Chapter 16

Show that when \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) is reduced to half its original value, the \(\mathrm{pH}\) of a solution increases by 0.30 unit, regardless ofthe initial \(p H .\) Is it also true that when any solution is diluted to half its original concentration, the pH increases by 0.30 unit? Explain.

Explain why \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) in a strong acid solution doubles as the total acid concentration doubles, whereas in a weak acid solution, \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) increases only by about a factor of \(\sqrt{2}\)

You are asked to prepare a 100.0 mL sample of a solution with a pH of 5.50 by dissolving the appropriate amount of a solute in water with \(\mathrm{pH}=7.00 .\) Which of these solutes would you use, and in what quantity? Explain your choice. (a) \(15 \mathrm{M} \mathrm{NH}_{3}(\mathrm{aq}) ;\) (b) \(12 \mathrm{M} \mathrm{HCl}(\mathrm{aq})\) (c) \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{s}) ;\) (d) glacial (pure) acetic acid, \(\mathrm{CH}_{3} \mathrm{COOH}\)

It is possible to write simple equations to relate \(\mathrm{pH}\) \(\mathrm{p} K,\) and molarities \((\mathrm{M})\) of various solutions. Three such equations are shown here. $$\begin{aligned} &\text {Weak acid: } \quad \mathrm{pH}=\frac{1}{2} \mathrm{pK}_{\mathrm{a}}-\frac{1}{2} \log \mathrm{M}\\\ &\text { Weak base: } \mathrm{pH}=14.00-\frac{1}{2} \mathrm{pK}_{\mathrm{b}}+\frac{1}{2} \log \mathrm{M} \end{aligned}$$ Salt ofweak \(\operatorname{acid}\left(\mathrm{pK}_{\mathrm{a}}\right)\) and strong base: \(\quad \mathrm{pH}=14.00-\frac{1}{2} \mathrm{pK}_{\mathrm{w}}+\frac{1}{2} \mathrm{p} K_{\mathrm{a}}+\frac{1}{2} \log \mathrm{M}\) (a) Derive these three equations, and point out the assumptions involved in the derivations. (b) Use these equations to determine the pH of 0.10 \(\mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}(\mathrm{aq}), 0.10 \mathrm{M} \mathrm{NH}_{3}(\mathrm{aq}),\) and \(0.10 \mathrm{M}\) \(\mathrm{NaCH}_{3} \mathrm{COO} .\) Verify that the equations give correct results by determining these pH values in the usual way.

Oxalic acid, HOOCCOOH, a weak diprotic acid, has \(\mathrm{p} K_{\mathrm{a}_{1}}=1.25\) and \(\mathrm{p} K_{\mathrm{a}_{2}}=3.81 .\) A related diprotic acid, suberic acid, \(\mathrm{HOOC}\left(\mathrm{CH}_{2}\right)_{8} \mathrm{COOH}\) has \(\mathrm{p} K_{\mathrm{a}_{1}}=4.21\) and \(\mathrm{p} K_{\mathrm{a}_{2}}=5.40 .\) Offer a plausible reason as to why the difference between \(\mathrm{pK}_{\mathrm{a}_{1}}\) and \(\mathrm{pK}_{\mathrm{a}_{2}}\) is so much greater for oxalic acid than for suberic acid.

Here is a way to test the validity of the statement made on page 719 in conjunction with the three key ideas governing the ionization of polyprotic acids. Determine the \(\mathrm{pH}\) of \(0.100 \mathrm{M}\) succinic acid in two ways: first by assuming that \(\mathrm{H}_{3} \mathrm{O}^{+}\) is produced only in the first ionization step, and then by allowing for the possibility that some \(\mathrm{H}_{3} \mathrm{O}^{+}\) is also produced in the second ionization step. Compare the results, and discuss the significance of your finding. $$\begin{array}{c} \mathrm{H}_{2} \mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{4}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{HC}_{4} \mathrm{H}_{4} \mathrm{O}_{4}^{-} \\ &K_{\mathrm{a}_{1}}=6.2 \times 10^{-5} \\ \mathrm{HC}_{4} \mathrm{H}_{4} \mathrm{O}_{4}^{-}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{4}^{2-} \\ &K_{\mathrm{a}_{2}}=2.3 \times 10^{-6} \end{array}$$

Phosphorous acid is listed in Appendix D as a diprotic acid. Propose a Lewis structure for phosphorous acid that is consistent with this fact.

