially attractive, the solute is effectively more dissolved (that is, more intermixed) than an ideal solute. The vapor pressure of the solvent is lower than predicted by Raoult’s law. The partial pressure of a dilute solute is higher than that predicted by Henry’s law.

When solute-solvent interactions are especially repulsive, the solute is effectively less intermixed than an ideal solute. The vapor pressure of the solution is higher than predicted by Raoult’s law. The partial pressure of a dilute solute is lower than that predicted by Henry’s law.

To account for nonideal behavior, chemists use the concept of Activity, The effective concentration of a component in solution. When the activity of a component differs significantly from its formal concentration, chemists often use an experimentally determined Activity coefficient In their calculations. The concentration of the nonideal component (its molarity, molality or mole fraction) is multiplied by an activity coefficient, y, to produce an effective concentration for the calculation:

Activity = yx Concentration

In This Chapter

^ Summarizing what you need to remember

^ Testing your knowledge with some practice questions

^ Finding explanations for the answers

Chapter 11 describes the different kinds of interactions between particles within different phases of matter and how changes in temperature and pressure can cause matter to move between phases. Chapter 11 also explores solutions — what they are, how to measure their concentration, and how their behavior changes with added solute. Just to be certain you remember the key points of Chapter 11, we’ve included those important concepts for you to review in this chapter before you take a stab at answering questions about solids, liquids, and solutions.

Getting a Grip on What Not to Forget

Here is a collection of the most important points to remember for the AP exam about how particles behave in different states of matter, how samples move between states, and how solute particles interact with solvent within solutions.

Kinetic theory

Just as kinetic theory can explain gas behavior, the following list shows how kinetic theory can also help explain the properties and behavior of the Condensed states — liquids and solids, in case you haven’t read Chapter 11:

Particles within liquids are close together, but can slide past one another (that is, Translate), So that liquids are fluid, meaning liquids have Short-range order.

Particles within a solid cannot translate past one another, but vibrate about an average position. So solids have Long-range order.

In condensed states, interparticle attractions and repulsions are critical in determining the properties of the substance.

Solid states

Solid states include several categories with distinct characteristics:

The particles within Ionic solids Are strongly attracted to one another, and these solids have high melting points. Lattice energy Measures the strength of the ion-ion interactions within these solids.

Molecular solids Have weaker attractions between particles and typically have lower melting points.

Covalent (network) solids Are bound together by multiple covalent bonds and tend to be exceptionally strong.

I Metallic solids Consist of a lattice of positively charged atoms within a sea of mobile electrons coming from valence shells, which accounts for the high electrical conductivity of metals.

I Particles within Crystalline solids Pack into highly ordered arrangements of a repeating Unit cell And tend to have well-defined melting temperatures. Particles within Amorphous solids Exhibit far less long-range order and tend to melt over broad temperature ranges.

Condensed states

Within condensed states, a collection of "weak" forces (that is generally, but not always, weaker than covalent or ionic bonds) can play important roles:

I Hydrogen bonds Can occur when two electronegative atoms (like oxygen, nitrogen, or fluorine) essentially "share" an electropositive hydrogen atom. Formally, the hydrogen is covalently bound to one of the electronegative atoms.

Dipole-dipole Forces can occur between the partially charged parts of polar molecules. Opposite partial charges attract and same-sign partial charges repel. Dipoles can also interact with ions according the the same basic concept.

I London dispersion forces Are attractive forces that are generally weaker than hydrogen bonds, dipole-dipole, and ion-dipole forces at long distances. London forces occur between Induced dipoles, Partial charges that flicker into and out of existence as electron clouds interact with one another.

Phase diagrams

Phase diagrams Reveal the effects of temperature and pressure on the Phase (physical state) of a substance. The following list describes how to interpret the diagrams:

I A field of the phase diagram represents boundaries between phases. Crossing a line indicates a Phase change, Such as melting, freezing, boiling, condensing, subliming, or desubliming (depositing).

I The Triple point Represents a substance-specific combination of temperature and pressure at which the solid, liquid, and gas phases of a substance coexist.

At very high temperatures and/or very low pressures, gases can move into Plasma phase, In which ionized particles intermingle with free electrons.

I At temperatures and pressures above a substance-specific condition called the Critical point, The distinction between liquid and gas phase disappears. A substance in this condition is called a Supercritical fluid.

I Heating curves Show how the temperature of a substance varies as heat is added to it. These curves tend to exhibit a staircase-pattern in which temperature increases as heat is added at a constant rate, and then levels off during phase changes because heat must be added simply to shift the substance from one phase to another.

Solutions

Solutions Are mixtures in which different components are completely and evenly mixed down to the level of individual molecules, ions, or atoms.

The major component of a solution is the Solvent. Minor components are Solutes.

I Substances Dissolve If and when solvent-solute attractions dominate over solvent-solvent and solute-solute attractions.

I Saturated Solutions are those that hold the maximum amount of a dissolved solute. Unsaturated Solutions can accommodate further solute additions.

I The Solubility Of a solute is the concentration of the substance required to produce a saturated solution. So, substances with large solubility can be dissolved to a large degree, while smaller amounts of substances with low solubility will dissolve.

I Solubility can vary in the following ways, depending on temperature, pressure, and the physical/chemical properties (especially Polarity) Of the solute and solvent:

• Increasing temperature increases the solubility of most (but not all) solid solutes in liquid solutions.

