MCAT General Chemistry Review
Part I Review
Chapter 8: Phases and Phase Changes
Thwak! Thwak! “Stupid ketchup bottle! Why . . . won’t you . . . come . . . out?!” Few things are more frustrating than ketchup that just refuses to budge. It usually happens with newly opened bottles, and the “stuck ketchup” phenomenon is so common that there’s almost a ritualized nature to the process of getting it “unstuck”: Unscrew the top, turn the bottle on its side, and give it a few gentle shakes. If it doesn’t come out right away, the next step is the administration of a few sturdy whacks with the palm of the hand against the bottom of the bottle. This is usually accompanied by some mild epithet suggestive of ketchup’s alleged lack of intelligence (see quote above). More often than not, the physical abuse imposed upon the bottle only results in soft-tissue bruising and perhaps an alarming increase in the violent nature of the anti-ketchup epithets. Finally the ritual ends in an act of stabbing, and the evidence to convict is the spilled pool of red and the seemingly blood-coated butter knife that rests along the edge of the plate next to the pile of crispy french fries.
You can’t really blame the ketchup, though. It doesn’t know any better. In fact, it’s only acting according to its nature as a member of a unique class of liquids called Bingham fluids. Bingham fluids do not begin to flow immediately upon application of shear stress. Unlike Newtonian fluids, such as water or vegetable oil, which begin to flow as soon as a finite amount of shear stress is applied, Bingham fluids will only begin to flow when a minimum force value called the yield value is exceeded. Essentially, Bingham fluids behave like solids under static conditions and flow, as fluids, only when a shear stress at least equal to the yield value is applied. The sharp blows that you apply to the bottle of ketchup are usually strong enough to exceed ketchup’s yield value. Unfortunately for the diner who ends up with a plate (and probably lap) flooded with ketchup, ketchup also belongs to a class of liquids known as pseudoplastic fluids, which demonstrate the property of shear thinning. Shear-thinning liquids display reducing viscosity with increasing shear rate (related to fluid velocity). That ketchup is stuck, like a solid, in that bottle, until it isn’t (because the yield value has been exceeded), at which point it begins to flow and the faster it flows, the more it “thins” and becomes less viscous. The result is the mess on your plate and lap.
Our discussion in this chapter will focus on the three phases of matter, with particular emphasis on liquids and solids. (The gaseous phase has been discussed extensively in the previous chapter.) When the attractive forces between molecules (i.e., van der Waals forces, etc.) overcome the kinetic energy that keeps them apart in the gas phase, the molecules move closer together, entering the liquid or solid phase. The liquid and solid phases are often referred to as the condensed phases because of their higher densities compared to that of the gaseous phase. Molecules in the liquid and solid phases have lower degrees of freedom of movement than those in the gaseous phase as a result of the stronger intermolecular forces that dominate in the liquid and solid phases. After characterizing fluids and solids, we will review phase equilibria and phase diagrams. We will conclude our consideration of the phases of matter by reviewing the colligative properties of solutions.
Because the molecules in liquids and solids are much closer together than those in a gas, intermolecular forces must be considered as though there is no such thing as “ideal” behavior. These forces do allow us to predict behavior, although differently so.
We recognize solids by their rigidity and resistance to flow. The intermolecular attractive forces among the atoms, ions, or molecules of the solid matter hold them in a rigid arrangement. Although particles in the solid phase do not demonstrate linear motion, this does not mean that they do not possess any kinetic energy. The motion of particles in the solid phase, however, is mostly limited to vibration. As a result, solids have definite shapes (usually independent of the shape of a container) and volumes. Note that on the MCAT, solids (and liquids, for that matter) are considered to be incompressible; that is, a given mass of any solid or liquid will have a constant volume regardless of changes in pressure.
For most substances, the solid phase is the densest phase. A notable, and tested, exception to this generalization is water. Water in its solid phase (ice) is less dense than it is in its liquid phase due to the grater spacing between the molecules in the crystalline structure of ice. The spacious lattice of ice crystals is stabilized by the hydrogen bonds between water molecules. Water molecules in the liquid phase also interact through hydrogen bonds, but because the water molecules are moving around, the lattice arrangement is absent, and the molecules are able to move closer to each other. In fact, water’s density reaches a maximum around 4°C. The density decreases at temperatures above 4°C because the increasing kinetic energy of the water molecules causes the molecules to move further apart. Between 4°C and 0°C, the density decreases because the lattice organization of hydrogen bonds is beginning to form.
Crystalline structures allow for a balance of both attractive and repulsive forces to minimize energy.