The following four equilibria lie to the right: \(\mathrm{N}_{2} \mathrm{H}_{5}^{+}+\) \(\mathrm{CH}_{3} \mathrm{NH}_{2} \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}+\mathrm{CH}_{3} \mathrm{NH}_{3}^{+} ; \mathrm{H}_{2} \mathrm{SO}_{3}+\mathrm{F}^{-} \longrightarrow\) \(\mathrm{HSO}_{3}^{-}+\mathrm{HF} ; \mathrm{CH}_{3} \mathrm{NH}_{3}^{+}+\mathrm{OH}^{-} \longrightarrow \mathrm{CH}_{3} \mathrm{NH}_{2}+\) \(\mathrm{H}_{2} \mathrm{O} ;\) and \(\mathrm{HF}+\mathrm{N}_{2} \mathrm{H}_{4} \longrightarrow \mathrm{F}^{-}+\mathrm{N}_{2} \mathrm{H}_{5}^{+}\) (a) Rank all the acids involved in order of decreasing acid strength. (b) Rank all the bases involved in order of decreasing base strength. (c) State whether each of the following two equilibria lies primarily to the right or to the left: (i) \(\mathrm{HF}+\mathrm{OH}^{-} \longrightarrow \mathrm{F}^{-}+\mathrm{H}_{2} \mathrm{O} ;\) (ii) \(\mathrm{CH}_{3} \mathrm{NH}_{3}^{+}+\) \(\mathrm{HSO}_{3}^{-} \longrightarrow \mathrm{CH}_{3} \mathrm{NH}_{2}+\mathrm{H}_{2} \mathrm{SO}_{3}\).

Maleic acid is a carbon-hydrogen-oxygen compound used in dyeing and finishing fabrics and as a preservative of oils and fats. In a combustion analysis, a 1.054 g sample of maleic acid yields \(1.599 \mathrm{g}\) \(\mathrm{CO}_{2}\) and \(0.327 \mathrm{g} \mathrm{H}_{2} \mathrm{O} .\) In a freezing-point depression experiment, a \(0.615 \mathrm{g}\) sample of maleic acid dissolved in 25.10 g of glacial acetic acid, \(\mathrm{CH}_{3} \mathrm{COOH}(1) \quad\) (which has the freezing-point depression constant \(K_{\mathrm{f}}=3.90^{\circ} \mathrm{C} m^{-1}\) and in which maleic acid does not ionize), lowers the freezing point by \(0.82^{\circ} \mathrm{C} .\) In a titration experiment, a \(0.4250 \mathrm{g}\) sample of maleic acid is dissolved in water and requires \(34.03 \mathrm{mL}\) of \(0.2152 \mathrm{M} \mathrm{KOH}\) for its complete neutralization. The \(\mathrm{pH}\) of a \(0.215 \mathrm{g}\) sample of maleic acid dissolved in \(50.00 \mathrm{mL}\) of aqueous solution is found to be \(1.80 .\) (a) Determine the empirical and molecular formulas of maleic acid. [Hint: Which experiment(s) provide the necessary data?] (b) Use the results of part (a) and the titration data to rewrite the molecular formula to reflect the number of ionizable \(\mathrm{H}\) atoms in the molecule. (c) Given that the ionizable \(\mathrm{H}\) atom(s) is(are) associated with the carboxyl group(s), write the plausible condensed structural formula of maleic acid. (d) Determine the ionization constant(s) of maleic acid. If the data supplied are insufficient, indicate what additional data would be needed. (e) Calculate the expected \(\mathrm{pH}\) of a \(0.0500 \mathrm{M}\) aqueous solution of maleic acid. Indicate any assumptions required in this calculation.

In your own words, define or explain the following terms or symbols: (a) \(K_{\mathrm{w}} ;\) (b) \(\mathrm{pH} ;\) (c) \(\mathrm{p} K_{\mathrm{a}} ;\) (d) hydrolysis; (e) Lewis acid.

Briefly describe each of the following ideas or phenomena: (a) conjugate base; (b) percent ionization of an acid or base; (c) self-ionization; (d) amphiprotic behavior.

Explain the important distinctions between each pair of terms: (a) Bronsted- Lowry acid and base; (b) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) and \(\mathrm{pH} ;\) (c) \(K_{\mathrm{a}}\) for \(\mathrm{NH}_{4}^{+}\) and \(K_{\mathrm{b}}\) for \(\mathrm{NH}_{3} ;\) (d) leveling effect and electron- withdrawing effect.

Of the following, the amphiprotic ion is (a) \(\mathrm{HCO}_{3}^{-}\) (b) \(\mathrm{CO}_{3}^{2-} ;\) (c) \(\mathrm{NH}_{4}^{+} ;\) (d) \(\mathrm{CH}_{3} \mathrm{NH}_{3}^{+} ;\) (e) \(\mathrm{ClO}_{4}^{-}\).

