2.7 Solubility

The general rule of solubility is that “like dissolves like.” This means that polar compounds tend to be soluble in polar solvents but insoluble in nonpolar solvents, and nonpolar compounds tend to be soluble in nonpolar solvents but insoluble in polar solvents. These tendencies are outcomes of the intermolecular interactions at play in the pure solute, the pure solvent, and the mixture of the two—the solution.

To see how, we begin with the concept of entropy. As you may recall from general chemistry, entropy is a thermodynamic quantity that increases with the number of equivalent ways the energy in a system can be arranged. Many people like to think of entropy as a measure of disorder, and a system with greater entropy (i.e., one that is more disordered) tends to be more likely to occur than one with less entropy. Importantly, two substances have greater entropy when they are mixed. Therefore:

An increase in entropy provides the driving force for two substances to mix.

If entropy were the only factor, then a given solute would be soluble in any solvent. However, the intermolecular interactions that exist in the mixed and unmixed states must also be considered.

Substances tend not to mix if the intermolecular interactions in the pure solute and pure solvent are sufficiently stronger than those in the solution.

This explains why hexane (CH3CH2CH2CH2CH2CH3), a nonpolar compound, is essentially insoluble in water. As shown in Figure 2-19, induced dipole–induced dipole interactions dominate in pure hexane, whereas hydrogen bonding dominates in pure water. In the hypothetical solution, induced dipole–induced dipole interactions dominate. The much stronger hydrogen bonding that exists in the unmixed state is what prevents the solute and solvent from mixing.

Illustrations of the formation of a hypothetical solution of hexane and water shows three beakers. Two beakers with a plus sign between them are each half-filled with a liquid. The first beaker contains pure hexane with induced dipole-induced dipole interactions, as represented by zigzag line structures with three crests and three troughs. The second beaker contains water, as represented by the structural formulas showing an oxygen atom bonded to two hydrogen atoms, with hydrogen bonds between two molecules. A note above these beakers reads, �Significantly stronger intermolecular interactions exist in the separated substances, so the compounds are not miscible.� An arrow from these two beakers leads to a third beaker that is nearly filled with a hypothetical solution of hexane and water with induced dipole-induced dipole interactions. There is a large red X over the third beaker. The caption reads, �Intermolecular interactions and the insolubility of hexane in water: Thedominant intermolecular interactions present in pure hexane are induced dipole�induceddipole interactions. The dominant intermolecular interaction in pure water is hydrogenbonding. When we consider the hypothetical solution, induced dipole�induced dipoleinteractions remain but hydrogen bonding is diminished. This favors the pure substances onthe left, which explains why hexane is insoluble in water.�
FIGURE 2-19 Intermolecular interactions and the insolubility of hexane in water The dominant intermolecular interactions present in pure hexane are induced dipole–induced dipole interactions. The dominant intermolecular interaction in pure water is hydrogen bonding. When we consider the hypothetical solution, induced dipole–induced dipole interactions remain but hydrogen bonding is diminished. This favors the pure substances on the left, which explains why hexane is insoluble in water.

The story changes when the solute and solvent are both polar or both nonpolar. Ethanol (CH3CH2OH), for example, is infinitely soluble in water. Once again, the strongest intermolecular interaction that exists in the pure separated substances is hydrogen bonding, both in water and in ethanol (Fig. 2-20). Unlike the hexane–water example, however, substantial hydrogen bonding also exists between the solute and solvent molecules in the ethanol–water solution. In this case, the intermolecular interactions are similar in strength in the mixed and unmixed states, so the increase in entropy causes the substances to mix.