The molecular arrangement of particles in the solid phase can be either crystalline or amorphous. Crystalline solids, such as the ionic compounds (e.g., NaCl), possess an ordered structure; their atoms exist in a specific three-dimensional geometric arrangement or lattice with repeating patterns of atoms, ions, or molecules. Amorphous solids, such as glass, plastic, and candle wax, lack an ordered three-dimensional arrangement. The particles of amorphous solids are fixed in place but not in the lattice arrangement that characterizes crystalline solids. Most solids are crystalline in structure. The two most common forms of crystals are metallic and ionic crystals.
Ionic solids are aggregates of positively and negatively charged ions that repeat according to defined patterns of alternating cations and anions. As a result, the solid mass of a compound, such as NaCl, does not contain discrete molecules (see Chapter 4, Compounds and Stoichiometry). The physical properties of ionic solids include high melting points, high boiling points, and poor electrical conductivity in the solid state but high conductivity in the molten state or in aqueous solution. These properties are due to the compounds’ strong electrostatic interactions, which also cause the ions to be relatively immobile in the solid phase. Ionic structures are given by empirical formulas that describe the ratio of atoms in the lowest possible whole numbers. For example, the empirical formula BaCl2 gives the ratio of barium to chloride atoms within the crystal.
Ionic solids often have extremely strong attractive forces, thereby causing extremely high melting points.
Metallic solids consist of metal atoms packed together as closely as possible. Metallic solids have high melting and boiling points as a result of their strong covalent attractions. Pure metallic masses (consisting of a single metal element) are usually described as layers of spheres of roughly similar radii, stacked layer upon layer in a “staggered” arrangement such that one sphere in one layer fits into the indented space between the spheres that sit above and below it. These staggered arrangements (body-centered cubic and face-centered cubic, see below) are more common than layers of spheres stacked to form perfectly aligned columns of spheres (see simple cubic, below), because the staggered arrangement minimizes the separation between the atoms.
The repeating units of crystals (both ionic and metallic) are represented by unit cells. There are many types of unit cells. Chapter 4, Compounds and Stoichiometry, referred to the geometric arrangement of Na+ and Cl- ions in table salt as 6:6 coordinated, meaning that each sodium ion is surrounded by (coordinated by) six chloride ions, and each chloride ion is surrounded by (coordinated by) six sodium ions. This particular arrangement is also known as face-centered cubic. There are three cubic unit cells, and you should recognize these for the MCAT: simple cubic, body-centered cubic, and face-centered cubic. Figure 8.2 illustrates these unit cells as ball-and-stick models.
In the ball-and-stick models illustrated, the anions are represented as small spheres separated by a lot of space, but more accurately, the spheres are packed quite closely. Figure 8.3 illustrates this. In the ionic unit cell, the spheres represent the anions; the spaces between the anions are occupied by the smaller cations. In most ionic compounds, the anion, which has gained one or more electrons, is much larger than the cation, which has lost one or more electrons. (The cations are not shown in Figures 8.2 and 8.3.)
The liquid phase, along with the solid phase, is considered a condensed phase because the spacing between the particles is reduced in comparison to that between gas particles. Furthermore, we assume that liquids, like solids, are incompressible, meaning that their volumes do not change in any significant way as a result of moderate pressure changes. But don’t let all this talk of liquid as a “condensed phase” mislead you: There is still a lot of space separating liquid particles. You can “observe” this space for yourself through a very simple experiment. Fill a glass with very hot tap water all the way to the top of the glass, making sure that the water surface is actually “bulging” up above the level of the rim of the glass. Carefully add powdered sugar, by the teaspoon, to the water. Do not allow the spoon to touch the surface of the water, and do not stir the solution. The hot water will dissolve the sugar on its own. Repeat the process. You will be able to add several teaspoons of sugar to the water before it spills out of the cup. The sugar dissolved into the empty spaces that separate the water molecules!
Liquids are categorized as fluids (along with gases) because they do not resist shearing forces and flow when subjected to them. They also conform to the shapes of their containers. These behaviors are a result of the high degree of freedom of movement liquids possess. Like gas molecules, liquid molecules can move about in random motion and are disordered in their arrangement. Both liquids and gases are able to diffuse. Liquid molecules near the surface of the liquid can gain enough kinetic energy to escape into the gas phase; this is called evaporation.
One of the most important properties of liquids is their ability to mix—both with each other and with other phases—to form solutions (see Chapter 9, Solutions). The degree to which two liquids can mix is called their miscibility. While ethanol and water are completely miscible, oil and water are almost completely immiscible; that is, their molecules tend to repel each other due to their polarity differences. You’re certainly familiar with the expression “Like dissolves like.” Oil and water normally form separate layers when mixed, with the oil layer above the water because it is less dense. Organic chemistry takes advantage of the solubility differences of immiscible liquids to separate compounds through the method of liquid-liquid extraction. Agitation of two immiscible liquids can result in the formation of a fairly homogenous mixture called an emulsion. Although they look like solutions, emulsions are actually mixtures of discrete particles too small to be seen distinctly. Shaking a cruet of extra virgin olive oil and balsamic vinegar, seasoned with sea salt and fresh ground pepper, makes for a simple but delicious emulsion for your mixed baby greens salad.
