Chapter 16

In which of the following cases is the approximation that the equilibrium concentration of \(\mathrm{H}^{+}(a q)\) is small relative to the initial concentration of HA likely to be most valid: (a) initial \([\mathrm{HA}]=0.100 \mathrm{M}\) and \(K_{a}=1.0 \times 10^{-6}\), (b) initial \([\mathrm{HA}]=0.100 \mathrm{M}\) and \(K_{a}=1.0 \times 10^{-4}\), (c) initial \([\mathrm{HA}]=0.100 \mathrm{M}\) and \(K_{a}=1.0 \times 10^{-3} ?[\) Section \(16.6]\)

Rank the following acids in order of increasing acidity: \(\mathrm{CH}_{3} \mathrm{COOH}, \mathrm{CH}_{2} \mathrm{ClCOOH}, \mathrm{CHCl}_{2} \mathrm{COOH}, \mathrm{CCl}_{3} \mathrm{COOH}\) \(\mathrm{CF}_{3} \mathrm{COOH}\). [Section 16.10]

Although \(\mathrm{HCl}\) and \(\mathrm{H}_{2} \mathrm{SO}_{4}\) have very different properties as pure substances, their aqueous solutions possess many common properties. List some general properties of these solutions, and explain their common behavior in terms of the species present.

Although pure \(\mathrm{NaOH}\) and \(\mathrm{NH}_{3}\) have very different properties, their aqueous solutions possess many common properties. List some general properties of these solutions, and explain their common behavior in terms of the species present.

(a) What is the difference between the Arrhenius and the Bronsted-Lowry definitions of a base? (b) When ammonia is dissolved in water, it behaves both as an Arrhenius base and as a Bronsted-Lowry base. Explain.

(a) Give the conjugate base of the following BronstedLowry acids: (i) \(\mathrm{HIO}_{3}\), (ii) \(\mathrm{NH}_{4}{\underline{\phantom{xx}}}^{+}\). (b) Give the conjugate acid of the following Bronsted-Lowry bases: (i) \(\mathrm{O}^{2-}\), (ii) \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\).

(a) Give the conjugate base of the following BrønstedLowry acids: (i) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\). (ii) \(\mathrm{HPO}_{4}{\underline{\phantom{xx}}}^{2-}\). (b) Give the conjugate acid of the following Brønsted-Lowry bases: (i) \(\mathrm{CO}_{3}{\underline{\phantom{xx}}}^{2-}\), (ii) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\).

Designate the Brønsted-Lowry acid and the BrønstedLowry base on the left side of each of the following equations, and also designate the conjugate acid and conjugate base on the right side: (a) \(\mathrm{NH}_{4}{\underline{\phantom{xx}}}^{+}(a q)+\mathrm{CN}^{-}(a q) \rightleftharpoons \mathrm{HCN}(a q)+\mathrm{NH}_{3}(a q)\) (b) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{~N}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons\) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{NH}^{+}(a q)+\mathrm{OH}^{-}(a q)\) (c) \(\mathrm{HCHO}_{2}(a q)+\mathrm{PO}_{4}{\underline{\phantom{xx}}}^{3-}(a q) \rightleftharpoons\) \(\mathrm{CHO}_{2}^{-}(a q)+\mathrm{HPO}_{4}^{2-}(a q)\)

Designate the Brønsted-Lowry acid and the BrønstedLowry base on the left side of each equation, and also designate the conjugate acid and conjugate base on the right side. (a) \(\mathrm{HBrO}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{BrO}^{-}(a q)\) (b) \(\mathrm{HSO}_{4}^{-}(a q)+\mathrm{HCO}_{3}^{-}(a q) \rightleftharpoons\) \(\mathrm{SO}_{4}{\underline{\phantom{xx}}}^{2-}(a q)+\mathrm{H}_{2} \mathrm{CO}_{3}(a q)\) (c) \(\mathrm{HSO}_{3}^{-}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q) \rightleftharpoons \mathrm{H}_{2} \mathrm{SO}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\)

(a) The hydrogen oxalate ion \(\left(\mathrm{HC}_{2} \mathrm{O}_{4}{\underline{\phantom{xx}}}^{-}\right)\) is amphiprotic. Write a balanced chemical equation showing how it acts as an acid toward water and another equation showing how it acts as a base toward water. (b) What is the conjugate acid of \(\mathrm{HC}_{2} \mathrm{O}_{4}^{-} ?\) What is its conjugate base?

