Kaplan MCAT General Chemistry Review

Let x equal the concentration of Pb²⁺. Then 2 x equals the concentration of Br^– in the saturated solution at equilibrium (as [Br^-] is 2 times [Pb²⁺]).

(x)(2x)² = 4x³

2.1 × 10^-6 = 4x³

Key Concept

Every slightly soluble salt of general formula MX will have K_sp = x², where x is the molar solubility.K_sp =x², where x is

Solving for x, the concentration of Pb²⁺ in a saturated solution is 8.07 × 10^-3 M and the concentration of Br^– (2x) is 1.61 × 10^-2 M. Next, we convert 5 g of PbBr₂ into moles:

1.36 × 10^-2 mol of PbBr₂ is dissolved in 1 L of solution, so the concentration of the solution 1.36 × 10^-2 M. Because this is higher than the concentration of a saturated solution, this solution would be supersaturated.

THE COMMON ION EFFECT

The solubility of a substance varies depending on the temperature of the solution, the solvent, and, in the case of a gas-phase solute, the pressure. Solubility is also affected by the addition of other substances to the solution.

One of the more common solution chemistry problems on the MCAT is calculation of the concentration of a salt in a solution that already contains a common ionic constituent. The solubility of a salt is considerably reduced when it is dissolved in a solution that already contains one of its constituent ions compared to its solubility in the pure solvent. This reduction in molar solubility is called the common ion effect. Molar solubility (M ) is the concentration, in moles per liter (mol/L), of the solute in the solution at equilibrium at a given temperature. If X moles of A_mB_n (s) can be dissolved in Y liters of solution to reach saturation, then the molar solubility of A_mB_n (s) is X mol/Y L. Let us repeat the important effect of the common ion: Its presence results in a reduction in the molar solubility of the salt. Note well that the presence of the common ion has no effect on the value of the solubility product constant for the salt. For example, if a salt such as CaF₂ is dissolved into a solvent already containing Ca²⁺ ions (from some other salt, perhaps CaCl₂), the solution will dissolve less CaF₂ compared to the amount that would be dissolved in the pure solvent before the I.P. equals K_sp. The common ion effect is really nothing other than Le Châtelier’s principle in action. Because the solution already contains one of the constituent ions from the right side of the dissociation equilibrium, we can see that the system will shift away from that side toward the left side, where we find the solid salt. A solution system shifting toward the left (solid salt reactant) is not going to favor dissolution. As a result, molar solubility for the solid is reduced, and less of the solid dissolves in the solution (for the same K_sp).

Example: The K_sp of Agl in aqueous solution is 1 × 10^-16 mol/L. If a 1 × 10^-5 M solution of AgNO₃ is saturated with AgI, what will be the final concentration of the iodide ion?

Solution: The concentration of Ag⁺ in the original AgNO₃ solution will be 1 × 10^-5 mol/L. After AgI is added to saturation, the iodide concentration can be found by this formula:

If the AgI had been dissolved in pure water, the concentration of both Ag⁺ and I^- would have been 1 × 10^-8 mol/L. The presence of the common ion, silver, at a concentration 1,000 times higher than what it would normally be in a silver iodide solution has reduced the iodide concentration to 1,000 of what it would have been otherwise. An additional 1 × 10^-11 mol/L of silver will, of course, dissolve in solution along with the iodide ion, but this will not significantly affect the final silver concentration, which is much higher.

Conclusion

Our review of solution chemistry has provided an opportunity for us to consider the nature of solutions, solutes, and solvents and the manner of interaction between solutes and solvents in the formation of solutions. We reviewed solubility and the rules that reflect the solubility of common compounds in water. The different ways of expressing the amount of solute in solution were identified, and examples were given for each unit of concentration, including percent composition, mole fraction, molarity, molality, and normality. Finally, we reviewed the thermodynamic principles of solution equilibria and defined unsaturated, saturated, and supersaturated solutions with reference to ion product (I.P.) and solubility product constant (K_sp), as well as the common ion effect from the perspective of Le Châtelier’s principle for a solution at equilibrium.

CONCEPTS TO REMEMBER