Chapter 12

Explain what happens to (a) the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\)ions in an acetic acid solution when solid sodium acetate is added; (b) the percentage deprotonation of benzoic acid in a benzoic acid solution when hydrochloric acid is added; (c) the \(\mathrm{pH}\) of the solution when solid ammonium chloride is added to aqueous ammonia.

Explain what happens to (a) the \(\mathrm{pH}\) of a solution of phosphoric acid after the addition of solid sodium dihydrogen phosphate; (b) the percentage deprotonation of \(\mathrm{HCN}\) in a hydrocyanic acid solution after the addition of hydrobromic acid; (c) the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\)ions when pyridinium chloride is added to an aqueous solution of the base pyridine.

A solution of equal concentrations of barbituric acid and sodium barbiturate was found to have \(\mathrm{pH}=4.01\). (a) What are the values of \(\mathrm{p} K_{\mathrm{a}}\) and \(K_{\mathrm{a}}\) of barbituric acid? (b) What would the \(\mathrm{pH}\) be if the concentration of acid was twice that of the salt?

Calculate the \(\mathrm{pH}\) and \(\mathrm{pOH}\) of (a) a solution that is \(0.17 \mathrm{M}\) \(\mathrm{Na}_{2} \mathrm{HPO}_{4}(\mathrm{aq})\) and \(0.25 \mathrm{M} \mathrm{Na}_{3} \mathrm{PO}_{4}(\mathrm{aq})\); (b) a solution that is \(0.66 \mathrm{M}\) \(\mathrm{Na}_{2} \mathrm{HPO}_{4}(\mathrm{aq})\) and \(0.42 \mathrm{M} \mathrm{Na}_{3} \mathrm{PO}_{4}(\mathrm{aq})\); (c) a solution that is \(0.12 \mathrm{M}\) \(\mathrm{Na}_{2} \mathrm{HPO}_{4}(\mathrm{aq})\) and \(0.12 \mathrm{M} \mathrm{Na}_{3} \mathrm{PO}_{4}(\mathrm{aq})\).

A buffer solution of volume \(100.0 \mathrm{~mL}\) is \(0.100 \mathrm{M}\) \(\mathrm{CH}_{3} \mathrm{COOH}(\mathrm{aq})\) and \(0.100 \mathrm{M} \mathrm{NaCH} \mathrm{CO}_{2}(\mathrm{aq})\). (a) What are the \(\mathrm{pH}\) and the pH change resulting from the addition of \(10.0 \mathrm{~mL}\) of \(0.950 \mathrm{M} \mathrm{NaOH}(\mathrm{aq})\) to the buffer solution? (b) What are the \(\mathrm{pH}\) and the \(\mathrm{pH}\) change resulting from the addition of \(20.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{HNO}_{3}(\mathrm{aq})\) to the initial buffer solution?

Predict the pH region in which each of the following buffers will be effective, assuming equal molarities of the acid and its conjugate base: (a) sodium lactate and lactic acid; (b) sodium benzoate and benzoic acid; (c) potassium hydrogen phosphate and potassium phosphate; (d) potassium hydrogen phosphate and potassium dihydrogen phosphate; (e) hydroxylamine and hydroxylammonium chloride.

Predict the pH region in which each of the following buffers will be effective, assuming equal molarities of the acid and its conjugate base: (a) sodium nitrite and nitrous acid; (b) sodium formate and formic acid; (c) sodium carbonate and sodium hydrogen carbonate; (d) ammonia and ammonium chloride; (c) pyridine and pyridinium chloride.