In an isolated system, phase changes (solid liquid gas) are reversible, and equilibrium of phases will eventually be reached. For example, at 1 atm and 0°C in an isolated system, an ice cube and the water in which it is floats are in equilibrium. In other words, some of the ice may absorb heat (from the liquid water) and melt, but since that heat is being removed from the liquid water, an equal amount of the liquid water will freeze and form ice. Thus, the relative amounts of ice and water remain constant. Equilibrium between the liquid and gas states of water will be established in a closed container, such as a plastic water bottle with the cap screwed on tightly. At room temperature and atmospheric pressure, most of the water in the bottle will be in the liquid phase, but a small number of molecules at the surface will gain enough kinetic energy to escape into the gas phase; likewise, a small number of gas molecules will lose sufficient kinetic energy to re-enter the liquid phase. After a while, equilibrium is established, and the relative amounts of water in the liquid and gas phases become constant—at room temperature and atmospheric pressure, equilibrium occurs when the air above the water has about 3 percent humidity. Phase equilibria are analogous to the dynamic equilibria of reversible chemical reactions for which the concentrations of reactants and products are constant because the rates of the forward and reverse reactions are equal.
As with all equilibria, the rates of the forward and reverse processes will be the same.
The temperature of any substance in any phase is related to the average kinetic energy of the molecules that make up the substance. However, as we saw in Chapter 7, not all the molecules have exactly the same instantaneous speeds. Therefore, the molecules possess a range of instantaneous kinetic energy values. In the liquid phase, the molecules have relatively large degrees of freedom of movement. Some of the molecules near the surface of the liquid may have enough kinetic energy to leave the liquid phase and escape into the gaseous phase. This process is known as evaporation(or vaporization). Each time the liquid loses a high-energy particle, the temperature of the remaining liquid decreases. Evaporation is an endothermic process for which the heat source is the liquid water. Of course, the liquid water itself may be receiving thermal energy from some other source, as in the case of a puddle of water drying up under the hot summer sun or a pot of water on the stove-top. Given enough energy, the liquid will completely evaporate.
In covered or closed container, the escaping molecules are trapped above the solution. These molecules exert a countering pressure, which forces some of the gas back into the liquid phase; this process is called condensation. Condensation is facilitated by lower temperature or higher pressure. Atmospheric pressure acts on a liquid in a manner similar to that of an actual physical lid. As evaporation and condensation proceed, the respective rates of the two processes become equal, and equilibrium is reached. The pressure that the gas exerts over the liquid at equilibrium is the vapor pressure of the liquid. Vapor pressure increases as temperature increases, since more molecules have sufficient kinetic energy to escape into the gas phase. The temperature at which the vapor pressure of the liquid equals the ambient (also known as external, applied, or atmospheric) pressure is called the boiling point: At boiling, vaporization happens throughout the entire volume of the liquid, not just near its surface. The bubbles of gas that rise from your pot of boiling pasta water are gaseous water molecules, plus the small amounts of atmospheric gases (mostly nitrogen and oxygen gas) that had been dissolved in the water.
We’ve already illustrated the equilibrium that can exist between the liquid and the solid phases of water at 0°C. Even though the atoms or molecules of a solid are confined to definite locations, each atom or molecule can undergo motions about some equilibrium position. These vibrational motions increase when heat is applied. From our understanding of entropy, we can say that the availability of energy microstates increases as the temperature of the solid increases. In basic terms, this means that the molecules have greater freedom of movement, and energy disperses. If atoms or molecules in the solid phase absorb enough energy, the three-dimensional structure of the solid will break down, and the atoms or molecules will escape into the liquid phase. The transition from solid to liquid is called fusion or melting. The reverse process, from liquid to solid, is called solidification,crystallization, or freezing. The temperature at which these processes occur is called the melting point or freezing point, depending on the direction of the transition. Whereas pure crystalline solids have distinct, very sharp melting points, amorphous solids, such as glass, plastic, and candle wax, tend to melt (or solidify) over a larger range of temperatures due to their less-ordered molecular distribution. One of the surest signs that a dinner party has come to its natural and necessary conclusion is when the dinner guests start playing with the liquid wax dripping down the side of the candlesticks, allowing it to cool and solidify on their fingertips.
