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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