CHEMISTRY THE CENTRAL SCIENCE
13 PROPERTIES OF SOLUTIONS
13.3 FACTORS AFFECTING SOLUBILITY
The extent to which one substance dissolves in another depends on the nature of both substances. (Section 13.1) It also depends on temperature and, at least for gases, on pressure.
The natural tendency of substances to mix and the various interactions among solute and solvent particles are all involved in determining solubilities. Nevertheless, insight into variations in solubility can often be gained by simply focusing on the interaction between the solute and solvent. The data in TABLE 13.1 show, for example, that the solubilities of various simple gases in water increase with increasing molecular mass or increasing polarity. The attractive forces between the gas molecules and solvent molecules are mainly dispersion forces, which increase with increasing size and molecular mass. (Section 11.2) Thus, the data indicate that the solubilities of gases in water increase as the attraction between solute (gas) and solvent (water) increases. In general, when other factors are comparable, the stronger the attractions between solute and solvent molecules, the greater the solubility of the solute in that solvent.
TABLE 13.1 • Solubilities of Gases in Water at 20 °C, with 1 atm Gas Pressure
Because of favorable dipole-dipole attractions between solvent molecules and solute molecules, polar liquids tend to dissolve in polar solvents. Water is both polar and able to form hydrogen bonds. (Section 11.2) Thus, polar molecules, especially those that can form hydrogen bonds with water molecules, tend to be soluble in water. For example, acetone, a polar molecule with the structural formula shown in the margin, mixes in all proportions with water. Acetone has a strongly polar C═O bond and pairs of nonbonding electrons on the O atom that can form hydrogen bonds with water.
Pairs of liquids that mix in all proportions, such as acetone and water, are miscible, whereas those that do not dissolve in one another are immiscible. Gasoline, which is a mixture of hydrocarbons, is immiscible with water. Hydrocarbons are nonpolar substances because of several factors: The C—C bonds are nonpolar, the C—H bonds are nearly nonpolar, and the molecules are symmetrical enough to cancel much of the weak C—H bond dipoles. The attraction between the polar water molecules and the nonpolar hydrocarbon molecules is not sufficiently strong to allow the formation of a solution. Nonpolar liquids tend to be insoluble in polar liquids, as FIGURE 13.10 shows for hexane (C6H14) and water.
FIGURE 13.10 Hexane is immiscible with water. Hexane is the top layer because it is less dense than water.
Many organic compounds have polar groups attached to a nonpolar framework of carbon and hydrogen atoms. For example, the series of organic compounds in TABLE 13.2 all contain the polar OH group. Organic compounds with this molecular feature are called alcohols. The O — H bond is able to form hydrogen bonds. For example, ethanol (CH3CH2OH) molecules can form hydrogen bonds with water molecules as well as with each other (FIGURE 13.11). As a result, the solute-solute, solvent-solvent, and solute-solvent forces are not greatly different in a mixture of CH3CH2OH and H2O. No major change occurs in the environments of the molecules as they are mixed. Therefore, the increased entropy when the components mix plays a significant role in solution formation, and ethanol is completely miscible with water.
FIGURE 13.11 Hydrogen bonding involving OH groups.
Notice in Table 13.2 that the number of carbon atoms in an alcohol affects its solubility in water. As this number increases, the polar OH group becomes an ever smaller part of the molecule, and the molecule behaves more like a hydrocarbon. The solubility of the alcohol in water decreases correspondingly. On the other hand, the solubility of alcohols in a nonpolar solvent like hexane (C6H14) increases as the nonpolar hydrocarbon chain lengthens.
FIGURE 13.12 Structure and solubility.
One way to enhance the solubility of a substance in water is to increase the number of polar groups the substance contains. For example, increasing the number of OH groups in a solute increases the extent of hydrogen bonding between that solute and water, thereby increasing solubility. Glucose (C6H12O6, FIGURE 13.12) has five OH groups on a six-carbon framework, which makes the molecule very soluble in water (83 g dissolves in 100 mL of water at 17.5°C).
TABLE 13.2 • Solubilities of Some Alcohols in Water and in Hexane*
*Expressed in mol alcohol/100 g solvent at 20 °C (∞). The infinity symbol indicates that the alcohol is completely miscible with the solvent.
CHEMISTRY AND LIFE
FAT-SOLUBLE AND WATER-SOLUBLE VITAMINS
Vitamins have unique chemical structures that affect their solubilities in different parts of the human body. Vitamin C and the B vitamins are soluble in water, for example, whereas vitamins A, D, E, and K are soluble in nonpolar solvents and in fatty tissue (which is nonpolar). Because of their water solubility, vitamins B and C are not stored to any appreciable extent in the body, and so foods containing these vitamins should be included in the daily diet. In contrast, the fat-soluble vitamins are stored in sufficient quantities to keep vitamin-deficiency diseases from appearing even after a person has subsisted for a long period on a vitamin-deficient diet.