The final phase equilibrium is that which exists between the gas and solid phase. When a solid goes directly into the gas phase, the process is called sublimation. Dry ice (solid CO2) sublimes at room temperature and atmospheric pressure; the absence of the liquid phase makes it a convenient refrigerant and a fun addition to punch bowls at parties. The reverse transition, from the gaseous to the solid phase, is called deposition. In organic chemistry, a device known as the cold finger (the name sounds more malicious than it actually is) is used to purify a product that is heated under reduced pressure to cause it to sublimate. The desired product is usually more volatile than the impurities, so the gas is purer than the original product and the impurities are left in the solid state. The gas then deposits onto the cold finger, which has cold water flowing through it, yielding a purified solid product that can be collected. Another common instance of sublimation is “freezer burn” on meats and vegetables that are stored for long periods in the freezer. The frozen water in the meat or vegetables will slowly sublimate over time, and what is left is fit only for the garbage. On the other hand, sublimation is used to produce freeze-dried foods, such as coffee, “emergency survival meals,” and perhaps most (in)famously, astronaut ice cream. The crackly frost of late autumn mornings in colder climates is formed by deposition of water vapor in the air.
THE GIBBS FUNCTION
As with all equilibria, the thermodynamic criterion for each of the phase equilibria is that the change in Gibbs free energy must be equal to zero (G = 0). For an equilibrium between a gas and a solid,
G = G(g) - G(s) = 0
G(g) = G(s)
The same is true of the Gibbs functions for any other phase equilibria.
When a compound is heated, the temperature rises until the melting or boiling points are reached. Then the temperature remains constant as the compound is converted to the next phase (i.e., liquid or gas, respectively). Once the entire sample is converted, then the temperature begins to rise again. See the heating curves depicted in Figure 8.4.
Phase diagrams are graphs that show the temperatures and pressures at which a substance will be thermodynamically stable in a particular phase. They also show the temperatures and pressures at which phases will be in equilibrium.
Every pure substance has a characteristic phase diagram.
The phase diagram for a single compound is shown in Figure 8.5.
Because of H2O’s unique properties, ice floats and ice skates flow smoothly over ice. This all “boils” down to the negative slope of the solid-liquid equilibrium line in its phase diagram. Because the density of ice is less than that of liquid H2O, an increase in pressure (at a constant temperature) will actually melt ice (the opposite of the substance seen in Figure 8.5).
The lines on a phase diagram are called the lines of equilibrium or the phase boundaries and indicate the temperature and pressure values for the equilibria between phases. The lines of equilibrium divide the diagram into three regions corresponding to the three phases—solid, liquid, and gas—and they themselves represent the phase transformations. Line A represents crystallization/fusion, line B vaporization/ condensation, and line C sublimation/deposition. In general, the gas phase is found at high temperatures and low pressures, the solid phase is found at low temperatures and high pressures, and the liquid phase is found at moderate temperatures and moderate pressures. The point at which the three phase boundaries meet is called the triple point. This is the temperature and pressure at which the three phases exist in equilibrium. The phase boundary that separates the solid and the liquid phases extends indefinitely from the triple point. The phase boundary between the liquid and gas phases, however, terminates at a point called the critical point. This is the temperature and pressure above which there is no distinction between the phases. Although this may seem to be an impossibility—after all, it’s possible always to distinguish between the liquid and the solid phase—such “supercritical fluids” are perfectly logical. As a liquid is heated in a closed system its density decreases and the density of the vapor sitting above it increases. The critical point is the temperature and pressure at which the two densities become equal and there is no distinction between the two phases. The heat of vaporization at this point and for all temperatures and pressures above the critical point values is zero. So it’s certainly possible to create a supercritical fluid, but definitely not common (in everyday life). Rest assured that you have never come close to approaching, say, the critical point temperature and pressure for water, no matter how much “industrial strength” your high-pressure home espresso machine possesses: 647 K (374°C or 705°F) and 22.064 MPa (218 atm).
The phase diagram for a mixture of two or more components is complicated by the requirement that the composition of the mixture, as well as the temperature and pressure, must be specified. For example, consider a solution of two liquids, A and B, shown in Figure 8.7. The vapor above the solution is a mixture of the vapors of A and B. The pressures exerted by vapor A and vapor B on the solution are the vapor pressures that each exerts above its individual liquid phase. Raoult’s law enables one to determine the relationship between the vapor pressure of gaseous A and the concentration of liquid A in the solution.
Curves such as this show the different compositions of the liquid phase and the vapor phase above a solution for different temperatures. The upper curve is the composition of the vapor, while the lower curve is that of the liquid. It is this difference in composition that forms the basis of distillation, an important separation technique in organic chemistry. For example, if we were to start with a mixture of A and B at a proportion of 40 percent A and 60 percent B and heat it to that solution’s boiling point (85°C), the resulting vapor would not have the same composition as the liquid solution because the two compounds have different volatilities. Compound B is more volatile because it has the lower boiling point. Therefore, vapor B should be in larger proportion to vapor A, compared to the proportion of B to A in the liquid phase. Because the boiling point temperature for this 60–40 mixture is 85°C, the vapor will also be at 85°C. At this temperature, we can tell from the graph that the vapor composition will be 30 percent A and 70 percent B. Indeed, the proportion of the more volatile compound, in this case compound B, has been enhanced. Repeated rounds of boiling (vaporization) and condensation will ultimately yield a pure sample of compound B.
