6.12: Problems

1. Write equilibrium constant expressions for the following reactions. What is the value for each reaction’s equilibrium constant?

(a) \(\mathrm{NH}_{3}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q) \rightleftharpoons \mathrm{N} \mathrm{H}_{4}^{+}(a q)\)

(b) \(\operatorname{PbI}_{2}(s)+\mathrm{S}^{2-}(a q) \rightleftharpoons \operatorname{PbS}(s)+2 \mathrm{I}^{-}(a q)\)

(c) \(\operatorname{CdY}^{2-}(a q)+4 \mathrm{CN}^{-}(a q) \rightleftharpoons \mathrm{Cd}(\mathrm{CN})_{4}^{2-}(a q)+\mathrm{Y}^{4-}(a q)\); note: Y is the shorthand symbol for EDTA

(d) \(\mathrm{AgCl}(s)+2 \mathrm{NH}_{3}(a q)\rightleftharpoons\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}^{+}(a q)+\mathrm{Cl}^{-}(a q)\)

(e) \(\mathrm{BaCO}_{3}(s)+2 \mathrm{H}_{3} \mathrm{O}^{+}(a q)\rightleftharpoons \mathrm{Ba}^{2+}(a q)+\mathrm{H}_{2} \mathrm{CO}_{3}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l)\)

2. Use a ladder diagram to explain why the first reaction is favorable and why the second reaction is unfavorable.

\[\mathrm{H}_{3} \mathrm{PO}_{4}(a q)+\mathrm{F}^{-}(a q)\rightleftharpoons\mathrm{HF}(a q)+\mathrm{H}_{2} \mathrm{PO}_{4}^{-}(a q) \nonumber\]

\[\mathrm{H}_{3} \mathrm{PO}_{4}(a q)+2 \mathrm{F}^{-}(a q)\rightleftharpoons2 \mathrm{HF}(a q)+\mathrm{HPO}_{4}^{2-}(a q) \nonumber\]

Determine the equilibrium constant for these reactions and verify that they are consistent with your ladder diagram.

3. Calculate the potential for the following redox reaction for a solution in which [Fe³⁺] = 0.050 M, [Fe²⁺] = 0.030 M, [Sn²⁺] = 0.015 M and [Sn⁴⁺] = 0.020 M.

\[2 \mathrm{Fe}^{3+}(a q)+\mathrm{Sn}^{2+}(a q)\rightleftharpoons\mathrm{Sn}^{4+}(a q)+2 \mathrm{Fe}^{2+}(a q) \nonumber\]

4. Calculate the standard state potential and the equilibrium constant for each of the following redox reactions. Assume that [H₃O⁺] is 1.0 M for an acidic solution and that [OH^–] is 1.0 M for a basic solution. Note that these reactions are not balanced. Reactions (a) and (b) are in acidic solution; reaction (c) is in a basic solution.

(a) \(\mathrm{MnO}_{4}^{-}(a q)+\mathrm{H}_{2} \mathrm{SO}_{3}(a q)\rightleftharpoons \mathrm{Mn}^{2+}(a q)+\mathrm{SO}_{4}^{2-}(a q)\)

(b) \(\mathrm{IO}_{3}^{-}(a q)+\mathrm{I}^{-}(a q) \rightleftharpoons \mathrm{I}_{2}(a q)\)

(c) \(\mathrm{ClO}^{-}(a q)+\mathrm{I}^{-}(a q) \rightleftharpoons \mathrm{IO}_{3}^{-}(a q)+\mathrm{Cl}^{-}(a q)\)

5. One analytical method for determining the concentration of sulfur is to oxidize it to \(\text{SO}_4^{2-}\) and then precipitate it as BaSO₄ by adding BaCl₂. The mass of the resulting precipitate is proportional to the amount of sulfur in the original sample. The accuracy of this method depends on the solubility of BaSO₄, the reaction for which is shown here.

\[\mathrm{BaSO}_{4}(s) \rightleftharpoons \mathrm{Ba}^{2+}(a q)+\mathrm{SO}_{4}^{2-}(a q) \nonumber\]

For each of the following, predict the affect on the solubility of BaSO₄: (a) decreasing the solution’s pH; (b) adding more BaCl₂; and (c) increasing the solution’s volume by adding H₂O.

6. Write a charge balance equation and one or more mass balance equations for the following solutions.

(a) 0.10 M NaCl

(b) 0.10 M HCl

(c) 0.10 M HF

(d) 0.10 M NaH₂PO₄

(e) MgCO₃ (saturated solution)

(f) 0.10 M \(\text{Ag(CN)}_2^-\) (prepared using AgNO₃ and KCN)

(g) 0.10 M HCl and 0.050 M NaNO₂

7. Use the systematic approach to equilibrium problems to calculate the pH of the following solutions. Be sure to state and justify any assumptions you make in solving the problems.

(a) 0.050 M HClO₄

(b) \(1.00 \times 10^{-7}\) M HCl

(c) 0.025 M HClO

(d) 0.010 M HCOOH

(e) 0.050 M Ba(OH)₂

(f) 0.010 M C₅H₅N

8. Construct ladder diagrams for the following diprotic weak acids (H₂A) and estimate the pH of 0.10 M solutions of H₂A, NaHA, and Na₂A.