Of the following, the amphiprotic ion is (a) \(\mathrm{HCO}_{3}^{-}\) (b) \(\mathrm{CO}_{3}^{2-} ;\) (c) \(\mathrm{NH}_{4}^{+} ;\) (d) \(\mathrm{CH}_{3} \mathrm{NH}_{3}^{+} ;\) (e) \(\mathrm{ClO}_{4}^{-}\).The \(\mathrm{pH}\) in \(0.10 \mathrm{M} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH}(\mathrm{aq})\) must be (a) equal to \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) in \(0.10 \mathrm{M} \mathrm{HNO}_{2}(\mathrm{aq}) ;\) (b) less than the \(\mathrm{pH}\) in \(0.10 \mathrm{M} \mathrm{HI}(\mathrm{aq}) ;\) (c) greater than the \(\mathrm{pH}\) in \(0.10 \mathrm{M} \mathrm{HBr}(\mathrm{aq}) ;\) (d) equal to \(1.0.\)

In \(0.10 \mathrm{M} \quad \mathrm{CH}_{3} \mathrm{NH}_{2}(\mathrm{aq}), \quad\) (a) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=0.10 \mathrm{M}\) (b) \(\left[\mathrm{OH}^{-}\right]=0.10 \mathrm{M} ;(\mathrm{c}) \mathrm{pH}<7 ;(\mathrm{d}) \mathrm{pH}<13\).

The reaction of \(\mathrm{CH}_{3} \mathrm{COOH}(\) aq) proceeds furthest toward completion with a base when that base is (a) \(\mathrm{H}_{2} \mathrm{O} ;\) (b) \(\mathrm{CH}_{3} \mathrm{NH}_{3}^{+} ;\) (c) \(\mathrm{NH}_{4}^{+} ;\) (d) \(\mathrm{Cl}^{-} ;\) (e) \(\mathrm{CO}_{3}^{2-}\).

\(\operatorname{In} 0.10 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}),\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) is equal to \((\mathrm{a}) 0.050 \mathrm{M}\) (b) \(0.10 \mathrm{M} ;\) (c) \(0.11 \mathrm{M} ;\) (d) \(0.20 \mathrm{M}\).

What is the pH of the solution obtained by mixing \(24.80 \mathrm{mL}\) of \(0.248 \mathrm{M} \mathrm{HNO}_{3}\) and \(15.40 \mathrm{mL}\) of \(0.394 \mathrm{M}\) \(\space\) \(KOH?\)

Propionic acid, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH},\) is \(0.42 \%\) ionized in \(0.80 \mathrm{M}\) solution. The \(K_{\mathrm{a}}\) for this acid is (a) \(1.42 \times 10^{-5}\) (b) \(1.42 \times 10^{-7} ;\) (c) \(1.77 \times 10^{-5} ;\) (d) \(6.15 \times 10^{4}\) (e) none of these.

The conjugate acid of \(\mathrm{HPO}_{4}^{2-}\) is (a) \(\mathrm{PO}_{4}^{3-}\) (b) \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-} ;(\mathrm{c}) \mathrm{H}_{3} \mathrm{PO}_{4} ;(\mathrm{d}) \mathrm{H}_{3} \mathrm{O}^{+} ;\) (e) none of these.

The equilibria \(\mathrm{OH}^{-}+\mathrm{HClO} \longrightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{ClO}^{-}\) and \(\mathrm{ClO}^{-}+\mathrm{HNO}_{2} \longrightarrow \mathrm{HClO}+\mathrm{NO}_{2}^{-}\) both lie to the right. Which of the following is a list of acids ranked in order of decreasing strength? (a) \(\mathrm{HClO}>\mathrm{HNO}_{2}>\mathrm{H}_{2} \mathrm{O}\) (b) \(\mathrm{ClO}^{-}>\mathrm{NO}_{2}^{-}>\mathrm{OH}^{-}\) (c) \(\mathrm{NO}_{2}^{-}>\mathrm{ClO}^{-}>\mathrm{OH}\) (d) \(\mathrm{HNO}_{2}>\mathrm{HClO}>\mathrm{H}_{2} \mathrm{O}\) (e) none of these

\(3.00 \mathrm{mol}\) of calcium chlorite is dissolved in enough water to produce 2.50 L of solution. \(K_{\mathrm{a}}=2.9 \times 10^{-8}\) for \(\mathrm{HClO}\), and \(K_{\mathrm{a}}=1.1 \times 10^{-2}\) for \(\mathrm{HClO}_{2}\). Compute the pH of the solution.