13.7: End-of-Chapter Material

Exercises (Chemical Equilibrium)

1. Define the law of mass action.

2. What is an equilibrium constant for a chemical reaction? How is it constructed?

3. Write the Keq expression for each reaction.

a. \(\mathrm{H}_2+\mathrm{Cl}_2 \rightleftarrows 2 \mathrm{HCl}\)
b. \(\mathrm{NO}+\mathrm{NO}_2 \rightleftarrows \mathrm{N}_2 \mathrm{O}_3\)

4. Write the Keq expression for each reaction.

a. \(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}+\mathrm{NaI} \rightleftarrows \mathrm{C}_2 \mathrm{H}_5 \mathrm{I}+\mathrm{NaOH}\)
b. \(\mathrm{PCl}_3+\mathrm{Cl}_2 \rightleftarrows \mathrm{PCl}_5\)

5. Write the KP expression for each reaction.

a. \(2 \mathrm{H}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightleftarrows 2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})\)
b. \(2 \mathrm{H}_2 \mathrm{O}_2(\mathrm{~g}) \rightleftarrows 2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})+\mathrm{O}_2(\mathrm{~g})\)

6. Write the KP expression for each reaction.

a. \(\mathrm{CH}_4(\mathrm{~g})+2 \mathrm{O}_2(\mathrm{~g}) \rightleftarrows \mathrm{CO}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})\)
b. \(\mathrm{CH}_4(\mathrm{~g})+4 \mathrm{Cl}_2(\mathrm{~g}) \rightleftarrows \mathrm{CCl}_4(\mathrm{~g})+4 \mathrm{HCl}(\mathrm{g})\)

7. The following reaction is at equilibrium:
\( \quad \quad \quad
\mathrm{PBr}_3+\mathrm{Br}_2 \rightleftarrows \mathrm{PBr}_5
\)

The equilibrium \(\left[\mathrm{Br}_2\right]\) and \(\left[\mathrm{PBr}_5\right]\) are \(2.05 \mathrm{M}\) and \(0.55 \mathrm{M}\), respectively. If the \(\mathrm{Keq}_{\mathrm{eq}}\) is 1.65 , what is the equilibrium \([\mathrm{PBr} 3]\) ?

8. The following reaction is at equilibrium:
\( \quad \quad \quad
\mathrm{CO}+\mathrm{Cl}_2 \rightleftarrows \mathrm{CoCl}_2
\)

The equilibrium [CO] and \(\left[\mathrm{Cl}_2\right]\) are \(0.088 \mathrm{M}\) and \(0.103 \mathrm{M}\), respectively. If the \(K_{\mathrm{eq}}\) is 0.225 , what is the equilibrium \(\left[\mathrm{COCl}_2\right]\) ?

9. The following reaction is at equilibrium:
\( \quad \quad \quad
\mathrm{CH}_4+2 \mathrm{Cl}_2 \rightleftarrows \mathrm{CH}_2 \mathrm{Cl}_2+2 \mathrm{HCl}
\)

If \(\left[\mathrm{CH}_4\right]\) is \(0.250 \mathrm{M},\left[\mathrm{Cl}_2\right]\) is \(0.150 \mathrm{M}\), and \(\left[\mathrm{CH}_2 \mathrm{Cl}_2\right]\) is \(0.175 \mathrm{M}\) at equilibrium, what is [ \(\mathrm{HCl}]\) at equilibrium if the \(K_{\text {eq }}\) is 2.30 ?

10. The following reaction is at equilibrium:
\( \quad \quad \quad
4 \mathrm{HBr}+\mathrm{O}_2 \rightleftarrows 2 \mathrm{H}_2 \mathrm{O}+2 \mathrm{Br}_2
\)

If \([\mathrm{HBr}]\) is \(0.100 \mathrm{M},\left[\mathrm{O}_2\right]\) is \(0.250 \mathrm{M}\), and \(\left[\mathrm{H}_2 \mathrm{O}\right]\) is \(0.0500 \mathrm{M}\) at equilibrium, what is [Br2] at equilibrium if the \(K_{\text {eq }}\) is 0.770 ?