On the MCAT, you should be able to identify and understand each area and every line of a phase diagram.
All the way back at the start of this book, we suggested that adding salt to water will yield a solution whose boiling point is higher than that of the pure water. While this is a true statement, we also suggested that the quantity of salt that is normally added to a pot of cooking water is not sufficient to cause a significant rise in the boiling point or a significant decrease in the cooking time. In culinary practice, adding salt to your cooking water merely (but importantly) contributes to the flavor of the food. The measurable change in boiling point of a solution compared to that of the pure solvent is one of the colligative properties of solutions. The colligative properties are physical properties of solutions that are dependent upon the concentration of dissolved particles but not upon the chemical identity of the dissolved particles. These properties—vapor pressure depression, boiling point elevation, freezing point depression, and osmotic pressure—are usually associated with dilute solutions (see Chapter 9, Solutions).
VAPOR PRESSURE DEPRESSION
When you add solute to a solvent and the solute dissolves, the solvent in solution has a vapor pressure that is lower than the vapor pressure of the pure solvent for all temperatures. For example, consider compound A in Figure 8.7. Compound A in its pure form (mole fraction = 1.0) has a boiling point of 100°C. Based on this information alone, we can assume that compound A is water. Compound B, which is more volatile than water and boils in pure form (mole fraction = 1.0) at around 80°C could be ethanol, which has a boiling point of 78.3°C. When a small amount of ethanol is added to water to create a dilute solution, say 90 percent water and 10 percent alcohol, the boiling point is around 95°C, and the vapor composition above the solution will be about 80 percent water and 20 percent ethanol. The relative decrease in the proportion of water in the vapor above the dilute water-alcohol solution is related to the decrease in the vapor pressure of water above the solution.
This goes hand in hand with boiling point elevation. The lowering of a solution’s vapor pressure would mean that a higher temperature is required to overcome atmospheric pressure, thereby raising the boiling point.
If the vapor pressure of A above pure solvent A is designated by and the vapor pressure of A above the solution containing B is PA, the vapor pressure decreases as follows:
In the late 1800s, the French chemist François Marie Raoult determined that this vapor pressure decrease is also equivalent to
where XB is the mole fraction of the solute B in solution with solvent A. Because XB = 1 - XA and substitution into the previous equation leads to the common form of Raoult’s law:
where XA is the mole fraction of the solvent A in the solution. Similarly, the expression for the vapor pressure of the solute in solution (assuming it is volatile) is given by:
Raoult’s law holds only when the attraction between the molecules of the different components of the mixture is equal to the attraction between the molecules of any one component in its pure state. When this condition does not hold, the relationship between mole fraction and vapor pressure will deviate from Raoult’s law. Solutions that obey Raoult’s law are called ideal solutions.
BOILING POINT ELEVATION
When a nonvolatile solute is dissolved into a solvent to create a solution, the boiling point of the solution will be greater than that of the pure solvent. Earlier, we defined the boiling point as the temperature at which the vapor pressure of the liquid equals the ambient (external) pressure. We’ve just seen that adding solute to a solvent results in a decrease in the vapor pressure of the solvent in the solution at all temperatures. If the vapor pressure of a solution is lower than that of the pure solvent, then more energy (and consequently a higher temperature) will be required before its vapor pressure equals the ambient pressure. The extent to which the boiling point of a solution is raised relative to that of the pure solvent is given by the following formula:
Tb = iKbm
where Tb is the boiling point elevation, Kb is a proportionality constant characteristic of a particular solvent (and will be given to you on Test Day), m is the molality of the solution [molality = moles of solute per kilogram of solvent (mol/kg); see Chapter 9, Solutions] and i is the van’t Hoff factor, which is the moles of particles dissolved into a solution per mole of solute molecules. For example, i = 2 for NaCl because each molecule of sodium chloride dissociates into two particles, a sodium ion and a chloride ion, when it dissolves.
FREEZING POINT DEPRESSION
The presence of solute particles in a solution interferes with the formation of the lattice arrangement of solvent molecules associated with the solid state. Thus, a greater amount of energy must be removed from the solution (resulting in a lower temperature) in order for the solution to solidify. For example, pure water freezes at 0°C, but for every mole of solute dissolved in 1 kg (1 liter) of water, the freezing point is lowered by 1.86°C. Therefore, the Kf for water is -1.86°C/m. As is the case for Kb, the values for Kf are unique to each solvent and will be given to you on Test Day. The formula for calculating the freezing point depression for a solution is
Tf = iKfm
where Tf is the freezing point depression, Kf is the proportionality constant characteristic of a particular solvent, m is the molality of the solution, and i is the van’t Hoff factor.