(a) What must be the ratio of the concentrations of \(\mathrm{CO}_{3}^{2-}\) and \(\mathrm{HCO}_{3}{\underline{\phantom{xx}}}^{-}\)ions in a buffer solution having a \(\mathrm{pH}\) of \(11.0\) ? (b) What mass of \(\mathrm{K}_{2} \mathrm{CO}_{3}\) must be added to \(1.00 \mathrm{~L}\) of \(0.100 \mathrm{M}\) \(\mathrm{KHCO}_{3}(\mathrm{aq})\) to prepare a buffer solution with a \(\mathrm{pH}\) of \(11.0\) ? (c) What mass of \(\mathrm{KHCO}_{3}\) must be added to \(1.00 \mathrm{~L}\) of \(0.100 \mathrm{M}\) \(\mathrm{K}_{2} \mathrm{CO}_{3}(\mathrm{aq})\) to prepare a buffer solution with a \(\mathrm{pH}\) of \(11.0\) ? (d) What volume of \(0.200 \mathrm{M} \mathrm{K}_{2} \mathrm{CO}_{3}(\mathrm{aq})\) must be added to 100 . \(\mathrm{mL}\) of \(0.100 \mathrm{M} \mathrm{KHCO}_{3}(\mathrm{aq})\) to prepare a buffer solution with a \(\mathrm{pH}\) of \(11.0\) ?

(a) Sketch the titration curve for the titration of \(5.00 \mathrm{~mL}\) \(0.010 \mathrm{M} \mathrm{NaOH}(\mathrm{aq})\) with \(0.005 \mathrm{M} \mathrm{HCl}(\mathrm{aq})\), indicating the \(\mathrm{pH}\) of the initial and final solutions and the \(\mathrm{pH}\) at the stoichiometric point. What volume of \(\mathrm{HCl}\) has been added at (b) the stoichiometric point; (c) the halfway point of the titration?

Calculate the volume of \(0.150 \mathrm{M} \mathrm{HCl}(\mathrm{aq})\) required to neutralize (a) one-half and (b) all the hydroxide ions in \(25.0 \mathrm{~mL}\) of \(0.110 \mathrm{M} \mathrm{NaOH}(\mathrm{aq})\). (c) What is the molarity of \(\mathrm{Na}^{+}\)ions at the stoichiometric point? (d) Calculate the \(\mathrm{pH}\) of the solution after the addition of \(20.0 \mathrm{~mL}\) of \(0.150 \mathrm{M} \mathrm{HCl}(\mathrm{aq})\) to \(25.0 \mathrm{~mL}\) of \(0.110 \mathrm{M}\) \(\mathrm{NaOH}(\mathrm{aq})\).

Suppose that \(4.25 \mathrm{~g}\) of an unknown monoprotic weak acid, \(\mathrm{HA}\), is dissolved in water. Titration of the solution with \(0.350 \mathrm{M}\) \(\mathrm{NaOH}(\mathrm{aq})\) required \(52.0 \mathrm{~mL}\) to reach the stoichiometric point. After the addition of \(26.0 \mathrm{~mL}\), the \(\mathrm{pH}\) of the solution was found to be \(3.82\). (a) What is the molar mass of the acid? (b) What is the value of \(\mathrm{p} K_{\mathrm{a}}\) for the acid?

Suppose that \(0.483 \mathrm{~g}\) of an unknown monoprotic weak acid, HA, is dissolved in water. Titration of the solution with \(0.2 .50 \mathrm{M}\) \(\mathrm{NaOH}\) (aq) required \(42.0 \mathrm{~mL}\) to reach the stoichiometric point. After the addition of \(21.0 \mathrm{~mL}\), the \(\mathrm{pH}\) of the solution was found to be \(3.75\). (a) What is the molar mass of the acid? (b) What is the value of \(\mathrm{p} K_{\mathrm{a}}\) for the acid? Can you identify the acid?

Calculate the \(\mathrm{pH}\) at each stage in the titration for the addition of \(0.150 \mathrm{M} \mathrm{HCl}(\mathrm{aq})\) to \(25.0 \mathrm{~mL}\) of \(0.110 \mathrm{M} \mathrm{NaOH}(\mathrm{aq})\) : (a) initially; (b) after the addition of \(5.0 \mathrm{~mL}\) of acid; (c) after the addition of a further \(5.0 \mathrm{~mL}\); (d) at the stoichiometric point; (e) after the addition of \(5.0 \mathrm{~mL}\) of acid beyond the stoichiometric point; (f) after the addition of \(10.0 \mathrm{~mL}\) of acid beyond the stoichiometric point.