• Increasing temperature decreases the solubility of gases in liquid solutions.

• Increasing pressure increases the solubility of gases in liquid solutions, as expressed by Henry’s law: S1 / P1 = S2 / P2.

• Polar solutes dissolve best in polar solvents. Nonpolar solutes dissolve best in nonpolar solvents. In other words, "like dissolves like."

Ideal solutions have some important points to remember:

Ideal solutions obey Raoult’s law. This law states that in the vapor over a liquid solution, each solution component should have a partial pressure in proportion to its mole fraction within the solution. Raoult’s law implies that adding a solute to a solvent should reduce the partial pressure of the solvent within the vapor over the solution.

I In Ideal solutions (those which are dilute and in which all intermolecular forces are about the same strength), adding solute particles has predictable effects on Colligative properties Like boiling point, freezing point, and osmotic pressure. Most AP questions involve only nonvolatile solutes — those that have essentially no vapor pressure of their own to add to that of the solvent. Thus only the solvent properties are affected.

• Adding solute particles raises the boiling point of a solvent in a phenomenon called Boiling point elevation: ATb = Kb X m.

• Adding solute particles lowers the freezing point of a solvent in a phenomenon called Freezing point depression: ATf = Kf X m.

• Adding solute particles increases the Osmotic pressure, N, of a solution.

Many real-life solutions are nonideal solutions, especially at high concentrations or when one kind of intermolecular force dominates over others in solution. (Fortunately, AP examinations never ask about these.) We give you examples of some nonideal solution effects in the following list:

I Strong solute-solvent interactions lead to vapor pressures lower than those predicted by Raoult’s law.

I Weak solute-solvent interactions lead to vapor pressures higher than those predicted by Raoult’s law.

I The activity coefficient, y, is used to correct for nonideal solution effects on solute concentration: Activity = yx Concentration.

More concentrated solutions can be diluted with solvent to yield less-concentrated solutions, as expressed by the Dilution equation: C1 x V1 = C2 x V2.

Reporting the concentration of a solute

Different methods for reporting the concentration of a solute include molarity, molality, percent solution, mole fraction, and partial pressure. The following list reminds you how those methods are expressed:

Ii* Molarity: M = moles solute / liters solution Ii* Molality: M = moles solute particles / kilograms solution

I Percent solution Can refer to mass percent, volume percent, or mass/volume percent:

• Mass % = 100% x (mass solute / total mass solution)

• Volume % = 100% x (volume solute / total volume solution)

• Mass/Volume % = 100% x (grams solute / 100 milliliters solution) I Mole fraction: % = moles component / total moles of all components I Partial pressure Of A, PA = mole fraction of A x total pressure

Testing Your Knowledge

No matter how we summarize it, clearly you need to know a lot about solids, liquids, gases, and solutions. Test your mastery of the material in Chapter 11 by giving these questions a try.

Questions 1 through 5 refer to the phase diagram below.

Temperature

1. Which points correspond to a melting/freezing equilibrium?

(A) 1 and 5

(B) 1 and 3

(C) 2 and 4

(D) 6 and 7

(E) 7 and 8

2. Which point(s) correspond(s) to homogenous phase(s)?

3. Which point corresponds to a sublimation/deposition equilibrium?

(A) 1

(B) 3

(C) 5

(D) 6

(E) 8

4. Which point corresponds to the critical point?

(A) 1

(B) 2

(C) 5

(D) 7

(E) 9

5. Which point corresponds to the triple point?

(A) 1

(B) 2

(C) 5

(D) 7

(E) 9

6. How much water must be added to 150mL of 0.500M KCl to make 0.150M KCl?

(A) 45mL

(B) 150.mL

(C) 350.mL

(D) 500.mL

(E) 650.mL

7. The Ksp Of lead (II) chloride is 1.7 x 10-5. What is the molar concentration of a chloride ion in 1.0L of a saturated PbCl2 solution?

(A) 5.7 x 10-6

(B) 1.1 x 10-5

(C) 1.6 x 10-2

(D) 2.6 x 10-2

(E) 3.2 x 10-2

8. You can prepare 0.75 molal NaCl by dissolving 15g NaCl in what amount of water?

(A) 0.40kg

(B) 0.34kg

(C) 0.27kg

(D) 0.20kg

(E) 0.26kg

9. If 1.6 x 10-3 moles of an ideal gas are dissolved in 2L of a saturated aqueous solution at 1atm pressure, what will be the molar concentration of the gas under 2.5atm pressure?

(A) 1.6 x 10-3

(B) 0.8 x 10-3

(C) 4.0 x 10-3

(D) 2.0 x 10-3

(E) 3.2 x 10-3

Questions 10 through 14 refer to the following set of choices:

(A) Particles vibrate about average positions.

(B) Particles are ordered and occur within a sea of mobile electrons.

(C) Particles are ionized, disordered and highly energetic.

(D) Particles diffuse rapidly and can dissolve many solutes.

(E) Particles do not translate but lack long-range order.

10. Supercritical fluid

11. Metallic solid

12. Amorphous solid

13. Plasma

14. Crystalline solid

15. One mole of glucose, C6H12O6, dissolved in 1.00kg water results in a solution that boils at 100.52 °C and freezes at -1.86 °C. If 300. grams of ribose, C5H10O5, are dissolved in 4.00kg water, what will be the boiling and freezing points of the resulting solution?