If you’ve ever wondered why we salt roads in the winter, this is why: The salt mixes with the snow and ice and initially dissolves into the small amount of liquid water that is in equilibrium with the solid phase (the snow and ice). The solute in solution causes a disturbance to the equilibrium such that the rate of melting is unchanged (because the salt can’t interact with the solid water that is stabilized in a rigid lattice arrangement), but the rate of freezing is decreased (the solute displaces some of the water molecules from the solid-liquid interface and prevents liquid water from entering into the solid phase).
This imbalance causes more ice to melt than water to freeze. Melting is an endothermic process, so heat is initially absorbed from the liquid solution, causing the solution temperature to fall below the ambient temperature. Now, there is a temperature gradient and heat flows from the “warmer” air to the “cooler” aqueous solution; this additional heat facilitates more melting—even though the temperature of the solution is actually colder than it was before the solute was added! The more the ice melts into liquid water, the more the solute is dispersed through the liquid. The resulting salt solution, by virtue of the presence of the solute particles, has a lower freezing point than the pure water and remains in the liquid state even at temperatures that would normally cause pure water to freeze.
Could we use table sugar instead of salt? Absolutely—but sugar is more expensive. Could we use LiCl instead of NaCl? Absolutely—but NaCl is a lot easier and more economical. Besides, we’ve heard of manic drivers in need of a mood stabilizer, but manic roads? Could we use magical fairy dust? Absolutely—as long as magical fairy dust is soluble in water. In other words, it doesn’t matter what the solute is. Freezing point depression is a colligative property that depends only upon the concentration of particles, not upon their identity.
One of the most important roles of the cell membrane is to maintain the unique differences between the intracellular and extracellular compartments. Both of these compartments are aqueous solutions separated by the cell membrane, which functions as a semipermeable barrier. Channels and pumps in the membrane serve to create and maintain concentration gradients of various solutes on either side of the membrane. A delicate balance of water influx and efflux must be established in order to prevent the cell from becoming dehydrated and shrinking or waterlogged and possibly bursting. The extracellular compartment itself is in continuity with the plasma compartment of the blood. A balance between these two compartments is dependent upon two pressures: the hydrostatic pressure of the blood generated by the contraction of the heart and the osmotic pressure of the plasma compartment, primarily established by the concentration of plasma proteins such as albumin. (Since the osmotic pressure of the plasma compartment is based on the concentration of plasma protein, it is also called oncotic pressure.) The hydrostatic pressure tends to push fluid volume out of the vascular compartment into the extracellular compartment, while the osmotic pressure tends to pull fluid volume back into the vascular compartment from the extracellular compartment.
Consider a container separated into two compartments by a semipermeable membrane (which, by definition, selectively permits the passage of certain molecules). One compartment contains pure water, while the other contains water with dissolved solute. The membrane allows water but not solute to pass through. Because substances tend to flow, or diffuse, from higher to lower concentration (which results in an increase in entropy), water will diffuse from the compartment containing pure water into the compartment containing the water-solute mixture. This net flow will cause the water level in the compartment containing the solution to rise above the level in the compartment containing pure water.
Because the solute cannot pass through the membrane, the concentrations of solute in the two compartments can never be equal. However, the hydrostatic pressure exerted by the water level in the solute-containing compartment will eventually oppose the influx of water; thus, the water level will rise only to the point at which it exerts a sufficient pressure to counterbalance the tendency of water to flow across the membrane. This pressure, defined as the osmotic pressure (? ) of the solution, is given by this formula:
? = iM RT
where M is the molarity of the solution, R is the ideal gas constant, T is the absolute temperature (in Kelvin), and i is the van’t Hoff factor. The equation clearly shows that osmotic pressure is directly proportional to the molarity of the solution. Thus, osmotic pressure, like all colligative properties, depends only upon the presence of the solute, not its chemical identity.
Osmosis explains how many biological systems regulate their fluid levels.
On the MCAT, remember always to use Kelvin temperatures when T is in an equation!
One application of osmotic pressure is a particular method of water purification called reverse osmosis (RO). In reverse osmosis, impure water is placed into one container separated from another container by a semipermeable membrane. High pressure is applied to the impure water, which forces it to diffuse across the membrane, filling the compartment on the other side of the membrane with purified water. Because the water is being forced across the membrane in the direction opposite its concentration gradient (that is, the water is being forced from the compartment with the lower concentration of water to the compartment with the higher concentration of water), large pressures (higher than the solution’s osmotic pressure) are needed to accomplish the purification.