Illustrations of the formation of a solution of ethanol and water shows three beakers. Two beakers with a plus sign between them are each half-filled with a liquid. The first beaker contains pure ethanol, as represented by the structural formulas showing a hydroxyl group bonded to an inverted V, with hydrogen bonds between two molecules. The second beaker contains water, as represented by the structural formulas showing an oxygen atom bonded to two hydrogen atoms, with hydrogen bonds between two molecules. An arrow from these two beakers leads to a third beaker that is nearly filled with a solution of ethanol and water with hydrogen bonding between the molecules. There is a large green check mark over the third beaker, and a note that reads, �Similar intermolecular interactions exist in the mixed and unmixed states, so the mixed state is favored due to entropy.� The caption reads, Intermolecularinteractions and the solubility ofethanol in water: Hydrogen bondingexists in pure ethanol, shown in blue, andin pure water, shown in red. Substantialhydrogen bonding also exists betweenmolecules of water and ethanol in asolution, allowing the two substancesto dissolve readily and in anyproportion.
FIGURE 2-20 Intermolecular interactions and the solubility of ethanol in water Hydrogen bonding exists in pure ethanol (blue) and in pure water (red). Substantial hydrogen bonding also exists between molecules of water and ethanol in a solution, allowing the two substances to dissolve readily and in any proportion.

YOUR TURN 2.15
SHOW ANSWERS

Which compound, A or B, do you expect to be more soluble in H2O?

Two skeletal structural formulas showing two different molecules. Each structure shows a zigzag line with three crests and three troughs. The position at the end of the line in the second structure is occupied by an amine group.

The amineBis more soluble in H2O than the alkaneA because RNH2 is capable of hydrogen bonding with H2O, whereas RCH3 is not.

Connections Toluene is an important organic solvent, but it is also a precursor in the production of 2,4,6-trinitrotoluene (TNT) and other industrial compounds. In biochemistry, red blood cells can be lysed by toluene to extract hemoglobin.

An illustration shows a cluster of biconcave red blood cells.

Solved Problem 2.16

Would you expect butan-1-ol or diethyl ether to be more soluble in toluene (C6H5CH3)? Explain.

Skeletal structural formulas of toluene, butan-1-ol, and diethyl ether. The structure of toluene shows a benzene ring bonded to a methyl group. The structure of butan-1-ol shows a zigzag four-carbon chain with a hydroxyl group at the first position. The structure of diethyl ether shows an oxygen atom bonded to two ethyl groups.

Think
SHOW SECTION

What are the relative strengths of the intermolecular interactions in the pure substances that would be disrupted on mixing? How do these compare to the strengths of the intermolecular interactions that would be gained?

Solve
SHOW SECTION

Toluene is nonpolar, so the only interactions that can exist between toluene and each of the given compounds involve a relatively weak induced dipole on toluene. As such, the solute–solvent interactions are roughly the same in both mixtures. The dominant interactions that would be lost from pure diethyl ether are dipole–dipole interactions, whereas hydrogen bonding would be lost from pure butan-1-ol. Because hydrogen bonding is typically stronger than dipole–dipole interactions, mixing is less favorable for butan-1-ol, making diethyl ether more soluble in toluene.

problem 2.17 Which compound, C or D, would you expect to be more soluble in toluene (C6H5CH3)? Explain.

Skeletal structural formulas of two molecules labeled C and D. The first structure shows a benzene ring bonded to a carboxyl group. The second structure shows a benzene ring bonded to a carbon atom, which is bonded by a double bond to an oxygen atom and by a single bond to another oxygen atom, which is bonded to a sodium atom.

2.7a The Solubility of Ionic Compounds: Ion–Dipole Interactions and Solvation

Based on what we’ve discussed so far, it might seem peculiar that an ionic compound such as sodium methanoate (sodium formate, Na+) dissolves in a polar solvent like water, because doing so eliminates ion–ion interactions, the strongest of the intermolecular forces. Yet sodium methanoate does dissolve in water, and its water solubility (like that of most ionic compounds) is quite high (Table 2-4, p. 81). Why?

When an ionic compound like sodium methanoate dissolves in water, it does so as its individual ions, Na+ and , not as uncharged formula units. These free ions can interact with water molecules via ion–dipole interactions, a kind of intermolecular interaction different from the ones we have examined thus far. In these particular ion–dipole interactions, the positive end of water’s dipole attracts a anion and the negative end attracts a Na+ cation (Fig. 2-21).