(A) 100.26 °C, -0.93 °C

(B) 100.13 °C, -0.47 °C

(C) 100.52 °C, -1.86 °C

(D) 101.04 °C, -3.72 °C

(E) 101.56 °C, -5.58 °C

17. Ethanol, CH3CH2OH, engages in which of the following types of intermolecular interactions?

I. Hydrogen bonding

II. Dipole-dipole interactions

III. London forces

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) I, II, and III

Questions 18 through 22 refer to the following diagram and the accompanying set of choices with regard to the heat being transferred:

Heat Added

(A) Liquid phase

(B) Increase in average kinetic energy of particles

(C) Decrease in average kinetic energy of particles

(D) Heat of fusion

(E) Heat of vaporization

18. Segment 2 corresponds to this phase or phase change.

19. Moving left to right on segment 1 represents this.

20. Moving right to left on segment 5 represents this.

21. Segment 4 corresponds to this phase or phase change.

22. Segment 3 corresponds to this phase or phase change..

Checking Your Work

Dissolve any lingering uncertainties you have about your answers. Check them here. The following diagram refers to items explained in the answers to questions 1 through 5:

Supercritical fluid

Liquid

Critical point

Gas

Tempe rature

1. (B). The melting/freezing equilibrium occurs at the boundary line between solid and liquid phases. Although different substances have differently shaped phase diagrams, it is typically the case that low temperature-high pressure conditions favor solid phase; high temperature-low pressure conditions favor gas phase; and liquid phases occur at intermediate temperatures and pressures.

2. (B). Homogenous phases are those that are uniform throughout and not in equilibrium between multiple phases. So, on a phase diagram, homogenous phases are found in the open spaces between phase boundary lines.

3. (E). Sublimation is direct movement from solid to gas phase, and deposition is the reverse of that process. So, a sublimation/deposition equilibrium occurs at the boundary line between solid and gas phases.

4. (C). The critical point for a substance is the unque combination of pressure and temperature beyond which liquid and gas phases cease to be distinct. Any combination of temperature and pressure that is simultaneously above both the critical temperature and critical pressure causes the substance to become a supercritical fluid.

5. (D). The triple point for a substance is a unique combination of temperature and pressure at which all three major phases (solid, liquid, and gas) are in simultaneous equilibrium. The triple point occurs at the convergence of the three phase boundary lines.

6. (C). Attack this problem by using the dilution equation: C1 x V1 = C2 X V2.

(0.500M) x (150mL) = (0.150M) x V2

Solving for V2 gives you 500mL. So, the final solution should have a volume of 500mL. Because the initial solution had a volume of 150mL, you must add 350mL of water to achieve the desired final volume.

7. (E). Solving this question requires you to understand the dissolution reaction of lead (II) chloride and the definition of the solubility product constant, Ksp.

PbCl2(s) + H2O(Q Pb2+(aq) + 2Cl-(ag)

Ksp = 1.7 x 10-5 = [Pb2+][Cl-]2

Notice from the dissolution reaction equation that for every mole of PbCl2 that dissolves, you get one mole of Pb2+ cation and Two Moles of Cl – anions. Using this fact, we can substitute into the equation for the Ksp:

1.7 x 10-5 = [x][2x]2

1.7 x 10-5 = 4×3

Solving for x, you get 1.6 x 10-2. However, the concentration of Cl – is 2x, so the answer is 3.2 x 10-2.

8. (B). To answer this question, you must know the definition of molality, M = (moles solute) / (kilograms solvent). Next, you must find the moles of NaCl solute by converting from the given mass of 15 grams. Because the molar mass of NaCl is 58.45 g mol-1, you have 0.257mol NaCl. Next, substitute into the definition of molality:

0.75m = (0.257mol NaCl) / (X kilograms water)

Solving for X, you get 0.34kg water.

9. (D). This question requires you to apply a result of Henry’s law, stating that the solubility of an ideal gas in a liquid solvent is directly proportional to the pressure: S1 / P1= S2 / P2.

Before substituting into the proportion, however, you should calculate the initial molar solubility:

Molarity = (1.6 x 10-3mol) / (2L) = 0.80 x 10-3 M Substituting into the proportion, you get (0.80 x 10-3 M) / (1atm) = S2 / (2.5atm) Solving for S2 gives you 2.0 x 10-3 M.

10. (D). Supercritical fluids occur in high temperature-high pressure conditions beyond the thermodynamic critical point of a substance. Under these conditions, the substance has properties of both a gas (high diffusivity) and a liquid (ability to dissolve solute).

11. (B). The atoms of a metallic solid are packed within an ordered lattice, but are so electropositive that electrons move freely about the lattice, which accounts for the high electrical conductivity of metals.

12. (E). In an amorphous solid, particles — often polymers — are packed tightly enough that the substance isn’t fluid, but lack the extreme order and structural regularity of a crystalline solid.

13. (C). Provided enough energy, the particles of a gas (often, a superheated gas) can ionize to create plasma, a state of matter that is diffuse and fluid like gas, but has unusual properties due to its ionic nature.