Calculate the \(\mathrm{pH}\) at each stage in the titration for the addition of \(0.150 \mathrm{M} \mathrm{HCl}(\mathrm{aq})\) to \(25.0 \mathrm{~mL}\) of \(0.110 \mathrm{M} \mathrm{NaOH}(\mathrm{aq})\) : (a) initially; (b) after the addition of \(5.0 \mathrm{~mL}\) of acid; (c) after the addition of a further \(5.0 \mathrm{~mL}\); (d) at the stoichiometric point; (e) after the addition of \(5.0 \mathrm{~mL}\) of acid beyond the stoichiometric point; (f) after the addition of \(10.0 \mathrm{~mL}\) of acid beyond the stoichiometric point.

Suppose that \(1.436 \mathrm{~g}\) of impure sodium hydroxide is dissolved in \(300 . \mathrm{mL}\) of aqueous solution and that \(25.00 \mathrm{~mL}\) of this solution is titrated to the stoichiometric point with \(34.20 \mathrm{~mL}\) of \(0.0695 \mathrm{M} \mathrm{HCl}(\mathrm{aq})\). What is the percentage purity of the original sample?

What volume of \(0.123 \mathrm{M} \mathrm{NaOH}(\mathrm{aq})\) must be added to \(125 \mathrm{~mL}\) of \(0.197 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{3}(\mathrm{aq})\) to reach (a) the first stoichiometric point; (b) the second stoichiometric point?

Determine \(K_{\mathrm{sp}}\) for each of the following sparingly soluble substances, given their molar solubilities: (a) \(\mathrm{AgBr}\), \(8.8 \times 10^{-7} \mathrm{~mol} \cdot \mathrm{L}^{-1}\), (b) \(\mathrm{PbCrO}_{4}, 1.3 \times 10^{-7} \mathrm{~mol} \cdot \mathrm{L}^{-1}\) (c) \(\mathrm{Ba}(\mathrm{OH})_{2}, 0.11 \mathrm{~mol} \cdot \mathrm{L}^{-1}\); (d) \(\mathrm{MgF}_{2}, 1.2 \times 10^{-3} \mathrm{~mol} \cdot \mathrm{L}^{-1}\). For the purpose of this calculation, ignore any reaction of the anion with water and the autoprotolysis of water.

Determine \(K_{\mathrm{sp}}\) for each of the following sparingly soluble compounds, given their molar solubilities: (a) \(\mathrm{AgI}\), \(9.1 \times 10^{-9} \mathrm{~mol} \cdot \mathrm{L}^{-1}\); (b) \(\mathrm{Ca}(\mathrm{OH})_{2}, 0.011 \mathrm{~mol} \cdot \mathrm{L}^{-1}\); (c) \(\mathrm{Ag}_{3} \mathrm{PO}_{4}\), \(2.7 \times 10^{-6} \mathrm{~mol} \cdot \mathrm{L}^{-1}\); (d) \(\mathrm{Hg}_{2} \mathrm{Cl}_{2}, 5.2 \times 10^{-7} \mathrm{~mol} \cdot \mathrm{L}^{-1}\). For the purpose of this calculation, ignore any reaction of the anion with water and the autoprotolysis of water.

The molarity of \(\mathrm{CrO}_{4}^{2-}\) in a saturated \(\mathrm{Tl}_{2} \mathrm{CrO}_{4}\) solution is \(6.3 \times 10^{-5} \mathrm{~mol} \cdot \mathrm{L}^{-1}\). What is the \(K_{\mathrm{sp}}\) of \(\mathrm{Tl}_{2} \mathrm{CrO}_{4}\) ?

The molar solubility of cerium(III) hydroxide, \(\mathrm{Ce}(\mathrm{OH})_{3}\), is \(5.2 \times 10^{-6} \mathrm{~mol} \cdot \mathrm{L}^{-1}\). What is the \(K_{\mathrm{sp}}\) of cerium(III) hydroxide? For the purpose of this calculation, ignore the autoprotolysis of water.

12.79 You find a bottle of a pure silver halide that could be \(\mathrm{AgCl}\) or AgI. Develop a simple chemical test that would allow you to distinguish which compound was in the bottle.