Water will move toward the chamber with either greater molarity or (if the molarity is the same) to the chamber with higher temperature.
In this chapter, we have reviewed the important concepts and calculations related to the condensed phases of the solid and liquid states of matter. For solids, we learned that the organization of the particles is either in a three-dimensional lattice formation, producing a crystalline structure, or in a less-ordered arrangement described as amorphous. Ionic and metallic solids have crystalline structure, while glass, plastic, and candle wax have amorphous structure. The particles that make up a crystalline structure can be organized in many ways; the basic repeating unit of that organization is called the unit cell. We reviewed the three cubic unit cells. Liquids, like gases, are defined by their ability to flow in response to shearing forces. Liquids that can mix together are called miscible, while those that repel each other and separate into different layers, like oil and water, are called immiscible. We examined the equilibria that exist between the different phases and noted that the change in Gibbs function for each phase change in equilibrium is zero, as is the case for all equilibria. Finally, we examined the colligative properties of solutions and the mathematics that govern them. The colligative properties—vapor pressure depression, boiling point elevation, freezing point depression, and osmotic pressure—are physical properties of solutions that depend upon the concentration of dissolved particles but not upon their chemical identity.
We concluded this chapter with an overview of the colligative properties of solutions; the next chapter will continue the review of the behaviors and characteristics of solutions and the mathematics of solution chemistry that will earn you points on Test Day.
CONCEPTS TO REMEMBER
In the solid and liquid phases, the atoms, ions, or molecules are sufficiently condensed to allow the intermolecular forces, such as van der Waals, dipole–dipole, and hydrogen bonds, to hold the particles together and restrict their degrees of freedom of movement.
Solids are defined by their rigidity (ability to maintain a shape independent of a container) and resistance to flow.
The molecular arrangement in solids can be either crystalline or amorphous. Crystalline structure is a three-dimensional lattice arrangement of repeating units called the unit cell. Amorphous solids lack this lattice arrangement.
Liquids are defined as fluids because they flow in response to shearing forces and assume the shape of their container.
Liquids like water and alcohol will mix together and are called miscible; liquids like water and oil will not mix together and are called immiscible. Agitation of immiscible liquids will result in an emulsion.
Phase equilibria will exist at certain temperatures and pressures for each of the different phase changes: fusion (crystallization), vaporization (condensation), and sublimation (deposition).
The change in Gibbs free energy for phase equilibria is zero.
The phase diagram of a given system graphs the phases and phase equilibria as a function of temperature and pressure.
The phase diagram for a solution consisting of multiple components indicates the composition of the liquid and the vapor at different temperatures and pressures.
The colligative properties—vapor pressure depression, boiling point elevation, freezing point depression, and osmotic pressure—are physical properties of solutions that depend upon the concentration of dissolved particles but not upon their chemical identity.
EQUATIONS TO REMEMBER
PA = XA°PA
Tb = iKbm
Tf = iKfm
1. Which of the following substances is illustrated by the phase diagram in the figure below?
2. Which of the following proportionalities best describes the relationship between the number of intermolecular forces and heat of vaporization for a given substance?
A. They are proportional.
B. They are inversely proportional.
C. Their relationship cannot be generalized.
D. There is no relationship between them.
3. Which of the following molecules is likely to have the highest melting point?
4. Which of the following physical conditions favors a gaseous state for most substances?
A. High pressure and high temperature
B. Low pressure and low temperature
C. High pressure and low temperature
D. Low pressure and high temperature
5. Which of the following explanations best describes the mechanism by which solute particles affect the melting point of ice?
A. Melting point elevates because the kinetic energy of the substance increases.
B. Melting point elevates because the kinetic energy of the substance decreases.
C. Melting point depresses because solute particles interfere with lattice formation.
D. Melting point depresses because solute particles enhance lattice formation.
6. In the figure below, which phase change is represented by the arrow?
7. Which of the following situations would most favor the change of water from a liquid to a solid?
I. Decreased solute concentration of a substance
II. Decreased temperature of a substance
III. Decreased pressure on a substance
A. I only
B. II only
C. I and II only
D. II and III only
8. The heats of vaporization of four substances are given in the table below. Which of these substances has the lowest boiling point?
Comparative Heats of Vaporization
Heat Required (cal/g)
C. Carbon dioxide
9. What factor(s) determine whether or not two liquids are miscible?
A. Molecular size
B. Molecular polarity
D. Both B and C
10. Alloys are mixtures of new metals in either the liquid or solid phase. Which of the following is usually true of alloys?
A. The melting/freezing point of an alloy will be lower than that of either of the component metals because the new bonds are stronger.