11. Write the KP expression for the following gas-phase reaction:
\( \quad \quad \quad
4 \mathrm{NO}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightleftarrows 2 \mathrm{~N}_2 \mathrm{O}_5(\mathrm{~g})
\)

12. Write the KP expression for the following gas-phase reaction:
\( \quad \quad \quad
\mathrm{ClO}(\mathrm{g})+\mathrm{O}_3(\mathrm{~g}) \rightleftarrows \mathrm{ClO}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g})
\)

13. What is the equilibrium partial pressure of \(\mathrm{COBr}_2\) if the equilibrium partial pressures of \(\mathrm{CO}\) and \(\mathrm{Br}_2\) are \(0.666 \mathrm{~atm}\) and \(0.235 \mathrm{~atm}\) and the \(\mathrm{KP}_{\mathrm{P}}\) for this equilibrium is 4.08 ?
\( \quad \quad \quad
\mathrm{CO}(\mathrm{g})+\mathrm{Br}_2(\mathrm{~g}) \rightleftarrows \mathrm{COBr}_2(\mathrm{~g})
\)

14. What is the equilibrium partial pressure of \(\mathrm{O}_3\) if the equilibrium partial pressure of \(\mathrm{O}_2\) is \(0.0044 \mathrm{~atm}\) and \(\mathrm{KP}_{\mathrm{P}}\) for this equilibrium is 0.00755 ?
\( \quad \quad \quad
3 \mathrm{O}_2(\mathrm{~g}) \rightleftarrows 2 \mathrm{O}_3(\mathrm{~g})
\)

15. Calculate the \(K_P\) for this reaction at \(298 \mathrm{~K}\) if the \(K_{\text {eq }}=1.76 \times 10^{-3}\).
\( \quad \quad \quad
3 \mathrm{O}_2(\mathrm{~g}) \rightleftarrows 2 \mathrm{O}_3(\mathrm{~g})
\)

16. Calculate the \(K_P\) for this reaction at \(310 \mathrm{~K}\) if the \(K_{\text {eq }}=6.22 \times 10^3\).
\( \quad \quad \quad
4 \mathrm{NO}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightleftarrows 2 \mathrm{~N}_2 \mathrm{O}_5(\mathrm{~g})
\)

17. Calculate the \(K_{\text {eq }}\) for this reaction if the \(K_P=5.205 \times 10^{-3}\) at \(660^{\circ} \mathrm{C}\).
\( \quad \quad \quad
\mathrm{CO}(\mathrm{g})+\mathrm{F}_2(\mathrm{~g}) \rightleftarrows \mathrm{COF}_2(\mathrm{~g})
\)

18. Calculate the \(K_{\text {eq }}\) for this reaction if the \(K \mathrm{P}=78.3\) at \(100^{\circ} \mathrm{C}\).
\( \quad \quad \quad
4 \mathrm{HCl}(\mathrm{g})+\mathrm{O}_2(\mathrm{~g}) \rightleftarrows 2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})+2 \mathrm{Cl}_2(\mathrm{~g})
\)

19. Write the correct \(K_{\text {eq }}\) expression for this reaction.
\( \quad \quad \quad
\mathrm{NaOH}(\mathrm{aq})+\mathrm{HCl}(\mathrm{aq}) \rightleftarrows \mathrm{NaCl}(\mathrm{aq})+\mathrm{H}_2 \mathrm{O}(\ell)
\)

20. Write the correct \(K_{\text {eq }}\) expression for this reaction.
\( \quad \quad \quad
\mathrm{AgNO}_3(\mathrm{aq})+\mathrm{NaCl}(\mathrm{aq}) \rightleftarrows \mathrm{AgCl}(\mathrm{s})+\mathrm{NaNO}_3(\mathrm{aq})
\)

21. Write the correct KP expression for this reaction.
\( \quad \quad \quad
\mathrm{CaCO}_3(\mathrm{~s}) \rightleftarrows \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_2(\mathrm{~g})
\)