14. (A). Within a crystalline solid, particles are tightly packed within highly ordered, regularly repeating structural units called unit cells. So little translational freedom is available to the particles within a crystalline solid that all they can usually do is to vibrate in place. Such is the price of perfection.

15. (A). This question tests your knowledge of two colligative properties, boiling point elevation (ATb) and freezing point depression, (A7f). You are required to know that colligative properties, which apply to ideal solutions, depend solely on the number of solute particles in solution, and not on the physical or chemical properties of those particles. The number of solute particles is measured by molality, M. The effects of added solute on boiling and freezing points depend on the solvent. By giving you data on the boiling point and freezing point of a

1 M Glucose solution, the question essentuially gives you the boiling point and freezing point proportionality constants, Kb = 0.52 °C m"1 and Kf = -1.86 °C m"1. Next, you must determine the molality of the ribose solution. To do so, you must calculate the molar mass of ribose, 150 g mol-1. Because 300g ribose are dissolved, there are 2.0 moles ribose in the solution.

Molality = (2.0mol ribose) / (4.0kg solvent) = 0.50M

Next, substitute into the equations for boiling point elevation and freezing point depression:

ATb = (0.52 °C m"1) x (0.50m) = 0.26 °C

A7f = (°1.86 °C m"1) x (0.50m) = -0.93 °C

Adding these quantites to the standard boiling point and freezing point of water gives TB = 100.26 °C and TF = -0.93 °C.

16. (D). This question requires to understand that boiling point, as a colligative property, depends on the number of moles of solute Particles In solution, not on the number of moles of solute compound. For example, one mole of dissolved KCl contributes 2 moles of particles (one mole K+ and one mole Cl-). Taking this factor into account, it is clear that in 1.0M NaNO3, the NaNO3 contributes the fewest particles to solution (one mole Na+ and one mole of the polyatomic ion NO3-), and therefore elevates the boiling point the least.

17. (E). With its hydroxyl functional group, ethanol is quite capable of forming hydrogen bonds, which require a hydrogen covalently bonded to an electronegative atom (like oxygen) and also require a second electronegative atom (like the oxygen of a second ethanol molecule). Hydrogen bonds are themselves a kind of dipole-dipole interaction, employing the strong dipoles set up by the electronegative atoms. Finally, all condensed phase molecules engage in London dispersion interactions. So, ethanol participates in all three kinds of inter-molecular interactions.

18. (D). The heat added within this segment clearly does not go toward rasing the temperature of the substance. Instead, the added heat goes toward rearranging particles at a given temperature from solid phase into liquid phase. We know this as it is the first of the phase changes to be shown (moving left to right on the diagram).The heat required to accomplish this phase change is called the heat of fusion, AHfus.

19. (B). Heat added in this segment clearly goes toward increasing the temperature of the substance. Temperature is a measure of the average kinetic energy of the particles within a sample.

20. (C). Moving from right to left within the diagram corresponds to heat transferred out of the system, and doing so within this segement clearly results in a decrease in the temperature of the substance. Falling temperature corresponds to a decrease in the average kinetic energy of the particles in a system.

21. (E). The heat added within this segment clearly does not go toward raising the temperature of the substance. Instead the added heat goes toward rearranging particles at a given temperature from liquid phase to gas phase (the second phase change shown in the diagram). The heat required to accomplish this phase change is called the heat of vaporization, AHvap.

22. (A). This segment lies beween the plateaus corresponding to fusion (melting) and vaporization (boiling). The phase that sits between melting and boiling is liquid. Note that the average kinetic energy of the particles is increasing during this segment.

In This Chapter

► Keeping up with kinetic theory

► Going through the Gas Laws

► Digging in Dalton’s Law of Partial Pressures

► Checking out diffusion and Graham’s Law

► Encountering ideal and nonideal gases

T first pass, gases may seem to be the most mysterious of the states of matter. Nebulous and wispy, gases easily slip through our fingers. For all their diffuse fluidity, however, gases are actually the best understood of the states. The key to understanding gases is that they all tend to behave in the same ways — physically, if not chemically. For example, gases expand to fill the entire volume of any container in which you put them. Also, gases are easily compressed to fill smaller volumes.

Before taking the AP chemistry exam, you will need to become familiar with a body of equations called the ideal gas laws and should be able to choose the equation appropriate to a particular situation and manipulate it. You will also need to have a solid understanding of the underlying theory that describes the behavior of gases, including kinetic molecular theory and the differences between real and ideal gases. This chapter will familiarize you with all of these concepts, after that you should tackle Chapter 10, which includes questions on gases similar to those which will appear on the actual exam.

Moving and Bouncing: Kinetic Molecular Theory of Gases

Imagine two billiard balls, each glued to either end of a spring. How many different kinds of motion could this contraption undergo? You could twist along the axis of the spring. You could bend the spring or stretch it. You could twirl the whole thing around, or you could throw it through the air. Diatomic molecules have just such a structure and can undergo these same kinds of motions when you supply them with energy. As collections of molecules undergo changes in energy, those collections move through the states of matter — solid, liquid, and gas. Transitions between phases of matter will be described in detail in Chapter 11, while this chapter will lay out the basics of kinetic theory.