12.80 Which of the following compounds, if either, will dissolve in \(1.00 \mathrm{M} \mathrm{HNO}_{3}(\mathrm{aq})\) : (a) \(\mathrm{Bi}_{2} \mathrm{~S}_{3}\) (s); (b) \(\mathrm{FeS}(\mathrm{s})\) ? Substantiate your answer by giving an appropriate calculation.

\(12.85\) Malonic acid, \(\mathrm{HOOCCH}{\underline{\phantom{xx}}}_{2} \mathrm{COOH}\), a diprotic acid with \(\mathrm{p} K_{\mathrm{a} 1}=2.8\) and \(\mathrm{p} K_{\mathrm{a} 2}=5.7\), is titrated with \(\mathrm{KOH}(\mathrm{aq})\). (a) What is the \(\mathrm{pH}\) when \(\left[\mathrm{HOOCCH}{\underline{\phantom{xx}}}_{2} \mathrm{COOH}\right]=\left[\mathrm{HOOCCH}_{2} \mathrm{CO}_{2}{\underline{\phantom{xx}}}^{-}\right]\)? (b) What is the pH when \(\left[\mathrm{HOOCCH}_{2} \mathrm{CO}_{2}{\underline{\phantom{xx}}}^{-}\right]=\left[{ }^{-} \mathrm{O}_{2} \mathrm{CCH}_{2} \mathrm{CO}_{2}{\underline{\phantom{xx}}}^{-}\right]\) (c) Which is the predominant species at \(\mathrm{pH}=4.2\) ?

\(12.86\) A species that can accept two protons is classified as dibasic. The dibasic molecule 1,2 -ethanediamine, \(\mathrm{H}_{2} \mathrm{NC}_{2} \mathrm{H}_{4} \mathrm{NH}_{2}\), which has \(\mathrm{p} K_{\mathrm{b} 1}=3.19\) and \(\mathrm{p} K_{\mathrm{b} 2}=6.44\), is titrated with \(\mathrm{HCl}(\mathrm{aq})\). (a) What is the \(\mathrm{pH}\) when \(\left[\mathrm{H}_{2} \mathrm{NC}_{2} \mathrm{H}_{4} \mathrm{NH}_{2}\right]=\left[\mathrm{H}_{2} \mathrm{NC}_{2} \mathrm{H}_{4} \mathrm{NH}_{3}{\underline{\phantom{xx}}}^{+}\right]\)? (b) What is the \(\mathrm{pH}\) when \(\left[\mathrm{H}_{2} \mathrm{NC}_{2} \mathrm{H}_{4} \mathrm{NH}_{3}{\underline{\phantom{xx}}}^{+}\right]=\left[{ }^{+} \mathrm{H}_{3} \mathrm{NC}_{2} \mathrm{H}_{4} \mathrm{NH}_{3}{\underline{\phantom{xx}}}^{+}\right]\)? (c) Which is the predominant species at \(\mathrm{pH}=4.8\) ?

\(12.97\) In an attempt to determine the concentration of sulfur dioxide in the air near a power plant, two students set up a bubbler that passes air through \(50.00 \mathrm{~mL}\) of \(1.0 \times 10^{-4} \mathrm{M}\) \(\mathrm{NaOH}(\mathrm{aq})\). The temperature is \(22^{\circ} \mathrm{C}\), and the atmospheric pressure 753 Torr. The air is pumped for \(2.5 \mathrm{~h}\) at a flow rate of \(3.0 \mathrm{~L} \cdot \mathrm{h}^{-1}\). The students then returned to the laboratory and titrated the solution with \(1.5 \times 10^{-4} \mathrm{M} \mathrm{HCl}(\mathrm{aq})\) with phenolphthalein indicator to see how much \(\mathrm{NaOH}\) was left unreacted. They found that \(30.2 \mathrm{~mL}\) of \(\mathrm{HCl}(\mathrm{aq})\) was required to reach the stoichiometric point. (a) Write the balanced chemical equation for the reaction of \(\mathrm{SO}_{2}\) and water. (b) What amount of \(\mathrm{NaOH}\) (in mol) had reacted with the \(\mathrm{SO}_{2}\) ? (c) What was the concentration of sulfur dioxide in the air, in parts per million?