22. Write the correct KP expression for this reaction.

Answers

1. the relationship between the concentrations of reactants and products of a chemical reaction at equilibrium

3. a. \(\quad K_{\mathrm{eq}}=\dfrac{[\mathrm{HCl}]^2}{\left[\mathrm{H}_2\right]\left[\mathrm{Cl}_2\right]}\)
    b. \(K_{\mathrm{eq}}=\dfrac{\left[\mathrm{N}_2 \mathrm{O}_3\right]}{[\mathrm{NO}]\left[\mathrm{NO}_2\right]}\)

5. a. \(K_{\mathrm{P}}=\dfrac{P_{\mathrm{H}_2 \mathrm{O}}^2}{P_{\mathrm{H}_2}^2 P_{\mathrm{O}_2}}\)
    b. \(K_{\mathrm{P}}=\dfrac{P_{\mathrm{H}_2 \mathrm{O}}^2 P_{\mathrm{O}_2}}{P_{\mathrm{H}_2 \mathrm{O}_2}^2}\)

7. \(0.163 \mathrm{M}\)

9. \(0.272 \mathrm{M}\)

11. \(K_{\mathrm{P}}=\dfrac{P_{\mathrm{N}_2 \mathrm{O}_5}^2}{P_{\mathrm{NO}_2}^4 P_{\mathrm{O}_2}}\)

13. \(0.639 \mathrm{~atm}\)

15. \(7.20 \times 10^{-5}\)

17. \(K_{\text {eq }}=3.98 \times 10^{-1}\)

19. \(K_{\mathrm{eq}}=\dfrac{[\mathrm{NaCl}]}{[\mathrm{NaOH}][\mathrm{HCl}]}\)

21. \(K P=P_{C O}\)

Exercises (Le Chatelier’s principle)

1. Define Le Chatelier's principle.

2. What is meant by a stress? What are some of the ways an equilibrium can be stressed?

3. Given this equilibrium, predict the direction of shift for each stress.
\( \quad \quad \quad
\mathrm{H}_2(\mathrm{~g})+\mathrm{I}_2(\mathrm{~s})+53 \mathrm{~kJ} \rightleftarrows 2 \mathrm{HI}(\mathrm{g})
\)

a. decreased temperature
b. increased pressure
c. removal of \(\mathrm{HI}\)

4. Given this equilibrium, predict the direction of shift for each stress.
\( \quad \quad \quad
\mathrm{H}_2(\mathrm{~g})+\mathrm{F}_2(\mathrm{~g}) \rightleftarrows 2 \mathrm{HF}(\mathrm{g})+546 \mathrm{~kJ}
\)

a. increased temperature
b. addition of \(\mathrm{H}_2\)
c. decreased pressure

5. Given this equilibrium, predict the direction of shift for each stress.
\( \quad \quad \quad
2 \mathrm{SO}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightleftarrows 2 \mathrm{SO}_3(\mathrm{~g})+196 \mathrm{~kJ}
\)

a. removal of \(\mathrm{SO}_3\)
b. addition of \(\mathrm{O}_2\)
c. decreased temperature

6. Given this equilibrium, predict the direction of shift for each stress listed.
\( \quad \quad \quad
\mathrm{CO}_2(\mathrm{~g})+\mathrm{C}(\mathrm{s})+171 \mathrm{~kJ} \rightleftarrows 2 \mathrm{CO}(\mathrm{g})
\)

a. addition of \(\mathrm{CO}\)
b. increased pressure
c. addition of a catalyst

7. The synthesis of \(\mathrm{NH}_3\) uses this chemical reaction.
\( \quad \quad \quad
\mathrm{N}_2(\mathrm{~g})+3 \mathrm{H}_2(\mathrm{~g}) \rightleftarrows 2 \mathrm{NH}_3(\mathrm{~g})+92 \mathrm{~kJ}
\)

Identify three stresses that can be imposed on the equilibrium to maximize the amount of \(\mathrm{NH}_3\).