(a) Write an equation for the reaction in which \(\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{7} \mathrm{O}_{5}^{-}(a q)\) acts as a base in \(\mathrm{H}_{2} \mathrm{O}(l) .\) (b) Write an equation for the reaction in which \(\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{7} \mathrm{O}_{5}^{-}(a q)\) acts as an acid in \(\mathrm{H}_{2} \mathrm{O}(l) .(\mathrm{c})\) What is the conjugate acid of \(\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{7} \mathrm{O}_{5}^{-} ?\) What is its conjugate base?

Label each of the following as being a strong base, a weak base, or a species with negligible basicity. In each case write the formula of its conjugate acid, and indicate whether the conjugate acid is a strong acid, a weak acid, or a species with negligible acidity: (a) \(\mathrm{CH}_{3} \mathrm{COO}^{-}\), (b) \(\mathrm{HCO}_{3}^{-},(\mathrm{c}) \mathrm{O}^{2-},(\mathrm{d}) \mathrm{Cl}^{-},(\mathrm{e}) \mathrm{NH}_{3}\)

Label each of the following as being a strong acid, a weak acid, or a species with negligible acidity. In each case write the formula of its conjugate base, and indicate whether the conjugate base is a strong base, a weak base, or a species with negligible basicity: (a) \(\mathrm{HNO}_{2}\), (b) \(\mathrm{H}_{2} \mathrm{SO}_{4},(\mathrm{c}) \mathrm{HPO}_{4}{\underline{\phantom{xx}}}^{2-}\) (d) \(\mathrm{CH}_{4}\), (e) \(\mathrm{CH}_{3} \mathrm{NH}_{3}{\underline{\phantom{xx}}}^{+}\) (an ion related to \(\mathrm{NH}_{4}{\underline{\phantom{xx}}}^{+}\) ).

(a) Which of the following is the stronger BrønstedLowry acid, \(\mathrm{HBrO}\) or \(\mathrm{HBr}\) ? (b) Which is the stronger Brønsted-Lowry base, \(\mathrm{F}^{-}\) or \(\mathrm{Cl}^{-} ?\) Briefly explain your choices.

(a) Which of the following is the stronger BrønstedLowry acid, \(\mathrm{HBrO}\) or \(\mathrm{HBr}\) ? (b) Which is the stronger Brønsted-Lowry base, \(\mathrm{F}^{-}\) or \(\mathrm{Cl}^{-} ?\) Briefly explain your choices.

Predict the products of the following acid-base reactions, and predict whether the equilibrium lies to the left or to the right of the equation: (a) \(\mathrm{O}^{2-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons\) (b) \(\mathrm{CH}_{3} \mathrm{COOH}(a q)+\mathrm{HS}^{-}(a q) \rightleftharpoons\) (c) \(\mathrm{NO}_{2}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons\)

Predict the products of the following acid-base reactions, and predict whether the equilibrium lies to the left or to the right of the equation: (a) \(\mathrm{NH}_{4}{\underline{\phantom{xx}}}^{+}(a q)+\mathrm{OH}^{-}(a q) \rightleftharpoons\) (b) \(\mathrm{CH}_{3} \mathrm{COO}^{-}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q) \rightleftharpoons\) (c) \(\mathrm{HCO}_{3}^{-}(a q)+\mathrm{F}^{-}(a q) \rightleftharpoons\)

(a) What does the term autoionization mean? (b) Explain why pure water is a poor conductor of electricity. (c) You are told that an aqueous solution is acidic. What does this statement mean?

(a) Write a chemical equation that illustrates the autoionization of water. (b) Write the expression for the ion-product constant for water, \(K_{w}\). Why is \(\left[\mathrm{H}_{2} \mathrm{O}\right]\) absent from this expression? (c) A solution is described as basic. What does this statement mean?