Two illustrations show the interactions between an ion and a dipole. The first illustration shows the condensed structural formula of a methanoate ion below an electrostatic potential map of a water molecule, represented by a ball-and-stick model. The structure of the ion shows a central carbon atom bonded to an oxygen atom by a double bond, and to a hydrogen atom and an oxygen atom carrying a negative charge by single bonds. The ion is enclosed in a red circle. The triangular electrostatic map of water is shaded in red at the upper end representing the oxygen atom, and in blue at the two lower ends, each representing a hydrogen atom. The central portion is shaded in yellow, green, and turquoise from top to bottom. The lower end of the electrostatic map shows a partial positive charge. An arrow with a note, �Anion attracted to the dipole�s partial positive charge,� points to this illustration. The second illustration shows a positively charged sodium ion above an electrostatic potential map of a water molecule, represented by a ball-and-stick model. The triangular electrostatic map of water is shaded in the same manner as in the first illustration. Here, the upper end shows a partial negative charge. An arrow with a note, �Cation attracted to the dipole�s partial negative charge,� points to this illustration. The caption reads, �Ion�dipoleinteractions: a. An ion�dipoleinteraction between HCO22and H2O.The anion interacts with the positiveend of water�s dipole. b. An ion�dipole interaction between Na1 and amolecule of water. The cation interactswith the negative end of water�sdipole.�
FIGURE 2-21 Ion–dipole interactions (a) An ion–dipole interaction between HCO2- and H2O. The anion interacts with the positive end of water’s dipole. (b) An ion–dipole interaction between Na+ and a molecule of water. The cation interacts with the negative end of water’s dipole.

Notice that an ion–dipole interaction involves a full charge and a partial charge. The concentration of charge involved in an ion–dipole interaction is generally less than in an ion–ion interaction but more than in a dipole–dipole interaction. Consequently:

The strength of an ion–dipole interaction is intermediate between that of an ion–ion interaction and that of a dipole–dipole interaction.

How, then, are ion–dipole interactions capable of overcoming the stronger ion–ion interactions to dissolve an ionic compound? A major factor is solvation, depicted in Figure 2-22 (next page), in which an individual ion participates in multiple ion–dipole interactions with the solvent. When this occurs, the ions are said to be solvated. The collective stability from all of these ion–dipole interactions can be substantially greater than that of the ion–ion interactions in an ionic compound, thus making the mixture more favored (more stable).

Two illustrations show the interactions between an ion and a dipole when ionic compounds dissolve in water. The first illustration shows the condensed structural formula of a methanoate ion surrounded by electrostatic potential maps of six water molecule, each represented by a ball-and-stick model. The structure of the ion shows a central carbon atom bonded to an oxygen atom by a double bond, and to a hydrogen atom and an oxygen atom carrying a negative charge by single bonds. The ion is enclosed in a red circle. The triangular electrostatic map of each water molecule is shaded in red at the upper end representing the oxygen atom, and in blue at the two lower ends, each representing a hydrogen atom. The central portion is shaded in yellow, green, and turquoise from top to bottom. The blue ends of each electrostatic map show a partial positive charge and point toward the central ion. A note above this illustration reads, �The positive end of water�s dipole solvates the methanoate anion via multiple ion�dipole interactions.� The second illustration shows a positively charged sodium ion surrounded by electrostatic potential maps of six water molecule, each represented by a ball-and-stick model. The triangular electrostatic map of each water molecule is shaded in the same manner as in the first illustration. Here, the red end of each electrostatic map shows a partial negative charge, and points toward the central ion. A note above this illustration reads, �The negative end of water�s dipole solvates the sodium cation via multiple ion�dipole interactions.� The caption reads, Solvation: Ioniccompounds can dissolve in water asa result of solvation of the respectiveions. a. The positive end of water�sdipole solvates the HCO2 anion. b. The negativeend of water�s dipole solvates the sodium ion.
FIGURE 2-22 Solvation Ionic compounds can dissolve in water as a result of solvation of the respective ions. (a) The positive end of water’s dipole solvates HCO2-. (b) The negative end of water’s dipole solvates Na+.

YOUR TURN 2.16
SHOW ANSWERS

In Figure 2-22, how many total ion–dipole interactions are depicted for the two ions?

Each ion is shown with 6 ion–dipole interactions, giving 12 total for the two ions.