8. The synthesis of \(\mathrm{CaCO}_3\) uses this chemical reaction.
\( \quad \quad \quad
\mathrm{CaO}(\mathrm{s})+\mathrm{CO}_2(\mathrm{~g}) \rightleftarrows \mathrm{CaCO}_3(\mathrm{~s})+180 \mathrm{~kJ}
\)

Identify three stresses that can be imposed on the equilibrium to maximize the amount of \(\mathrm{CaCO}_3\).

Answers

1. When an equilibrium is stressed, the equilibrium shifts to minimize that stress.

3.

a. toward reactants
b. toward reactants
c. toward products

5.

a. toward products
b. toward products
c. toward products

7. increased pressure, decreased temperature, removal of \(\mathrm{NH}_3\)

Exercises (Calculating Equilibrium Constant Values)

1. Describe the three parts of an ICE chart.
2. What is the relationship between the equilibrium row in an ICE chart and the other two rows?
3. Set up (but do not solve) an ICE chart for this reaction, given the initial conditions.
\( \quad \quad \quad
\begin{array}{c}
3 \mathrm{O}_2(\mathrm{~g}) \\
0.075 \mathrm{M}
\end{array} \rightleftarrows 2 \mathrm{O}_3(\mathrm{~g})
\)
4. Set up (but do not solve) an ICE chart for this reaction, given the initial conditions.
\( \quad \quad \quad
\begin{array}{l}
\mathrm{CH}_4(\mathrm{~g})+2 \mathrm{O}_2(\mathrm{~g}) \rightleftarrows \mathrm{CO}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{g}) \\
0.750 \mathrm{M} \quad 0.450 \mathrm{M} \\
\end{array}
\)
5. Given that pure solids and liquids do not appear in Keq expressions, set up the ICE chart for this reaction, given the initial conditions.
\( \quad \quad \quad
\underset{0.0060 \mathrm{M}}{\mathrm{CH}_4(\mathrm{~g})}+\underset{0.055 \mathrm{M}}{2 \mathrm{O}_2(\mathrm{~g})} \underset{0}{0.05 \mathrm{CO}_2(\mathrm{~g})}+2 \mathrm{H}_2 \mathrm{O}(\ell)
\)
6. Given that pure solids and liquids do not appear in Keq expressions, set up the ICE chart for this reaction, given the initial conditions.
\( \quad \quad \quad
\begin{array}{l}
\mathrm{N}_2 \mathrm{H}_4(\ell)+\mathrm{O}_2(\mathrm{~g}) \rightleftarrows \mathrm{N}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\ell) \\
2.33 \mathrm{M} \quad 1.09 \mathrm{M} \\
\end{array}
\)
7. Determine the equilibrium concentrations for this chemical reaction with the given Keq.
\( \quad \quad \quad
\begin{array}{l}
\mathrm{HCN}(\mathrm{g}) \\
2.00 \mathrm{M}
\end{array} \rightleftarrows \mathrm{HNC}(\mathrm{g}) \quad K_{\mathrm{eq}}=4.50
\)
8. Determine the equilibrium concentrations for this chemical reaction with the given \(K_{\text {eq. }}\)
\( \quad \quad \quad
\begin{array}{l}
\mathrm{IF}_3(\mathrm{~g})+\mathrm{F}_2(\mathrm{~g}) \rightleftarrows \mathrm{IF}_5(\mathrm{~g}) \quad K_{\text {eq }}=7.59 \\
1.0 \mathrm{M} \quad 0.50 \mathrm{M} \\
\end{array}
\)
9. Determine the equilibrium concentrations for this chemical reaction with the given \(K_{\text {eq. }}\)
\( \quad \quad \quad
\begin{array}{l}
\mathrm{N}_2 \mathrm{O}_3(\mathrm{~g}) \rightleftarrows \mathrm{NO}(\mathrm{g})+\mathrm{NO}_2(\mathrm{~g}) \quad K_{\text {eq }}=2.50 \\
0.0663 \mathrm{M}
\end{array}
\)