*JJIBE*

The basics of kinetic theory

Kinetic theory, the body of ideas that explains the internal workings of gases and the phenomena caused by them, first made a name for itself when scientists attempted to explain and predict the properties of gases. Kinetic theory also explains the behavior of solids and liquids, and Chapter 11 will cover how it applies to each of those phases. Kinetic theory as applied to gases is particularly concerned with how the properties of a gas change with varying temperature and pressure. The underlying idea behind kinetic theory is the concept of kinetic energy, or the energy of motion. The particles of matter within a gas (atoms or molecules) undergo vigorous motion as a result of the kinetic energy within them.

Gas particles have a lot of kinetic energy and constantly zip about, colliding with one another or with other objects. This is a complicated picture, but scientists simplify things by imagining an ideal gas where

Particles move Randomly.

The only type of motion is Translation (moving from place to place, as opposed to twisting, vibrating, and spinning).

When particles collide, the collisions are Elastic (perfectly bouncy, with no loss of energy).

Gas particles Neither attract nor repel One another. Gases that actually behave in this simplified way are called Ideal.

The model of ideal gases explains why gas pressure increases with increased temperature. By heating a gas, you add kinetic energy to the particles. As a result, the particles collide with greater force upon other objects, so those objects experience greater pressure. In other words, as temperature increases, the average kinetic energy of gas particles increases and pressure increases proportionally as well.

Statistics in kinetic theory

The study of all matter, and gases in particular, is a study of statistics. Gas properties are measured in averages rather than absolutes. Note that above we spoke of temperature as being proportional to the average kinetic energy of the gas particles, not the kinetic energy of an individual gas particle. You could spend your whole life searching for a collection of gas molecules in which each individual particle is moving at the same speed as the next. Because gas particles collide and transfer energy between one another at random, neighboring gas particles generally experience different numbers of collisions and end up with different kinetic energies. If you were to measure the velocities of a whole slew of gas molecules, you would find that although they will have a distribution of varying velocities, they will be clustered around an average value. Remember that a liter of gas at STP contains 6.02 x 1023 gas particles, which is a lot to average!

Examine the two velocity distributions in Figure 9-1. Both show a similar bell-shaped curve (called a Maxwell-Boltzman distribution). Note that the probability of finding a gas particle at a certain velocity drops off precipitously as that velocity gets farther from the average velocity peak. Although both of the distributions in Figure 9-1 are Gaussians, there is one key difference between them: The figure on the left represents the velocity distribution of gas particles at a low temperature, and the figure on the right shows a similar distribution at a higher temperature.

Note the features of the low-temperature distribution: Ji* The peak of the velocity distribution is at a lower velocity.

Ji* The velocity distribution shows a pronounced peak with a relatively narrow range of velocities surrounding it.

Note the features of the high-temperature distribution:

Ji* The peak of the velocity distribution is at a higher velocity.

Ji* The velocity distribution shows a wider, flattened curve with a large range of velocities.

Figure 9-1:

Velocity distributions for gases at high and low temperatures.

Low Temperature

-.^ High Temperature

Speed

Particle velocities translate into average kinetic energies through the equation: KE = 34 mv2

This is the kinetic energy of an individual gas molecule, where m is the mass of the molecule and v is the velocity. To calculate an average kinetic energy, we therefore need an expression for the average velocity.

/3RT

U = .1—R-r-

V M

In this expression U Is the average velocity of a collection of particles, and is alternately written as urms (the root-mean-square velocity), R Is the ideal gas constant 8.314 J K"1 mol"1, T Is temperature, and M Is the molar mass. Although we will not derive this expression here, take a minute to look at it and assure yourself that it makes sense. The expression has temperature in the numerator of the velocity calculation, which means that as temperature increases, average velocity should as well. This is consistent with kinetic theory. Molar mass, however, appears in the denominator of the equation, which means that as molar mass increases, average velocity decreases. This too makes sense; kinetic energy depends on both mass and velocity, so heavier particles move more slowly than lighter particles at the same kinetic energy. You will also often see this expression written as the following, which is simply a variation of the equation above and will yield the same result:

/3kT U = A-

V M

Here, Boltzmann’s constant K (1.38 x 10"23 J K"1) replaces the ideal gas constant R, And M, The mass of an individual gas particle, replaces molar mass M.

The final equation that you may consider useful when calculating the kinetic energy of a system of molecules is the following expression for the kinetic energy Per mole Of a gas, which can be derived by plugging the first expression you were given for the average velocity of gas particles into the general equation for kinetic energy and solving for kinetic energy per mole, using this:

KE = KRT

Remember to always use R= 8.314 J K"1 mol"1 for these kinetic energy problems. If you use the wrong units for the gas constant, you will lose points on the AP exam.

Aspiring to Gassy Perfection: Ideal Gas Behavior

Like all ideals (the ideal job, the ideal mate, and so on), ideal gases are entirely fictional. All gas particles occupy some volume. All gas particles have some degree of interparticle attraction or repulsion. No collision of gas particles is perfectly elastic. But lack of perfection is no reason to remain unemployed or lonely. Neither is it a reason to abandon kinetic molecular theory of ideal gases. In this chapter, you will be introduced to a wide variety of applications of kinetic theory, which come in the form of the so-called "gas laws."

Relationships between four factors: pressure, volume, temperature, and number of particles are the domain of the gas laws. We take a look at the gas laws in the sections that follow.