Calculate \(\left[\mathrm{H}^{+}\right]\) for each of the following solutions, and indicate whether the solution is acidic, basic, or neutral: (a) \(\left[\mathrm{OH}^{-}\right]=0.00045 M ;\) (b) \(\left[\mathrm{OH}^{-}\right]=8.8 \times 10^{-9} \mathrm{M} ;(\mathrm{c}) \mathrm{a}\) solution in which \(\left[\mathrm{OH}^{-}\right]\) is 100 times greater than \(\left[\mathrm{H}^{+}\right]\).

Calculate [OH \(^{-}\) ] for each of the following solutions, and indicate whether the solution is acidic, basic, or neutral: (a) \(\left[\mathrm{H}^{+}\right]=0.0045 \mathrm{M}\) (b) \(\left[\mathrm{H}^{+}\right]=1.5 \times 10^{-9} \mathrm{M} ;\) (c) a solution in which \(\left[\mathrm{H}^{+}\right]\) is 10 times greater than \(\left[\mathrm{OH}^{-}\right]\).

At the freezing point of water \(\left(0^{\circ} \mathrm{C}\right), K_{w}=1.2 \times 10^{-15}\). Calculate \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) for a neutral solution at this temperature.

By what factor does \(\left[\mathrm{H}^{+}\right]\) change for a pH change of (a) \(2.00\) units, (b) \(0.50\) units?

Consider two solutions, solution \(\mathrm{A}\) and solution B. \(\left[\mathrm{H}^{+}\right]\) in solution \(\mathrm{A}\) is 500 times greater than that in solution \(\mathrm{B}\). What is the difference in the \(\mathrm{pH}\) values of the two solutions?

Carbon dioxide in the atmosphere dissolves in raindrops to produce carbonic acid \(\left(\mathrm{H}_{2} \mathrm{CO}_{3}\right)\), causing the \(\mathrm{pH}\) of clean, unpolluted rain to range from about \(5.2\) to \(5.6\). What are the ranges of \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) in the raindrops?

(a) What is a strong acid? (b) A solution is labeled \(0.500 \mathrm{M} \mathrm{HCl}\). What is \(\left[\mathrm{H}^{+}\right]\) for the solution? (c) Which of the following are strong acids: \(\mathrm{HF}, \mathrm{HCl}, \mathrm{HBr}, \mathrm{HI}\) ?

(a) What is a strong base? (b) A solution is labeled \(0.035 \mathrm{M} \mathrm{Sr}(\mathrm{OH})_{2}\). What is \(\left[\mathrm{OH}^{-}\right]\) for the solution? (c) Is the following statement true or false? Because \(\mathrm{Mg}(\mathrm{OH})_{2}\) is not very soluble, it cannot be a strong base. Explain.

Calculate the pH of each of the following strong acid solutions: (a) \(8.5 \times 10^{-3} \mathrm{M} \mathrm{HBr}\), (b) \(1.52 \mathrm{~g}\) of \(\mathrm{HNO}_{3}\) in \(575 \mathrm{~mL}\) of solution, \((\mathrm{c}) 5.00 \mathrm{~mL}\) of \(0.250 \mathrm{M} \mathrm{HClO}_{4}\) diluted to \(50.0 \mathrm{~mL}\), (d) a solution formed by mixing \(10.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{HBr}\) with \(20.0 \mathrm{~mL}\) of \(0.200 \mathrm{M} \mathrm{HCl}\).

