Kaplan MCAT General Chemistry Review

The spontaneity of dissolution is not dependent only upon the enthalpy change; solutions may form spontaneously for both endothermic and exothermic dissolutions. The second property that contributes to the spontaneity or nonspontaneity of a solution is the entropy change that occurs in the process. At constant temperature and pressure, entropy always increases upon dissolution. As with any process, the spontaneity or nonspontaneity of dissolution depends upon the change in Gibbs function: Spontaneous processes result in a decrease of free energy, while nonspontaneous processes result in an increase of free energy. Thus, whether dissolution will happen spontaneously or not depends upon both the change in enthalpy and change in entropy for the solute and solvent of the system.

Consider, for example, the formation of another common solution, one that we’ve mentioned a number of times in this book: sodium chloride, table salt, dissolved in water. When NaCl dissolves in water, its component ions dissociate from each other and become surrounded by water molecules. For this new interaction to occur, ion–ion interactions between the Na⁺ and Cl^- must be broken, and hydrogen bonds between water molecules must also be broken. This step requires energy and is therefore endothermic. Because water is polar, it can interact with each of the component ions through ion–dipole interactions: The partially positive hydrogen end of the water molecules will surround the Cl^- ions, and the partially negative oxygen end of the water molecules will surround the Na⁺ ions. The formation of these ion–dipole bonds is exothermic, but not as much so as the endothermicity of breaking the old ones (although it is quite close). As a result, the overall dissolution of table salt into water is endothermic (+0.93 J/mol) and favored at high temperatures.

We’ve considered the enthalpy change for the formation of a sodium chloride solution, and now we need to examine the entropy change. Remember that entropy can be thought of as the measure of the degree to which energy is disbursed throughout a system or the measure of the amount of energy distributed from the system to the surroundings at a given temperature. Another way to understand entropy is the measure of molecular disorder, or the number of energy microstates available to a system at a given temperature. When solid sodium chloride dissolves into water, the rigidly ordered arrangement of the sodium and chloride ions is broken up, as the ion–ion interactions are disrupted and new ion–dipole interactions with the water molecules are formed. The ions, freed from their lattice arrangement, have a greater number of energy microstates available to them (in simpler terms, they are freer to move around in different ways), and consequently, their energy is more distributed and their entropy increases. The water, however, becomes more restricted in its movement because it is now interacting with the ions. The number of energy microstates available to it (that is, the water molecules’ ability to move around in different ways) is reduced, so the entropy of the water decreases. But the increase in the entropy experienced by the dissolved sodium chloride is greater than the decrease in the entropy experienced by the water, so the overall entropy change is positive—energy is overall disbursed by the dissolution of sodium chloride in water. Because of the relatively low endothermicity and relatively large positive change in entropy, sodium chloride will spontaneously dissolve in liquid water.

SOLUBILITY

We need to know more than just whether or not dissolution of a solute into a solvent will be spontaneous or nonspontaneous. We also want to know how much solute will dissolve into a given solvent. The solubility of a substance is the maximum amount of that substance that can be dissolved in a particular solvent at a particular temperature. When this maximum amount of solute has been added, the dissolved solute is in equilibrium with its undissolved state, and we say that the solution is saturated. If more solute is added, it will not dissolve. For example, at 18°C, a maximum of 83 g of glucose (C₆H₁₂O₆) will dissolve in 100 mL of H₂O. Thus, the solubility of glucose is 83 g/100 mL. If more glucose is added to an already saturated glucose solution, it will not dissolve but rather will remain in solid form, precipitating to the bottom of the container. A solution in which the proportion of solute to solvent is small is said to be dilute, and one in which the proportion is large is said to be concentrated. Note that both dilute and concentrated solutions are still considered unsaturated if the maximum equilibrium concentration (saturation) has not been reached.