Boyle’s Law

The first of these relationships to have been formulated into a law is that between pressure and volume. Robert Boyle, an Irish gentleman regarded by some as the first chemist (or "chymist," as his friends might have said), is typically given credit for noticing that gas pressure and volume have an inverse relationship:

Volume = Constant x (1/Pressure)

This statement is true when the other two factors, temperature and number of particles, are fixed. Another way to express the same idea is to say that although pressure and volume may change, they do so in such a way that their product remains constant. So, as a gas undergoes change in pressure (P) And volume (V) Between two states, the following is true:

P1 x V1 = P2 x V2

The relationship makes good sense in light of kinetic molecular theory. At a given temperature and number of particles, more collisions will occur at smaller volumes. These increased collisions produce greater pressure. And vice versa. Boyle had some dubious ideas about alchemy, among other things, but he really struck gold with the pressure-volume relationship in gases.

Charles’s Law

*JJIBE*

Lest the Irish have all the gassy fun, the French contributed a gas law of their own. History attributes this law to French chemist Jacques Charles. Charles discovered a direct, linear relationship between the volume and the temperature of a gas:

Volume = Constant x Temperature

This statement is true when the other two factors, pressure and number of particles, are fixed. Another way to express the same idea is to say that although temperature and volume may change, they do so in such a way that their ratio remains constant. So, as a gas undergoes change in temperature (T) And volume (V) Between two states, the following is true:

Not to be outdone by the French, another Irish scientist took Charles’s observations and ran with them. William Thomson, eventually to be known as Lord Kelvin, took stock of all the data available in his mid-nineteenth century heyday and noticed a couple of things:

First, plotting the volume of a gas versus its temperature always produced a straight line.

Second, extending these various lines caused them all to converge at a single point, corresponding to a single temperature at zero volume. This temperature — though not directly accessible in experiments — was about "273 degrees Celsius. Kelvin took the opportunity to enshrine himself in the annals of scientific history by declaring that temperature as Absolute zero, The lowest temperature possible.

This declaration had at least two immediate benefits. First, it happened to be correct. Second, it allowed Kelvin to create the Kelvin temperature scale, with absolute zero as the Official Zero. Using the Kelvin scale (where °C = K + 273), everything makes a whole lot more sense. For example, doubling the Kelvin temperature of a gas doubles the volume of that gas. When you work with any gas law involving temperatures, converting Celsius temperatures to Kelvin is crucial.

The Combined and Ideal Gas Laws

Boyle’s and Charles’s laws are convenient if you happen to find yourself in situations where only two factors change at a time. However, the universe is rarely so well behaved. What if pressure, temperature, and volume all change at the same time? Is aspirin and a nap the only solution? No. Enter the Combined Gas Law:

P1 x V = P2 x V2 T T2

1 2

Of course, the real universe can fight back by changing another variable. In the real universe, for example, tires spring leaks. In such a situation, gas particles escape the confines of the tire. This escape decreases the number of particles, N, Within the tire. Cranky, tire-iron wielding motorists on the side of the road will attest that decreasing N Decreases volume. This relationship is sometimes expressed as Avogadro’s Law:

Volume = Constant x Number of particles

Combining Avogadro’s Law with the Combined Gas Law produces the wonderfully comprehensive relationship:

P1xV1 P2xV2

N1 x T N2 x T2

The final word on ideal gas behavior summarizes all four variables (pressure, temperature, volume, and number of particles) in one easy-to-use equation called the Ideal Gas Law:

PV = nRT

Here, R Is the gas constant, the one quantity of the equation that can’t change. Of course, the exact identity of this constant depends on the units you are using for pressure, temperature, and volume. A very common form of the gas constant as used by chemists is R = 0.08206L atm K"1 mol"1 (which can also be expressed as 62.4 L torr mol"1 K"1). Alternately, you may encounter R = 8.314L kPa K"1 mol"1.

Dalton’s Law of Partial Pressures

Gases mix. They do so better than liquids and infinitely better than solids. So, what’s the relationship between the total pressure of a gaseous mixture and the pressure contributions of the individual gases? Here is a satisfyingly simple answer: Each individual gas within the mixture contributes a partial pressure, and adding the partial pressures yields the total pressure. Fortunately, because the gases are ideal, the mass of the gas particles does not influence partial pressure. The number of molecules is the only factor that affects partial pressure. This relationship is summarized by Dalton’s Law of Partial Pressures, For a mixture of a number of individual gases:

PTotal = P1 + P2 + P3 + . . . + PN

This relationship makes sense if you think about pressure in terms of kinetic molecular theory. Adding a gaseous sample into a volume that already contains other gases increases the number of particles in that volume. Because pressure depends on the number of particles colliding with the container walls, increasing the number of particles increases the pressure proportionally. Remember, this assumes that the individual gas molecules are behaving ideally.

You can also calculate the partial pressure of an individual gas A in a mixture of gases using the equation:

PA = Ptotal x XA

Here XA represents the mole fraction of the gas in question, or the number of moles of that gas divided by the total number of gas moles in the mixture.

Graham’s Law and diffusion

"Wake up and smell the coffee." This command is usually issued in a scornful tone, but most people who have awakened to the smell of coffee remember the event fondly. The morning gift of coffee aroma is made possible by a phenomenon called Diffusion. Diffusion is the movement of a substance from an area of higher concentration to an area of lower concentration. Diffusion occurs spontaneously, on its own. Diffusion leads to mixing, eventually producing a homogenous mixture in which the concentration of any gaseous component is equal throughout an entire volume. Of course, that state of complete diffusion is an equilibrium state; achieving equilibrium can take time.