Calculate the \(\mathrm{pH}\) of each of the following strong acid solutions: (a) \(0.00135 \mathrm{M} \mathrm{HNO}_{3}\), (b) \(0.425 \mathrm{~g}\) of \(\mathrm{HClO}_{4}\) in \(2.00 \mathrm{~L}\) of solution, \((\mathrm{c}) 5.00 \mathrm{~mL}\) of \(1.00 \mathrm{M} \mathrm{HCl}\) diluted to \(0.500 \mathrm{~L},(\mathrm{~d})\) a mixture formed by adding \(50.0 \mathrm{~mL}\) of \(0.020 \mathrm{M} \mathrm{HCl}\) to \(150 \mathrm{~mL}\) of \(0.010 \mathrm{M} \mathrm{HI}\)

Calculate \(\left[\mathrm{OH}^{-}\right]\) and \(\mathrm{pH}\) for (a) \(1.5 \times 10^{-3} \mathrm{M} \mathrm{Sr}(\mathrm{OH})_{2}\) (b) \(2.250 \mathrm{~g}\) of \(\mathrm{LiOH}\) in \(250.0 \mathrm{~mL}\) of solution, \((c) 1.00 \mathrm{~mL}\) of \(0.175 \mathrm{M} \mathrm{NaOH}\) diluted to \(2.00 \mathrm{~L}\), (d) a solution formed by adding \(5.00 \mathrm{~mL}\) of \(0.105 \mathrm{M} \mathrm{KOH}\) to \(15.0 \mathrm{~mL}\) of \(9.5 \times 10^{-2} \mathrm{M} \mathrm{Ca}(\mathrm{OH})_{2}\).

Calculate \(\left[\mathrm{OH}^{-}\right]\) and \(\mathrm{pH}\) for each of the following strong base solutions: (a) \(0.082 \mathrm{M} \mathrm{KOH}\), (b) \(1.065 \mathrm{~g}\) of \(\mathrm{KOH}\) in \(500.0 \mathrm{~mL}\) of solution, (c) \(10.0 \mathrm{~mL}\) of \(0.0105 \mathrm{M} \mathrm{Ca}(\mathrm{OH})_{2}\) diluted to \(500.0 \mathrm{~mL}\), (d) a solution formed by mixing \(7.5 \times 10^{-3} \mathrm{M} \mathrm{NaOH}\)

Write the chemical equation and the \(K_{a}\) expression for the ionization of each of the following acids in aqueous solution. First show the reaction with \(\mathrm{H}^{+}(a q)\) as a product and then with the hydronium ion: (a) \(\mathrm{HBrO}_{2}\), (b) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOH}\).

Write the chemical equation and the \(K_{a}\) expression for the acid dissociation of each of the following acids in aqueous solution. First show the reaction with \(\mathrm{H}^{+}(a q)\) as a product and then with the hydronium ion: (a) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\), (b) \(\mathrm{HCO}_{3}^{-}\).

Lactic acid (CH \(\left._{3} \mathrm{CH}(\mathrm{OH}) \mathrm{COOH}\right)\) has one acidic hydrogen. A \(0.10 \mathrm{M}\) solution of lactic acid has a pH of \(2.44\). Calculate \(K_{a}\)

Phenylacetic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{COOH}\right)\) is one of the substances that accumulates in the blood of people with phenylketonuria, an inherited disorder that can cause mental retardation or even death. A \(0.085 \mathrm{M}\) solution of \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{COOH}\) has a pH of \(2.68\). Calculate the \(\mathrm{K}_{a}\) value for this acid.

A \(0.100 M\) solution of chloroacetic acid \(\left(\mathrm{ClCH}_{2} \mathrm{COOH}\right)\) is \(11.0 \%\) ionized. Using this information, calculate \(\left.\left[\mathrm{ClCH}_{2} \mathrm{COO}^{-}\right],\left[\mathrm{H}^{+}\right],\left[\mathrm{ClCH}_{2} \mathrm{COOH}\right)\right]\), and \(K_{a}\) for chloroacetic acid.

A \(0.100 \mathrm{M}\) solution of bromoacetic acid \(\left(\mathrm{BrCH}_{2} \mathrm{COOH}\right)\) is \(13.2 \%\) ionized. Calculate \(\left[\mathrm{H}^{+}\right],\left[\mathrm{BrCH}_{2} \mathrm{COO}^{-}\right]\), and \(\left[\mathrm{BrCH}_{2} \mathrm{COOH}\right]\).