(a) maleic acid

(b) malonic acid

(c) succinic acid

9. Use the systematic approach to solving equilibrium problems to calculate the pH of (a) malonic acid, H₂A; (b) sodium hydrogenmalonate, NaHA; and (c) sodium malonate, Na₂A. Be sure to state and justify any assumptions you make in solving the problems.

10. Ignoring activity effects, calculate the molar solubility of Hg₂Br₂ in the following solutions. Be sure to state and justify any assumption you make in solving the problems.

(a) a saturated solution of Hg₂Br₂

(b) 0.025 M Hg₂(NO₃)₂ saturated with Hg₂Br₂

(c) 0.050 M NaBr saturated with Hg₂Br₂

11. The solubility of CaF₂ is controlled by the following two reactions

\[\mathrm{CaF}_{2}(s) \rightleftharpoons \mathrm{Ca}^{2+}(a q)+2 \mathrm{F}^{-}(a q) \nonumber\]

\[\mathrm{HF}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\rightleftharpoons\mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{F}^{-}(a q) \nonumber\]

Calculate the molar solubility of CaF₂ in a solution that is buffered to a pH of 7.00. Use a ladder diagram to help simplify the calculations. How would your approach to this problem change if the pH is buffered to 2.00? What is the solubility of CaF₂ at this pH? Be sure to state and justify any assumptions you make in solving the problems.

12. Calculate the molar solubility of Mg(OH)₂ in a solution buffered to a pH of 7.00. How does this compare to its solubility in unbuffered deionized water with an initial pH of 7.00? Be sure to state and justify any assumptions you make in solving the problem.

13. Calculate the solubility of Ag₃PO₄ in a solution buffered to a pH of 9.00. Be sure to state and justify any assumptions you make in solving the problem.

14. Determine the equilibrium composition of saturated solution of AgCl. Assume that the solubility of AgCl is influenced by the following reactions

\[\mathrm{AgCl}(s) \rightleftharpoons \mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q) \nonumber\]

\[\operatorname{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q) \rightleftharpoons \operatorname{AgCl}(a q) \nonumber\]

\[\operatorname{AgCl}(a q)+\mathrm{Cl}^{-}(a q) \rightleftharpoons \operatorname{AgCl}_{2}^-(a q) \nonumber\]

Be sure to state and justify any assumptions you make in solving the problem.

15. Calculate the ionic strength of the following solutions

(a) 0.050 M NaCl

(b) 0.025 M CuCl₂

(c) 0.10 M Na₂SO₄

16. Repeat the calculations in Problem 10, this time correcting for the effect of ionic strength. Be sure to state and justify any assumptions you make in solving the problems.

17. Over what pH range do you expect Ca₃(PO₄)₂ to have its minimum solubility?

18. Construct ladder diagrams for the following systems, each of which consists of two or three equilibrium reactions. Using your ladder diagrams, identify all reactions that are likely to occur in each system?

(a) HF and H₃PO₄

(b) \(\text{Ag(CN)}_2^-\), \(\text{Ni(CN)}_4^{2-}\), and \(\text{Fe(CN)}_6^{3-}\)

(c) \(\text{Cr}_2\text{O}_7^{2-}/\text{Cr}^{3+}\) and Fe³⁺/Fe²⁺

19. Calculate the pH of the following acid–base buffers. Be sure to state and justify any assumptions you make in solving the problems.

(a) 100.0 mL of 0.025 M formic acid and 0.015 M sodium formate

(b) 50.00 mL of 0.12 M NH₃ and 3.50 mL of 1.0 M HCl

(c) 5.00 g of Na₂CO₃ and 5.00 g of NaHCO₃ diluted to 0.100 L

20. Calculate the pH of the buffers in Problem 19 after adding 5.0 mL of 0.10 M HCl. Be sure to state and justify any assumptions you make in solving the problems.

21. Calculate the pH of the buffers in Problem 19 after adding 5.0 mL of 0.10 M NaOH. Be sure to state and justify any assumptions you make in solving the problems.

22. Consider the following hypothetical complexation reaction between a metal, M, and a ligand, L

\[\mathrm{M}(a q)+\mathrm{L}(a q) \rightleftharpoons \mathrm{ML}(a q) \nonumber\]

for which the formation constant is \(1.5 \times 10^8\). (a) Derive an equation similar to the Henderson–Hasselbalch equation that relates pM to the concentrations of L and ML. (b) What is the pM for a solution that contains 0.010 mol of M and 0.020 mol of L? (c) What is pM if you add 0.002 mol of M to this solution? Be sure to state and justify any assumptions you make in solving the problem.

23. A redox buffer contains an oxidizing agent and its conjugate reducing agent. Calculate the potential of a solution that contains 0.010 mol of Fe³⁺ and 0.015 mol of Fe²⁺. What is the potential if you add sufficient oxidizing agent to convert 0.002 mol of Fe²⁺ to Fe³⁺? Be sure to state and justify any assumptions you make in solving the problem.

24. Use either Excel or R to solve the following problems. For these problems, make no simplifying assumptions.

(a) the solubility of CaF₂ in deionized water

(b) the solubility of AgCl in deionized water

(c) the pH of 0.10 M fumaric acid

25. Derive equation 6.10.1 for the rigorous solution to the pH of 0.1 M HF.