That some vitamins are soluble in water and others are not can be explained in terms of their structures. Notice in FIGURE 13.13 that vitamin A (retinol) is an alcohol with a very long carbon chain. Because the OH group is such a small part of the molecule, the molecule resembles the long-chain alcohols listed in Table 13.2. This vitamin is nearly nonpolar. In contrast, the vitamin C molecule is smaller and has several OH groups that can form hydrogen bonds with water. In this regard, it is somewhat like glucose.
RELATED EXERCISES: 13.7, 13.48
FIGURE 13.13 Vitamins A and C.
Over the years, examination of different solvent–solute combinations has led to an important generalization: Substances with similar intermolecular attractive forces tend to be soluble in one another. This generalization is often simply stated as “like dissolves like.” Nonpolar substances are more likely to be soluble in nonpolar solvents; ionic and polar solutes are more likely to be soluble in polar solvents. Network solids such as diamond and quartz are not soluble in either polar or nonpolar solvents because of the strong bonding forces within the solid.
GIVE IT SOME THOUGHT
Suppose the hydrogens on the OH groups in glucose (Figure 13.12) were replaced with methyl groups, CH3. Would you expect the water solubility of the resulting molecule to be higher than, lower than, or about the same as the solubility of glucose?
SAMPLE EXERCISE 13.1 Predicting Solubility Patterns
Predict whether each of the following substances is more likely to dissolve in the nonpolar solvent carbon tetrachloride (CCl4) or in water: C7H16, Na2SO4, HCl, and I2.
Analyze We are given two solvents, one that is nonpolar (CCl4) and the other that is polar (H2O), and asked to determine which will be the better solvent for each solute listed.
Plan By examining the formulas of the solutes, we can predict whether they are ionic or molecular. For those that are molecular, we can predict whether they are polar or nonpolar. We can then apply the idea that the nonpolar solvent will be better for the nonpolar solutes, whereas the polar solvent will be better for the ionic and polar solutes.
Solve C7H16 is a hydrocarbon, so it is molecular and nonpolar. Na2SO4, a compound containing a metal and nonmetals, is ionic. HCl, a diatomic molecule containing two nonmetals that differ in electronegativity, is polar. I2, a diatomic molecule with atoms of equal electronegativity, is nonpolar. We would therefore predict that C7H16 and I2 (the nonpolar solutes) would be more soluble in the nonpolar CCl4 than in polar H2O, whereas water would be the better solvent for Na2SO4 and HCl (the ionic and polar covalent solutes).
Arrange the following substances in order of increasing solubility in water:
Answer: C5H12<C5H11Cl<C5H11OH<C5H10(OH)2 (in order of increasing polarity and hydrogen-bonding ability)
The solubilities of solids and liquids are not appreciably affected by pressure, whereas the solubility of a gas in any solvent is increased as the partial pressure of the gas above the solvent increases. We can understand the effect of pressure on gas solubility by considering FIGURE 13.14, which shows carbon dioxide gas distributed between the gas and solution phases. When equilibrium is established, the rate at which gas molecules enter the solution equals the rate at which solute molecules escape from the solution to enter the gas phase. The equal number of up and down arrows in the left container in Figure 13.14 represent these opposing processes.
If the partial pressure of a gas over a solution is doubled, how has the concentration of gas in the solution changed after equilibrium is restored?
FIGURE 13.14 Effect of pressure on gas solubility.
Now suppose we exert greater pressure on the piston and compress the gas above the solution, as shown in the middle container in FIGURE 13.14. If we reduce the gas volume to half its original value, the pressure of the gas increases to about twice its original value. As a result of this pressure increase, the rate at which gas molecules strike the liquid surface and enter the solution phase increases. Thus, the solubility of the gas in the solution increases until equilibrium is again established; that is, solubility increases until the rate at which gas molecules enter the solution equals the rate at which they escape from the solution. Thus, the solubility of a gas in a liquid solvent increases in direct proportion to the partial pressure of the gas above the solution (FIGURE 13.15).
How do the slopes of the lines vary with the molecular weight of the gas? Explain the trend.
FIGURE 13.15 The solubility of a gas in water is directly proportional to the partial pressure of the gas. The solubilities are in millimoles per liter of solution.
The relationship between pressure and gas solubility is expressed by Henry's law:
Here, Sg is the solubility of the gas in the solvent (usually expressed as molarity), Pg is the partial pressure of the gas over the solution, and k is a proportionality constant known as the Henry's law constant. The value of this constant depends on the solute, solvent, and temperature. As an example, the solubility of N2 gas in water at 25 °C and 0.78 atm pressure is 4.75 × 10–4M. The Henry's law constant for N2 in 25 °C water is thus (4.75 × 10–4 mol/L)/0.78 atm = 6.1 × 10–4 mol/L-atm. If the partial pressure of N2 is doubled, Henry's law predicts that the solubility in water at 25 °C also doubles to 9.50 × 10–4M.