4

Different gases diffuse at different rates, depending on their molar masses (see Chapter 7 for details on molar masses). The rates at which two gases diffuse can be compared using Graham’s Law. Graham’s Law also applies to Effusion, The process in which gas molecules flow through a small hole in a container. Whether gases diffuse or effuse, they do so at a rate inversely proportional to the square root of their molar mass. In other words, more massive gas molecules diffuse and effuse more slowly than less massive gas molecules. So, for gases A and B

RateA RateB

.y/molar massB molar mass A

Getting Real: Nonideal Gas Behavior

«$JAB^ Ideal gas equations are idealizations based on the oversimplified assumptions of ideal gas theory. Real gases, however, do not obey the ideal gas laws. At certain temperatures and pressures, they provide good approximations, but there are situations when a more sophisticated (and therefore more complicated) equation is needed.

Chemists use a rearranged version of the ideal gas law to determine whether or not they can use it.

PV n RT

For an ideal gas, N Should equal one, so a gas for which the ideal gas law is a good approximation should have an N Value close to one. At high pressures and at low temperatures, this becomes increasingly unlikely and a new equation is needed.

Assuming that a gas is ideal means assuming that its particles occupy no space and do not attract one another, but real gas particles defy both of those postulates: They do occupy space and they do attract one another. At high pressures, this fact becomes increasingly difficult to ignore because the space between gas particles becomes smaller and smaller and the assumption is only valid when the space between gas molecules is much greater than the size of an individual gas molecule. At high temperatures, the internal energy of a gas molecule is great enough to vastly outweigh the attraction to neighboring molecules, but at low temperatures, hence low kinetic energy, the effect of molecular attraction becomes increasingly significant. In these situations it is necessary to add in a correction for the volume of molecules and another for intermolecular attractions. These corrections yield a modified version of the ideal gas law called the van der Waals equation, which is given on the AP exam, so there is no need to memorize it!

This equation should make it clear why chemists prefer to use the ideal gas law to minimize necessary computations. Two new constants, called the van der Waals constants, appear in this equation. The constant A Is a measurement of how strongly the gas molecules attract one another and has units of L2atm mol2. The constant B Is a measurement of the volume occupied by a mole of gas molecules and has units of L mol. These constants vary as the identity of the gas in question varies. Larger and more complex molecules generally have larger A And B Values because of their greater size and greater propensity to experience inter-molecular forces, or interactions between molecules.

In This Chapter

^ Remembering the important stuff

^ Having a gas with some practice questions

^ Going through answers with explanations

■ Mye Blew through the gas laws and kinetic theory in Chapter 9, so review this condensed ▼ ▼ list of key concepts. After you think you’ve got these concepts under control, try tackling the AP Chemistry exam-style questions later in this chapter. Make sure to attempt the problems using only your cheat sheet as a reference in the same way you would use your list of formulas and constants on the real AP exam.

Doing a Quick Review

Here is a brief outline of the concepts presented in Chapter 9. Review it before attempting the practice questions and see Chapter 9 for the details of anything you’re still a little rusty on:

Kinetic theory states that as the temperature of a gas increases, so do the kinetic energies and velocities of its constituent particles.

*»»T Ideal gases are those for which

• Particle motions are random.

• Particles undergo only translational motion and do not vibrate, spin, or twist.

• Collisions between particles are elastic, meaning that no kinetic energy is transformed.

• Neighboring gas particles do not exert forces (attraction or repulsion) on one another.

The average kinetic energy of a gas particle is KE = KMv2, where KE is kinetic energy, m is mass, and v is velocity.

Average particle velocity can be expressed as

I3RT u = J—Z-z—

V M

Or as

J3kT U = 4/-

V M

Where U Is the average velocity, R Is the ideal gas constant, T Is temperature, M Is the molar mass, K Is Boltzmann’s constant, and M Is the mass of an individual gas particle.

Ii The average kinetic energy per mole of a gas is KE = KRT, where R is the ideal gas constant and T is the temperature.

The Gas Laws

• Boyle’s Law: P1xV1 = P2xV2, where P1 and V1 Are the initial pressure and volume of the gas and P2 and V2 are the final

• Charles’ Law: V1-T1 = V2-T2. Here again, V1 And T1 Are the initial volume and temperature of the gas and V2 and T2 are the final.

• The Combined Gas Law:

P1 xV1 = P2 x V2 N1 x T1 n2 x T2

Where P1, V1, n1 and T1 are the initial pressure, volume, number of moles and temperature respectively and P2, V2, n2 and T2 are the final

• The Ideal Gas Law: PV = NRT, Where P Is pressure, V Is volume, N Is the number of moles, R Is the ideal gas constant and T Is temperature

• Dalton’s Law of Partial Pressures: Ptotal = P1 + P2 + P3 + . . . + Pn, where P1, P2, P3, etc. are the partial pressures of different components of the gas mixture

• Graham’s Law:

RateA – y/molar massB RateB .^molar massA

I Chemists use the expression PV

= n

RT

To determine whether or not a real gas resembles an ideal gas closely enough to use the ideal gas laws as approximations, which correlates to N Values near 1.