10. Determine the equilibrium concentrations for this chemical reaction with the given \(K_{\text {eq. }}\)
\( \quad \quad \quad
\begin{array}{l}
\mathrm{CO}(\mathrm{g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g}) \rightleftarrows \mathrm{CO}_2(\mathrm{~g})+\mathrm{H}_2(\mathrm{~g}) \quad K_{\text {eq }}= \\
0.750 \mathrm{M} \quad 0.750 \mathrm{M} \\
\end{array}
\)
11. Determine the equilibrium concentrations for this chemical reaction with the given Keq.
\( \quad \quad \quad
\begin{array}{l}
\mathrm{H}_2 \mathrm{~S}(\mathrm{~g}) \\
0.882 \mathrm{M}
\end{array} \rightleftarrows \mathrm{H}_2(\mathrm{~g})+\mathrm{S}(\mathrm{s}) \quad K_{\text {eq }}=0.055
\)
12. Determine the equilibrium concentrations for this chemical reaction with the given \(K_{\text {eq. }}\)
\( \quad \quad \quad
2 \mathrm{AgCl}(\mathrm{s})+\underset{1.99 \mathrm{M}}{\mathrm{F}_2(\mathrm{~g})} \rightleftarrows 2 \mathrm{AgF}(\mathrm{s})+\mathrm{Cl}_2(\mathrm{~g}) \quad K_{\mathrm{eq}}=
\)

Answers

1. \(\mathrm{I}=\) initial concentrations; \(\mathrm{C}=\) change in concentrations; \(\mathrm{E}=\) equilibrium concentrations

3.  

	\(3O_2\)	\(\rightleftarrows\)	\(2O_3\)
I	0.075		0
C	-3 x		+2 x
E	0.075-3 x		+2 x

5. 

	\(CH_4\)	+	2 \(O_2\)	\(\rightleftarrows\)	\(CO_2\)	+	\(2 H_2 O\)
I	0.0060		0.055		0		0
C	-x		-2 x		+x		-
E	0.0060-x		.055-2 x		+x		-

7. \([\mathrm{HCN}]=0.364 \mathrm{M} ;[\mathrm{HNC}]=1.64 \mathrm{M}\)

9. \(\left[\mathrm{N}_2 \mathrm{O}_3\right]=0.0017 \mathrm{M} ;[\mathrm{NO}]=\left[\mathrm{NO}_2\right]=0.0646 \mathrm{M}\)

11. \(\left[\mathrm{H}_2 \mathrm{~S}\right]=0.836 \mathrm{M} ;\left[\mathrm{H}_2\right]=0.046 \mathrm{M}\)

Exercises (Some Special Types of Equilibria)

1. Explain the difference between the \(K_{\text {eq }}\) and the \(K_{\mathrm{sp}}\).

2. Explain the difference between the \(K_{\mathrm{a}}\) and the \(\mathrm{Kb}\).

3. Write the balanced chemical equation that represents the equilibrium between \(\mathrm{HF}(\mathrm{aq})\) as reactants and \(\mathrm{H}^{+}(\mathrm{aq})\) and \(\mathrm{F}^{-}(\mathrm{aq})\) as products.

4. Write the balanced chemical equation that represents the equilibrium between \(\mathrm{CaF}_2(\mathrm{~s})\) as reactants and \(\mathrm{Ca}^{2+}(\mathrm{aq})\) and \(\mathrm{F}^{-}(\mathrm{aq})\) as products.

5. Assuming that all species are dissolved in solution, write the Keq expression for the chemical equation in Exercise 3.

6. Noting the phase labels, write the \(K_{\mathrm{Sp}}\) expression for the chemical equation in Exercise 4.

7. Determine the concentrations of all species in the ionization of \(0.100 \mathrm{M} \mathrm{HClO}_2\) in \(\mathrm{H}_2 \mathrm{O}\). The \(\mathrm{Ka}_{\mathrm{a}}\) for \(\mathrm{HClO}_2\) is \(1.1 \times 10^{-2}\).