Bottlers use the effect of pressure on solubility in producing carbonated beverages, which are bottled under a carbon dioxide pressure greater than 1 atm. When the bottles are opened to the air, the partial pressure of CO2 above the solution decreases. Hence, the solubility of CO2decreases, and CO2(g) escapes from the solution as bubbles (FIGURE 13.16).
FIGURE 13.16 Gas solubility decreases as pressure decreases. CO2 bubbles out of solution when a carbonated beverage is opened because the CO2 partial pressure above the solution is reduced.
SAMPLE EXERCISE 13.2 A Henry's Law Calculation
Calculate the concentration of CO2 in a soft drink that is bottled with a partial pressure of CO2 of 4.0 atm over the liquid at 25 °C. The Henry's law constant for CO2 in water at this temperature is 3.4 × 10–2 mol/L-atm.
Analyze We are given the partial pressure of CO2, PCO2, and the Henry's law constant, k, and asked to calculate the concentration of CO2 in the solution.
Plan With the information given, we can use Henry's law, Equation 13.4, to calculate the solubility, SCO2.
Solve SCO2 = kPCO2 = (3.4 × 10–2 mol/L-atm)(4.0 atm) = 0.14 mol/L = 0.14 M
Check The units are correct for solubility, and the answer has two significant figures consistent with both the partial pressure of CO2 and the value of Henry's constant.
Calculate the concentration of CO2 in a soft drink after the bottle is opened and equilibrates at 25 °C under a CO2 partial pressure of 3.0 × 10–4 atm.
Answer: 1.0 × 10–5M
CHEMISTRY AND LIFE
BLOOD GASES AND DEEP-SEA DIVING
Because gas solubility increases with increasing pressure, divers who breathe compressed air (FIGURE 13.17) must be concerned about the solubility of gases in their blood. Although the gases are not very soluble at sea level, their solubilities can be appreciable at deep levels where their partial pressures are greater. Thus, divers must ascend slowly to prevent dissolved gases from being released rapidly from solution and forming bubbles in the blood and other fluids in the body. These bubbles affect nerve impulses and cause decompression sickness, or “the bends,” which is a painful and potentially fatal condition. Nitrogen is the main problem because it has the highest partial pressure in air and because it can be removed from the body only through the respiratory system. Oxygen, in contrast, is consumed in metabolism.
Deep-sea divers sometimes substitute helium for nitrogen in the air they breathe because helium has a much lower solubility in biological fluids than N2. For example, divers working at a depth of 100 ft experience a pressure of about 4 atm. At this pressure a mixture of 95% helium and 5% oxygen gives an oxygen partial pressure of about 0.2 atm, which is the partial pressure of oxygen in normal air at 1 atm. If the oxygen partial pressure becomes too great, the urge to breathe is reduced, CO2 is not removed from the body, and CO2 poisoning occurs. At excessive concentrations in the body, carbon dioxide acts as a neurotoxin, interfering with nerve conduction and transmission.
RELATED EXERCISES: 13.59, 13.60, 13.107
FIGURE 13.17 Gas solubility increases as pressure increases. Divers who use compressed gases must be concerned about the solubility of the gases in their blood.
The solubility of most solid solutes in water increases as the solution temperature increases, as FIGURE 13.18 shows. There are exceptions to this rule, however, as seen for Ce2(SO4)3, whose solubility curve slopes downward with increasing temperature.
In contrast to solid solutes, the solubility of gases in water decreases with increasing temperature (FIGURE 13.19). If a glass of cold tap water is warmed, you can see bubbles on the inside of the glass because some of the dissolved air comes out of solution. Similarly, as carbonated beverages are allowed to warm, the solubility of CO2 decreases, and CO2(g) escapes from the solution.
How does the solubility of KCl at 80 °C compare with that of NaCl at the same temperature?
FIGURE 13.18 Solubilities of some ionic compounds in water as a function of temperature.
Where would you expect N2 to fit on this graph?
FIGURE 13.19 Solubilities of four gases in water as a function of temperature. The solubilities are in millimoles per liter of solution, for a constant total pressure of 1 atm in the gas phase.
The decreased solubility of O2 in water as temperature increases is one of the effects of thermal pollution of lakes and streams. The effect is particularly serious in deep lakes because warm water is less dense than cold water. Warm water therefore tends to remain on top of cold water, at the surface. This situation impedes the dissolving of oxygen in the deeper layers, thus stifling the respiration of all aquatic life needing oxygen. Fish may suffocate and die under these conditions.
GIVE IT SOME THOUGHT
Why do bubbles form on the inside wall of a cooking pot when water is heated on the stove, even though the water temperature is well below the boiling point of water?