For gases with N Values far from 1, the more complicated expression

Is used. Values of the parameters A And B Must be known for the gas in question.

Testing Your Knowledge

The following practice problems can help you capture the wispy gas laws in your brain once and for all.

1. Which of the following accounts for the fact that gases generally do not behave ideally under high pressures?

(A) They begin to undergo rotational motion.

(B) Collisions between gas molecules become inelastic.

(C) Average molecular speeds increase.

(D) Intermolecular forces are greater when molecules are close together.

(E) Collisions with the walls of the container become more frequent.

2. Which of the following will increase the rms speed of a molecule of gas, assuming that all other variables are kept constant?

I. Increasing pressure

II. Increasing temperature

III. Decreasing molar mass

(A) I only

(B) I and II

(C) I and III

(D) II and III

(E) I, II, and III

3. If gas A effuses (goes through a small hole into a vacuum) at three times the rate of gas B, then

(A) the molar mass of gas A is three times greater than the molar mass of gas B.

(B) the molar mass of gas B is three times greater than the molar mass of gas A.

(C) the molar mass of gas A is nine times greater than the molar mass of gas B.

(D) the molar mass of gas B is nine times greater than the molar mass of gas A.

(E) the molar masses of gas A and gas B are equal.

4. A sealed vessel contains 0.50 mol of neon gas, 0.20 mol hydrogen gas, and 0.3 mol oxygen gas. The total pressure of the the gas mixture is 8.0atm. The partial pressure of oxygen is

5. Molecules of an unknown gas diffuse at three times the rate of molecules of ammonia (NH3) under the same conditions. What is the molar mass of the unknown gas?

6. A rigid 10.0L cylinder contains 2.20g H2, 36.4g N2 and 51.7g O2.

(a) What is the total pressure of the gas mixture at 30°C?

(b) If the cylinder springs a leak, and the gases begin escaping, will the ratio of hydrogen remaining in the cylinder to the other two gases increase, decrease, or stay the same?

7. Samples of Br2 and Cl2 are placed in 1L containers at the conditions indicated in the diagram in Figure 10-1.

Figure 10-1:

Conditions for Br2 and Cl2 samples.

(a) Which of the two gases has the greater kinetic energy per mole? Justify your answer.

(b) If the volume of the container holding the Cl2 were decreased to 0.25L but the temperature remained the same, what would the change in pressure be? Assume that the gas behaves ideally.

8. Two flasks are connected by a stopcock as shown in Figure 10-2. The 10.0L flask contains CO2 at a pressure of 5atm and the 5.0L flask contains CO at a pressure of 1.5atm. What will the total pressure of the system be after the stopcock is opened?

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). High pressure gases do not behave ideally because their molecules are too close together to neglect intermolecular forces.

2. (C). Molecular speeds are proportional to temperature and inversely proportional to mass.

3. (D). Remember that Graham’s Law states that gases effuse at a rate inversely proportional to the square root of their molar masses.

4. You are given enough information to find the mole fraction of each gas. Oxygen is 0.3 mol out of a total of 1.0mol of gas, so its mole fraction is 0.3. Multiply this by the total pressure to get a partial pressure of 2.4 for oxygen.

5. 153g mol. This is another Graham’s Law problem. You know that the ratio of effusion rates is 3:1, so the left-hand side of Graham’s Law will be 3. You can also easily calculate the molar mass of ammonia, which is 17g mol. Plug these values into the equation to get

1 ~V 17

Square both sides to get rid of the square root and then multiply both sides by 17 to get 153g mol.

6. (a) 9.83atm. Begin by converting the masses you have been given to moles by dividing by their molar masses. Make sure to get in the habit of showing your work even on simple calculations such as these.

2.20gH2 x 1molH2 = 110molH

1 2.00gH2 1-lumuin:

34.6gN21molN2

–—- x-— = 1 23mol N

1 28.0gN2 1-"muilN;

51.7gO21molO2

-i x 32 0gO2 = 1.62molO

1 32.0gO2

Next, add these values to yield the total number of moles of gas (3.95mol). Plug this and your known values for volume and temperature into the equation P = nRTVV.

3.95mo/ x 0.0821 L X,Atn}r X 303K Mo

10.0 L

P =-^m°l X K-= 9.83am

(b) Decrease. Because hydrogen has the lowest molar mass, it will effuse the fastest under Graham’s Law, so the ratio of hydrogen to the two other gases in the container, which escape more slowly, will decrease.

7. (a) They are the same. The average kinetic energy per mole of a sample of gas depends on temperature, and the two gases are at the same temperature.

(b) 0.25atm. This is a simple application of Charles’s Law where V1 = 1.0L, V2 = 0.25L and P1 = 1atm. Plug these into the equation to yield

8. 3.8atm. Begin by finding the final pressure of each of the two gases when the entire volume is made available to them using Boyle’s Law

P2 of CO2 = P1V1 vV2 = 5.0atm x 10.0L 4 15.0L = 3.3atm

P2 of CO = P1V1^V2 = 1.5atm x 5.0L 4 15.0L = 0.5atm

According to Dalton’s Law of Partial Pressures, the final pressure of this gas mixture will simply be the sum of these two final pressures.

P2

V x P1 = 0.25L x 1atm

= 0.25atm

V1 1.0 L