8. Determine the concentrations of all species in the ionization of \(0.0800 \mathrm{M} \mathrm{HCN}\) in \(\mathrm{H}_2 \mathrm{O}\). The \(\mathrm{K}_{\mathrm{a}}\) for \(\mathrm{HCN}\) is \(6.2 \times 10^{-10}\).

9. Determine the \(\mathrm{pH}\) of a \(1.00 \mathrm{M}\) solution of \(\mathrm{HNO}_2\). The \(\mathrm{Ka}_{\mathrm{a}}\) for \(\mathrm{HNO}_2\) is \(5.6 \times 10^{-4}\).

10. Determine the \(\mathrm{pH}\) of a \(3.35 \mathrm{M}\) solution of \(\mathrm{HC}_2 \mathrm{H}_3 \mathrm{O}_2\). The \(\mathrm{Ka}_{\mathrm{a}}\) for \(\mathrm{HC}_2 \mathrm{H}_3 \mathrm{O}_2\) is \(1.8 \times\) \(10^{-5}\).

11. Write the chemical equations and \(K_{\mathrm{a}}\) expressions for the stepwise dissociation of \(\mathrm{H}_3 \mathrm{PO}_4\).

12. Write the chemical equations and \(K_{\mathrm{a}}\) expressions for the stepwise dissociation of \(\mathrm{H}_3 \mathrm{C}_6 \mathrm{H}_5 \mathrm{O}_7\).

13. If the \(\mathrm{Ka}_{\mathrm{a}}\) for \(\mathrm{HNO}_2\) is \(5.6 \times 10^{-4}\), what is the \(\mathrm{Kb}_{\mathrm{b}}\) for \(\mathrm{NO}_2^{-}(\mathrm{aq})\) ?

14. If the \(\mathrm{K}_{\mathrm{a}}\) for \(\mathrm{HCN}\) is \(6.2 \times 10^{-10}\), what is the \(\mathrm{Kb}_{\mathrm{b}}\) for \(\mathrm{CN}^{-}(\mathrm{aq})\) ?

15. What is \(\left[\mathrm{OH}^{-}\right]\)in a solution whose \(\left[\mathrm{H}^{+}\right]\)is \(3.23 \times 10^{-6} \mathrm{M}\) ?

16. What is \(\left[\mathrm{OH}^{-}\right]\)in a solution whose \(\left[\mathrm{H}^{+}\right]\)is \(9.44 \times 10^{-11} \mathrm{M}\) ?

17. What is \(\left[\mathrm{H}^{+}\right]\)in a solution whose \(\left[\mathrm{OH}^{-}\right]\)is \(2.09 \times 10^{-2} \mathrm{M}\) ?

18. What is \(\left[\mathrm{H}^{+}\right]\)in a solution whose \(\left[\mathrm{OH}^{-}\right]\)is \(4.07 \times 10^{-7} \mathrm{M}\) ?

19. Write the balanced chemical equation and the \(K_{\mathrm{sp}}\) expression for the slight solubility of \(\operatorname{Mg}(\mathrm{OH})_2(\mathrm{~s})\).

20. Write the balanced chemical equation and the \(K_{\mathrm{sp}}\) expression for the slight solubility of \(\mathrm{Fe}_2\left(\mathrm{SO}_4\right)_3(\mathrm{~s})\).

21. What are \(\left[\mathrm{Sr}^{2+}\right]\) and \(\left[\mathrm{SO}_4{ }^{2-}\right]\) in a saturated solution of \(\mathrm{SrSO}_4(\mathrm{~s})\) ? The \(\mathrm{K}_{\mathrm{Sp}}\) of \(\mathrm{SrSO}_4(\mathrm{~s})\) is \(3.8 \times 10^{-4}\).