A particular sample of vinegar has a pH of \(2.90\). If acetic acid is the only acid that vinegar contains \(\left(K_{a}=1.8 \times 10^{-5}\right)\), calculate the concentration of acetic acid in the vinegar.

How many moles of \(\mathrm{HF}\left(K_{a}=6.8 \times 10^{-4}\right)\) must be present in \(0.200 \mathrm{~L}\) to form a solution \(w\) ith a \(\mathrm{pH}\) of \(3.25\) ?

The acid-dissociation constant for hypochlorous acid \((\mathrm{HClO})\) is \(3.0 \times 10^{-8} .\) Calculate the concentrations of \(\mathrm{H}_{3} \mathrm{O}^{+}, \mathrm{ClO}^{-}\), and \(\mathrm{HClO}\) at equilibrium if the initial concentration of \(\mathrm{HClO}\) is \(0.0090 \mathrm{M}\).

Determine the \(\mathrm{pH}\) of each of the following solutions \(\left(K_{a}\right.\) and \(K_{b}\) values are given in Appendix D): (a) \(0.095 M\) hypochlorous acid, (b) \(0.0085 \mathrm{M}\) phenol, (c) \(0.095 \mathrm{M}\) hydroxylamine.

Saccharin, a sugar substitute, is a weak acid with \(\mathrm{pK}_{a}=2.32\) at \(25^{\circ} \mathrm{C}\). It ionizes in aqueous solution as follows: $$ \mathrm{HNC}_{7} \mathrm{H}_{4} \mathrm{SO}_{3}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{NC}_{7} \mathrm{H}_{4} \mathrm{SO}_{3}^{-}(a q) $$ What is the \(\mathrm{pH}\) of a \(0.10 \mathrm{M}\) solution of this substance?

The active ingredient in aspirin is acetylsalicylic acid \(\left(\mathrm{HC}_{9} \mathrm{H}_{7} \mathrm{O}_{4}\right)\), a monoprotic acid with \(K_{a}=3.3 \times 10^{-4}\) at \(25^{\circ} \mathrm{C}\). What is the \(\mathrm{pH}\) of a solution obtained by dissolving two extra-strength aspirin tablets, containing \(500 \mathrm{mg}\) of acetylsalicylic acid each, in \(250 \mathrm{~mL}\) of water?

What is the essential structural feature of all BrønstedLowry bases?

What are two kinds of molecules or ions that commonly function as weak bases?

Write the chemical equation and the \(K_{b}\) expression for the ionization of each of the following bases in aqueous solution: (a) dimethylamine, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH} ;\) (b) carbonate ion, \(\mathrm{CO}_{3}{\underline{\phantom{xx}}}^{2-} ;(\mathrm{c})\) formate ion, \(\mathrm{CHO}_{2}^{-}\).

Write the chemical equation and the \(K_{b}\) expression for the reaction of each of the following bases with water: (a) propylamine, \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{NH}_{2}\); (b) monohydrogen phosphate ion, \(\mathrm{HPO}_{4}{\underline{\phantom{xx}}}^{2-} ;\) (c) benzoate ion, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2}^{-}\)

Calculate the molar concentration of \(\mathrm{OH}^{-}\) ions in a \(0.075 \mathrm{M}\) solution of ethylamine \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2} ; \quad K_{b}=\right.\) \(6.4 \times 10^{-4}\) ). Calculate the pH of this solution.

Calculate the molar concentration of \(\mathrm{OH}^{-}\) ions in a \(0.550 \mathrm{M}\) solution of hypobromite ion \(\left(\mathrm{BrO}^{-} ;\right.\) \(K_{b}=4.0 \times 10^{-6}\) ). What is the \(\mathrm{pH}\) of this solution?

Codeine \(\left(\mathrm{C}_{18} \mathrm{H}_{21} \mathrm{NO}_{3}\right)\) is a weak organic base. \(\mathrm{A}\) \(5.0 \times 10^{-3} \mathrm{M}\) solution of codeine has a pH of 9.95. Calculate the value of \(K_{b}\) for this substance. What is the \(\mathrm{p} K_{b}\) for this base?