Key Concepts and Summary
Systems involving two or more chemical equilibria that share one or more reactant or product are called coupled equilibria. Common examples of coupled equilibria include the increased solubility of some compounds in acidic solutions (coupled dissolution and neutralization equilibria) and in solutions containing ligands (coupled dissolution and complex formation). The equilibrium tools from other chapters may be applied to describe and perform calculations on these systems.
Practice Questions
Refer to the Appendices for Ksp and Kf values when needed.
A saturated solution of a slightly soluble electrolyte in contact with some of the solid electrolyte is said to be a system in equilibrium. Explain. Why is such a system called a heterogeneous equilibrium?
Calculate the equilibrium concentration of Ni2+ in a 1.0-M solution [Ni(NH3)6](NO3)2.
Solution
0.014 M
Calculate the equilibrium concentration of Zn2+ in a 0.30-M solution of $Zn(CN)_4^{2-}$.
Calculate the equilibrium concentration of Cu2+ in a solution initially with 0.050 M Cu2+ and 1.00 M NH3.
Solution
$7.2×10^{-15}\;M$
Calculate the equilibrium concentration of Zn2+ in a solution initially with 0.150 M Zn2+ and 2.50 M CN–.
Calculate the molar solubility of Sn(OH)2 in a buffer solution containing equal concentrations of NH3 and $NH_4^+$.
What is the molar solubility of CaF2 in a 0.100-M solution of HF? Ka for HF = $6.4×10^{-4}$.
What is the molar solubility of Tl(OH)3 in a 0.10-M solution of NH3?
Both AgCl and AgI dissolve in NH3.
(a) What mass of AgI dissolves in 1.0 L of 1.0 M NH3?
(b) What mass of AgCl dissolves in 1.0 L of 1.0 M NH3?
The following question is taken from a Chemistry Advanced Placement Examination and is used with the permission of the Educational Testing Service.
Solve the following problem:
$$MgF_2(s)⇌Mg^{2+}(aq)+2F^-(aq)$$
In a saturated solution of MgF2 at 18 °C, the concentration of Mg2+ is $1.21×10^{-3}\;M$. The equilibrium is represented by the preceding equation.
(a) Write the expression for the solubility-product constant, Ksp, and calculate its value at 18 °C.
(b) Calculate the equilibrium concentration of Mg2+ in 1.000 L of saturated MgF2 solution at 18 °C to which 0.100 mol of solid KF has been added. The KF dissolves completely. Assume the volume change is negligible.
(c) Predict whether a precipitate of MgF2 will form when 100.0 mL of a $3.00×10^{-3}\;M$ solution of Mg(NO3)2 is mixed with 200.0 mL of a $2.00×10^{-3}\;M$ solution of NaF at 18 °C. Show the calculations to support your prediction.
(d) At 27 °C the concentration of Mg2+ in a saturated solution of MgF2 is $1.17×10^{-3}\;M$. Is the dissolving of MgF2 in water an endothermic or an exothermic process? Give an explanation to support your conclusion.
Solution
(a) Ksp = [Mg2+][F–]2 = $(1.21×10^{-3})(2×1.21×10^{-3})^2=7.09×10^{-7}\;M$
(b) $7.09×10^{-7}\;M$
(c) Determine the concentration of Mg2+ and F– that will be present in the final volume. Compare the value of the ion product [Mg2+][F–]2 with Ksp. If this value is larger than Ksp, precipitation will occur.
$0.1000 L\times 3.00×10^{-3}\;M$ $Mg(NO_3)_2=0.3000\;L\times M\;Mg(NO_3)_2$
M Mg(NO3)2 = $1.00×10^{-3}\;M$
$0.2000\;L\times 2.00×10^{-3}\;M\;\;NaF=0.3000\;L\times M\;NaF$
M NaF = $1.33×10^{-3}\;M$
ion product = $(1.00×10^{-3})(1.33×10^{-3})^2=1.77×10^{-9}$
This value is smaller than Ksp, so no precipitation will occur.
(d) MgF2 is less soluble at 27 °C than at 18 °C. Because added heat acts like an added reagent, when it appears on the product side, the Le Châtelier’s principle states that the equilibrium will shift to the reactants’ side to counter the stress. Consequently, less reagent will dissolve. This situation is found in our case. Therefore, the reaction is exothermic.
Which of the following compounds, when dissolved in a 0.01-M solution of HClO4, has a solubility greater than in pure water: CuCl, CaCO3, MnS, PbBr2, CaF2? Explain your answer.
Which of the following compounds, when dissolved in a 0.01-M solution of HClO4, has a solubility greater than in pure water: AgBr, BaF2, Ca3(PO4)2, ZnS, PbI2? Explain your answer.
Solution
BaF2, Ca3(PO4)2, ZnS; each is a salt of a weak acid, and the $[H_3O^+]$ from perchloric acid reduces the equilibrium concentration of the anion, thereby increasing the concentration of the cations
What is the effect on the amount of solid Mg(OH)2 that dissolves and the concentrations of Mg2+ and OH– when each of the following are added to a mixture of solid Mg(OH)2 and water at equilibrium?
(a) MgCl2
(b) KOH
(c) HClO4
(d) NaNO3
(e) Mg(OH)2
What is the effect on the amount of CaHPO4 that dissolves and the concentrations of Ca2+ and $HPO_4^{2-}$ when each of the following are added to a mixture of solid CaHPO4 and water at equilibrium?
(a) CaCl2
(b) HCl
(c) KClO4
(d) NaOH
(e) CaHPO4
Solution
Effect on amount of solid CaHPO4, [Ca2+], [OH–]: (a) increase, increase, decrease; (b) decrease, increase, decrease; (c) no effect, no effect, no effect; (d) decrease, increase, decrease; (e) increase, no effect, no effect
Identify all chemical species present in an aqueous solution of Ca3(PO4)2 and list these species in decreasing order of their concentrations. (Hint: Remember that the $PO_4^{3-}$ ion is a weak base.)
| What is your confidence level on this material after reading this Chapter on Other Equilibria? Choose either Green (confident), Yellow (somewhat confident), Red (not confident). |
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