22. What are \(\left[\mathrm{Ba}^{2+}\right]\) and \(\left[\mathrm{F}^{-}\right]\)in a saturated solution of \(\mathrm{BaF}_2(\mathrm{~s})\) ? The \(K_{\mathrm{sp}}\) of \(\mathrm{BaF}_2(\mathrm{~s})\) is \(1.8 \times 10^{-7}\).

23. What are \(\left[\mathrm{Ca}^{2+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\)in a saturated solution of \(\mathrm{Ca}(\mathrm{OH})_2(\mathrm{~s})\) ? The \(\mathrm{K}_{\mathrm{sp}}\) of \(\mathrm{Ca}(\mathrm{OH})_2(\mathrm{~s})\) is \(5.0 \times 10^{-6}\).

24. What are \(\left[\mathrm{Pb}^{2+}\right]\) and \(\left[\mathrm{I}^{-}\right]\)in a saturated solution of \(\mathrm{PbI}_2\) ? The \(K_{\mathrm{sp}}\) for \(\mathrm{PbI}_2\) is 9.8 \(\times 10^{-9}\).

Answers

1. The \(K_{\mathrm{sp}}\) is a special type of the \(K_{\mathrm{eq}}\) and applies to compounds that are only slightly soluble.

3. \(\mathrm{HF}(\mathrm{aq}) \rightleftarrows \mathrm{H}^{+}(\mathrm{aq})+\mathrm{F}^{-}(\mathrm{aq})\)

5. \(K_{\mathrm{eq}}=\dfrac{\left[\mathrm{H}^{+}\right]\left[\mathrm{F}^{-}\right]}{[\mathrm{HF}]}\)

7. \(\left[\mathrm{HClO}_2\right]=0.0719 \mathrm{M} ;\left[\mathrm{H}^{+}\right]=\left[\mathrm{ClO}_2^{-}\right]=0.0281 \mathrm{M}\)

9. 1.63

11.
\( \quad \quad \quad
\begin{array}{l}
\mathrm{H}_3 \mathrm{PO}_4(\mathrm{aq}) \rightleftarrows \mathrm{H}^{+}(\mathrm{aq})+\mathrm{H}_2 \mathrm{PO}_4{ }^{-}(\mathrm{aq}) ; K_{\mathrm{a}}=\dfrac{\left[\mathrm{H}^{+}\right]\left[\mathrm{H}_2 \mathrm{PO}_4^{-}\right]}{\left[\mathrm{H}_3 \mathrm{PO}_4\right]} \\
\mathrm{H}_2 \mathrm{PO}_4{ }^{-}(\mathrm{aq}) \rightleftarrows \mathrm{H}^{+}(\mathrm{aq})+\mathrm{HPO}_4{ }^{2-}(\mathrm{aq}) ; K_{\mathrm{a}}=\dfrac{\left[\mathrm{H}^{+}\right]\left[\mathrm{HPO}_4{ }^{2-}\right]}{\left[\mathrm{H}_2 \mathrm{PO}_4{ }^{-}\right]} \\
\mathrm{HPO}_4{ }^{2-}(\mathrm{aq}) \rightleftarrows \mathrm{H}^{+}(\mathrm{aq})+\mathrm{PO}_4{ }^{3-}(\mathrm{aq}) ; K_{\mathrm{a}}=\dfrac{\left[\mathrm{H}^{+}\right]\left[\mathrm{PO}_4{ }^{3-}\right]}{\left[\mathrm{HPO}_4{ }^{2-}\right]}
\end{array}
\)

13. \(1.8 \times 10^{-11}\)

15. \(3.10 \times 10^{-9} \mathrm{M}\)

17. \(4.78 \times 10^{-13} \mathrm{M}\)

19. \(\mathrm{MgOH}_2(\mathrm{~s}) \rightleftarrows \mathrm{Mg}^{2+}(\mathrm{aq})+2 \mathrm{OH}^{-}(\mathrm{aq}) ; \mathrm{K} \mathrm{sp}=\left[\mathrm{Mg}^{2+}\right]\left[\mathrm{OH}^{-}\right]^2\)

