15.3 Multiple equilibria  (Page 5/8)

Solubility equilibrium of a slightly soluble solid

(a) MgCl ₂

(b) KOH

(c) an acid

(d) NaNO ₃

(e) Mg(OH) ₂

Solution

(a) The reaction shifts to the left to relieve the stress produced by the additional Mg ²⁺ ion, in accordance with Le Châtelier’s principle. In quantitative terms, the added Mg ²⁺ causes the reaction quotient to be larger than the solubility product ( Q > K _sp ), and Mg(OH) ₂ forms until the reaction quotient again equals K _sp . At the new equilibrium, [OH ^– ] is less and [Mg ²⁺ ] is greater than in the solution of Mg(OH) ₂ in pure water. More solid Mg(OH) ₂ is present.

(b) The reaction shifts to the left to relieve the stress of the additional OH ^– ion. Mg(OH) ₂ forms until the reaction quotient again equals K _sp . At the new equilibrium, [OH ^– ] is greater and [Mg ²⁺ ] is less than in the solution of Mg(OH) ₂ in pure water. More solid Mg(OH) ₂ is present.

(c) The concentration of OH ^– is reduced as the OH ^– reacts with the acid. The reaction shifts to the right to relieve the stress of less OH ^– ion. In quantitative terms, the decrease in the OH ^– concentration causes the reaction quotient to be smaller than the solubility product ( Q < K _sp ), and additional Mg(OH) ₂ dissolves until the reaction quotient again equals K _sp . At the new equilibrium, [OH ^– ] is less and [Mg ²⁺ ] is greater than in the solution of Mg(OH) ₂ in pure water. More Mg(OH) ₂ is dissolved.

(d) NaNO ₃ contains none of the species involved in the equilibrium, so we should expect that it has no appreciable effect on the concentrations of Mg ²⁺ and OH ^– . (As we have seen previously, dissolved salts change the activities of the ions of an electrolyte. However, the salt effect is generally small, and we shall neglect the slight errors that may result from it.)

(e) The addition of solid Mg(OH) ₂ has no effect on the solubility of Mg(OH) ₂ or on the concentration of Mg ²⁺ and OH ^– . The concentration of Mg(OH) ₂ does not appear in the equation for the reaction quotient:

Thus, changing the amount of solid magnesium hydroxide in the mixture has no effect on the value of Q , and no shift is required to restore Q to the value of the equilibrium constant.

Check your learning

(a) Ni(NO ₃ ) ₂

(b) KClO ₄

(c) NiCO ₃

(d) K ₂ CO ₃

(e) HNO ₃ (reacts with carbonate giving ${\text{HCO}}_3{}^{\text{−}}$ or H ₂ O and CO ₂ )

Key concepts and summary

Several systems we encounter consist of multiple equilibria, systems where two or more equilibria processes are occurring simultaneously. Some common examples include acid rain, fluoridation, and dissolution of carbon dioxide in sea water. When looking at these systems, we need to consider each equilibrium separately and then combine the individual equilibrium constants into one solubility product or reaction quotient expression using the tools from the first equilibrium chapter. Le Châtelier’s principle also must be considered, as each reaction in a multiple equilibria system will shift toward reactants or products based on what is added to the initial reaction and how it affects each subsequent equilibrium reaction.