B. The melting/freezing point of an alloy will be lower than that of either of the component metals because the new bonds are weaker.
C. The melting/freezing point of an alloy will be greater than that of either of the component metals because the new bonds are weaker.
D. The melting/freezing point of an alloy will be greater than that of either of the component metals because the new bonds are stronger.
11. The osmotic pressure at STP of a solution made from 1 L of NaCl (aq) containing 117 g of NaCl is
A. 44.77 atm.
B. 48.87 atm.
C. 89.54 atm.
D. 117 atm.
Small Group Questions
1. On water’s pressure-temperature phase diagram, the boundary between liquid and solid has a negative slope. Explain this phenomenon, focusing on how density affects pressure and temperature.
2. Which would have a greater effect on the boiling point of one liter of water: 2 moles of sodium nitrate or 1 mole of carbonic acid? What pieces of information do we need to calculate this answer?
Explanations to Practice Questions
For the scope of the MCAT, water is the only substance that has a solid/liquid equilibrium line with a negative slope. We are not expected to know specific phase diagrams for other compounds.
Intermolecular forces hold molecules closer to one another, which relates to the compound’s phase. As there are more intermolecular forces, the amount of heat needed to change phase (such as in vaporization) increases as well, thus showing a proportional, positive relationship.
This molecule is likely to have unequal sharing of electrons, which means it will be polar. Polarity often leads to increased bonding because of the positive-negative attractive forces between molecules. Greater bonding or stronger intermolecular forces both lead to higher melting points, because more heat is needed to break these interactions and cause liquefaction. (A) is nonpolar, making its intermolecular forces weaker than (B) or (C). (D) is only weakly polar, because the geometry of this molecule will make some of the polarized bonds cancel each other out. (C) will have some polarity but less than (B), because only one bond is polarized.
We can imagine a high-pressure situation as one in which molecules are in close proximity (low-volume container) and forced to interact with one another. Intermolecular attractions are necessary in the solid and liquid phases but assumed to be negligible in the gas phase. So we can assume that high pressure is not conducive to the gaseous state. What about temperature? Because temperature is a measure of average kinetic energy of the molecules, an increase in the average kinetic energy increases molecules’ ability to move apart from one other, ultimately entering a gaseous state. Decreasing the temperature (or kinetic energy) or increasing pressure both favor the more organized liquid and solid phases.
Melting point depresses upon solute addition, making (A) and (B) incorrect. Solute particles interfere with lattice formation, the highly organized state in which solid molecules align themselves. Colder than normal conditions are necessary to create the solid structure.
This answer choice shows movement from the solid to gas phase, which is, by definition, sublimation.
Both I and II are correct. Dissolved solutes interfere with the crystalline lattice bonds of a solid and, therefore, favor the liquid side of the equilibrium. Conversely, a decreased amount of solute would favor a solid state (I). Additionally, decreased temperature (II) is a decrease in the average kinetic energy of the molecules, making lower-energy phases (i.e. solid) more likely to exist. Finally, decreasing pressure (III) would actually favor higher-energy phases (i.e., liquid or gas) over solids. The only answer choice that includes both I and II is (C).
(B) has the lowest heat required for vaporization, which by definition determines the boiling point or the lowest temperature required for phase change from liquid to gas. All of the other answer choices have higher heats of vaporization, as seen in the table associated with the question.
The miscibility of two liquids strongly depends on their polarities. A polar liquid can mix with another polar liquid, and a nonpolar liquid can mix with another nonpolar liquid. In general, however, polar and nonpolar liquids are not miscible with each other. (A), molecular size, and (C), the density of a liquid, do not directly affect the miscibility (although (C) should remind you that two immiscible liquids will form separate layers, with the denser liquid on the bottom). Thus, (B) is the only correct choice.
The bonds between different metal atoms in an alloy are much weaker than those between the atoms in pure metals. Therefore, breaking these bonds requires less energy than does breaking the bonds in pure metals. The more stable the bonds are in a compound, the higher the melting and freezing points. They tend to be lower for alloys than for pure metals. Alternately, an alloy can be looked at as a solid solution; impurities lower the melting point.
The osmotic pressure () of a solution is given by = iM RT. At STP, T = 273 K. R, the ideal gas constant, equals 8.2 × 10-2 L • atm/K • mol. To determine the molarity, find the formula weight of NaCl from the periodic table; FW = 58.5 g/mol. The number of moles in the solution described is
However, because NaCl is a strong electrolyte, it will completely dissociate in aqueous solution, yielding 4 moles of particles per liter of solution (i.e., 2 moles of Na+ and 2 moles of Cl-). Thus,
? = (4 mol/L)(8.2 × 10-2 L •atm/K •mol)(273 K) = 89.54 atm
Remember that colligative properties depend on the number of particles, not their identity.