21. \(\left[\mathrm{Sr}^{2+}\right]=\left[\mathrm{SO}_4{ }^{2-}\right]=1.9 \times 10^{-2} \mathrm{M}\)

23. \(\left[\mathrm{Ca}^{2+}\right]=0.011 \mathrm{M} ;\left[\mathrm{OH}^{-}\right]=0.022 \mathrm{M}\)

Additional Exercises

1. What is the relationship between the K_sp expressions for a chemical reaction and its reverse chemical reaction?
    
2. What is the relationship between the K_w value for H₂O and its reverse chemical reaction?
    
3. For the equilibrium \[PCl_{3}(g)+Cl^{2+}(g)\rightleftharpoons PCl_{5}(g)+60kJ\nonumber \]
   list four stresses that serve to increase the amount of PCl₅.
    
4. For the equilibrium \[N_{2}O_{4}+57kJ\rightleftharpoons 2NO_{2}\nonumber \]
   list four stresses that serve to increase the amount of NO₂.
    
5. Does a very large K_eq favor the reactants or the products? Explain your answer.
    
6. Is the K_eq for reactions that favor reactants large or small? Explain your answer.
    
7. Show that K_a × K_b = K_w by determining the expressions for these two reactions and multiplying them together. \[HX(aq)\rightleftharpoons H^{+}(aq)+X^{-}(aq)\\ X^{+}(aq)+H_{2}O(l)\rightleftharpoons HX(aq)+OH^{-}(aq)\nonumber \]
    
8. Is the conjugate base of a strong acid weak or strong? Explain your answer.
    
9. What is the solubility in moles per liter of AgCl? Use data from Table \(\PageIndex{2}\) - Solubility Product Constants for Slightly Soluble Ionic Compounds.
    
10. What is the solubility in moles per liter of Ca(OH)₂? Use data from Table \(\PageIndex{2}\) - Solubility Product Constants for Slightly Soluble Ionic Compounds.
     
11. Under what conditions is K_eq = K_P?
     
12. Under what conditions is K_eq > K_P when the temperature is 298 K?
     
13. What is the pH of a saturated solution of Mg(OH)₂? Use data from Table \(\PageIndex{2}\) - Solubility Product Constants for Slightly Soluble Ionic Compounds.
     
14. What are the pH and the pOH of a saturated solution of Fe(OH)₃? The K_sp of Fe(OH)₃ is 2.8 × 10⁻³⁹.

15. For a salt that has the general formula MX, an ICE chart shows that the K_sp is equal to x², where x is the concentration of the cation. What is the appropriate formula for the K_sp of a salt that has a general formula of MX₂?
     
16. Referring to Exercise 15, what is the appropriate formula for the K_sp of a salt that has a general formula of M₂X₃ if the concentration of the cation is defined as 2x, rather than x?
     
17. Consider a saturated solution of PbBr₂(s). If [Pb²⁺] is 1.33 × 10⁻⁵ M, find each of the following.
    1. [Br⁻]
    2. the K_sp of PbBr₂(s)
        
18. Consider a saturated solution of Pb₃(PO₄)₂(s). If [Pb²⁺] is 7.34 × 10⁻¹⁴ M, find each of the following.
    1. [PO₄³⁻]
    2. the K_sp of Pb₃(PO₄)₂(s)

Answers

1. They are reciprocals of each other.

3. increase the pressure; decrease the temperature; add \(\mathrm{PCl}_3\); add \(\mathrm{Cl}_2\); remove \(\mathrm{PCl}_5\)

5. favor products because the numerator of the ratio for the \(K_{\text {eq }}\) is larger than the denominator

9. \(1.3 \times 10^{-5} \mathrm{~mol} / \mathrm{L}\)

11. \(K_{\mathrm{eq}}=K_{\mathrm{P}}\) when the number of moles of gas on both sides of the reaction is the same.

13. 10.35

15. \(4 x^3\)

17. a. \(2.66 \times 10^{-5} \mathrm{M}\)
     b. \(9.41 \times 10^{-15}\)