Two illustrations determine the total ion�dipole interactions when ionic compounds dissolve in water. The first illustration shows the condensed structural formula of a methanoate ion surrounded by electrostatic potential maps of six water molecule, each represented by a ball-and-stick model. The structure of the ion shows a central carbon atom bonded to an oxygen atom by a double bond, and to a hydrogen atom and an oxygen atom carrying a negative charge by single bonds. The ion is enclosed in a red circle. The triangular electrostatic map of each water molecule is shaded in red at the upper end representing the oxygen atom, and in blue at the two lower ends, each representing a hydrogen atom. The central portion is shaded in yellow, green, and turquoise from top to bottom. The blue ends of each electrostatic map show a partial positive charge and point toward the central ion. The six partial positive charges of water molecules are pointed by dotted arrows to a common note above the illustration, which reads, �Anion attracted to the dipole�s partial positive charge.� The second illustration shows a positively charged sodium ion surrounded by electrostatic potential maps of six water molecule, each represented by a ball-and-stick model. The triangular electrostatic map of each water molecule is shaded in the same manner as in the first illustration. Here, the red end of each electrostatic map shows a partial negative charge, and points toward the central ion. The six partial negative charges of water molecules are pointed by dotted arrows to a common note below the illustration, which reads, �Cation attracted to the dipole�s partial negative charge.�

The strength of an individual ion–dipole interaction depends on the polarity of the solvent molecule, so the collective stability provided by solvation does, too (see Solved Problem 2.18). This is important because, as we discuss in Chapter 9, a solvent’s ability to solvate ions can have a dramatic effect on the outcome of reactions.

Solved Problem 2.18

In which solvent would you expect NaCl to be more soluble, diethyl ether (CH3CH2OCH2CH3) or propanal (CH3CH2CH═O)?

Think
SHOW SECTION

What are the most important intermolecular interactions that would be disrupted on dissolution? What intermolecular interactions would be gained in the solution? In which solvent are those intermolecular interactions stronger?

Solve
SHOW SECTION

Very strong ion–ion interactions are disrupted when NaCl dissolves. Both diethyl ether and propanal are polar molecules, so ion–dipole interactions would be present in solution with both solvents. Propanal, however, has a much larger dipole moment (compare the dipole moments of ethanal and dimethyl ether in Table 2-4, p. 81), so it will better solvate the Na+ and Cl– ions.

problem 2.19 NaCl is more soluble in methanol (CH3OH) than in propan-1-ol (CH3CH2CH2OH). Which solvent is better at solvating ions?

2.7b The Effect of Hydrocarbon Groups on Solubility

The types of functional groups present in a molecule have a direct effect on its solubility in various solvents, because the functional groups determine the kinds of intermolecular interactions that are available to the molecule. Alcohols, for example, can always hydrogen bond with water due to the presence of the hydrophilic (“water loving”) OH group. Thus, small alcohols like methanol (CH3OH), ethanol (CH3CH2OH), and propan-1-ol (CH3CH2CH2OH) are infinitely soluble in water, as shown in Table 2-6.

Table 2-6 shows, however, that the water solubility of an alcohol decreases as the size of the R group—the hydrocarbon portion of the molecule—increases. This is because R groups are highly nonpolar; they are hydrophobic (“water fearing”). We can generalize this trend as follows:

Table 2-6 is titled, water solubility of some simple alcohols (R-OH). The table has four columns and five rows. The rows represent different alcohol molecules. The columns represent the water solubility of these alcohols. Data are included in the accompanying table. | Alcohol Water solubility (grams per 100 grams of water) Alcohol Water solubility (grams per 100 grams of water) | Methanol, where a carbon is bonded to three hydrogen atoms and a hydroxyl group. Infinitely soluble Pentan-1-ol, with a five-carbon chain where carbon 1 is bonded to a hydroxyl group. 2.7 | Ethanol, with a two-carbon chain where carbon 1 is bonded to a hydroxyl group. Infinitely soluble Hexan-1-ol, with a six-carbon chain where carbon 1 is bonded to a hydroxyl group. 0.6 | Propan-1-ol, with a three-carbon chain where carbon 1 is bonded to a hydroxyl group. Infinitely soluble Heptan-1-ol, with a seven-carbon chain where carbon 1 is bonded to a hydroxyl group. 0.1 | Butan-1-ol, with a four-carbon chain where carbon 1 is bonded to a hydroxyl group. 7.7 Empty cell Empty cell

A species behaves more like a nonpolar alkane as the size of its alkyl group increases.

problem 2.20 Which functional groups in Table 1-6 (p. 35) would be considered hydrophilic? Which would be considered hydrophobic?

Condensed structural formula of sucrose, C12 H22 O12. The structure shows a chair-shaped six-membered ring, constituted by five carbon atoms, numbered from 1 to 5, and an oxygen atom, bonded via a connecting oxygen atom to a pentagonal, five-membered ring, constituted by four carbon atoms, numbered from 8 to 11, and an oxygen atom. Carbons 2, 3, and 4 in the chair-shaped ring are each bonded to a hydrogen atom and a hydroxyl group. Carbon 5 is bonded to carbon 6, which is bonded to a hydroxyl group. Carbon 1 is bonded to the connecting oxygen atom, which is bonded on the other side to carbon 8 in the pentagonal ring. Carbon 8 is bonded to carbon 7, which is bonded to a hydroxyl group. Carbons 9 and 10 are each bonded to a hydrogen atom and a hydroxyl group in reverse. Carbon 11 is bonded to a hydrogen atom and to carbon 12, which is bonded to a hydroxyl group. The caption reads, The water solubilityof sucrose: The large number of hydroxyl groups compared to carbon atoms makessucrose soluble in water.
FIGURE 2-23 The water solubility of sucrose The large number of OH groups compared to C atoms makes sucrose soluble in water.

Monoalcohols (i.e., alcohols with one OH group) are generally considered insoluble in water if they contain six or more carbons. The effect of the alkyl group, however, can be overcome by increasing the number of hydrophilic functional groups. Typically, molecules are found to be highly water soluble if the ratio of their total number of carbon atoms to the number of hydrophilic functional groups is less than about 3∶1. Sucrose (table sugar), for example, is highly soluble in water despite the fact that it has 12 carbon atoms (Fig. 2-23). This is because it contains eight hydrophilic OH groups, so its ratio of carbon atoms to hydrophilic groups is 12∶8 = 1.5∶1, which is less than 3∶1.

Solved Problem 2.21

Would you expect each of the following compounds to be soluble in water? Why or why not?

The skeletal structural formulas of three molecules, labeled A, B, and C. The third is a molecule of 2-naphthol. The first structure shows a zigzag line with four crests and three troughs. A hydroxyl group is bonded to the atom at the third position, and another hydroxyl group occupies the seventh position. The second structure shows a hexagonal six-membered ring with a hydroxyl group bonded to one of the atoms. The third structure is a molecule of 2-naphthol, which shows a benzene ring fused with another hexagonal, six-membered ring. In the second ring, double bonds exist between atoms 1 and 2, and atoms 3 and 4. A hydroxyl group is bonded to the atom in the second position in the second ring.

Think
SHOW SECTION

What is the ratio of alcohol groups to the number of carbon atoms of the hydrocarbon group?

Solve
SHOW SECTION

Molecule A contains six carbons and two hydrophilic OH groups, giving it a ratio of 3∶1. We therefore expect A to be highly soluble in water. For molecules B and C, however, the ratios are 6∶1 and 10∶1, respectively, both of which exceed the 3∶1 cutoff. We therefore expect nonpolar groups in B and C to dominate the intermolecular interactions, causing the molecules to be insoluble in water.

problem 2.22 Like alcohols, aldehydes (R—CH═O) become less soluble in water as the number of carbon atoms in the alkyl group R increases. Do you think the maximum number of carbon atoms for water-soluble aldehydes will be greater than or less than that for water-soluble alcohols? Explain.

Connections 2-Naphthol (molecule C in Solved Problem 2.21) is widely used as a precursor in the production of dyes, such as Sudan I.

An illustration shows the skeletal structural formula of a Sudan I molecule. The structure shows a benzene ring fused with another hexagonal, six-membered ring. In the second ring, double bonds exist between atoms 1 and 2, and atoms 3 and 4. A hydroxyl group is bonded to the atom in the second position in the second ring. Carbon 1 is bonded by a single bond to a nitrogen atom, which is bonded by a double bond to another nitrogen atom. This atom is bonded to a benzene ring.