Chapter 16

For each of the following cases, decide whether the \(\mathrm{pH}\) is less than \(7,\) equal to \(7,\) or greater than 7 (a) 25 mL of \(0.45 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) is mixed with \(25 \mathrm{mL}\) of 0.90 M NaOH. (b) 15 mL of \(0.050 \mathrm{M}\) formic acid, \(\mathrm{HCO}_{2} \mathrm{H}\), is mixed with \(15 \mathrm{mL}\) of \(0.050 \mathrm{M} \mathrm{NaOH}\). (c) \(25 \mathrm{mL}\) of \(0.15 \mathrm{M} \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) (oxalic acid) is mixed with \(25 \mathrm{mL}\) of \(0.30 \mathrm{M} \mathrm{NaOH}\). (Both \(\mathrm{H}^{+}\) ions of oxalic acid are removed with NaOH.)

Oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4},\) is a diprotic acid. Write a chemical equilibrium expression for each ionization step in water.

Sodium carbonate is a diprotic base. Write a chemical equilibrium expression for each of the two successive base reactions with water.

Prove that \(K_{\mathrm{a} 1} \times K_{\mathrm{b} 2}=K_{\mathrm{w}}\) for oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) by adding the chemical equilibrium expressions that correspond to first ionization step of the acid in water with the second step of the reaction of the fully deprotonated base, \(\mathrm{C}_{2} \mathrm{O}_{4}^{2-},\) with water.

Prove that \(K_{\mathrm{a} 3} \times K_{\mathrm{b} 1}=K_{\mathrm{w}}\) for phosphoric acid, \(\mathrm{H}_{3} \mathrm{PO}_{4},\) by adding the chemical equilibrium expressions that correspond to the third ionization step of the acid in water with the first of the three successive steps of the reaction of phosphate ion, \(\mathrm{PO}_{4}^{3-},\) with water.

Ascorbic acid (vitamin \(\mathrm{C}, \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\) ) is a diprotic acid \(\left(K_{\mathrm{al}}=6.8 \times 10^{-5} \text {and } K_{\mathrm{a} 2}=2.7 \times 10^{-12}\right)\) What is the pH of a solution that contains 5.0 \(\mathrm{mg}\) of acid per milliliter of solution?

Hydrazine, \(\mathrm{N}_{2} \mathrm{H}_{4},\) can interact with water in two steps. $$\begin{aligned} \mathrm{N}_{2} \mathrm{H}_{4}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) & \rightleftharpoons \mathrm{N}_{2} \mathrm{H}_{5}^{+}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq}) \\ K_{\mathrm{b} 1} &=8.5 \times 10^{-7} \\ \mathrm{N}_{2} \mathrm{H}_{5}^{+}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) & \rightleftarrows \mathrm{N}_{2} \mathrm{H}_{6}^{2+}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq}) \\ K_{\mathrm{b} 2} &=8.9 \times 10^{-16} \end{aligned}$$ (a) What is the concentration of \(\mathrm{OH}^{-}, \mathrm{N}_{2} \mathrm{H}_{5}^{+}\) and \(\mathrm{N}_{2} \mathrm{H}_{6}^{2+}\) in a \(0.010 \mathrm{M}\) aqueous solution of hydrazine? (b) What is the \(\mathrm{pH}\) of the 0.010 M solution of hydrazine?

Which should be the stronger acid, HOCN or HCN? Explain briefly. (In HOCN, the H \(^{+}\) ion is attached to the O atom of the OCN - ion.

Which should be the stronger Bronsted acid, \(\left[\mathrm{V}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) or \(\left[\mathrm{V}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+} ?\)

Explain why benzenesulfonic acid is a Bronsted acid.

Decide whether each of the following substances should be classified as a Lewis acid or a Lewis base. (a) \(\mathrm{H}_{2} \mathrm{NOH}\) in the reaction \(\mathrm{H}_{2} \mathrm{NOH}(\mathrm{aq})+\mathrm{HCl}(\mathrm{aq}) \longrightarrow\left[\mathrm{H}_{3} \mathrm{NOH}\right] \mathrm{Cl}(\mathrm{aq})\) (b) \(\mathrm{Fe}^{2+}\) (c) \(\mathrm{CH}_{3} \mathrm{NH}_{2}\) (Hint: Draw the electron dot structure.

Decide whether each of the following substances should be classified as a Lewis acid or a Lewis base. (a) \(\mathrm{BCl}_{3}\) (Hint: Draw the electron dot structure.) (b) \(\mathrm{H}_{2} \mathrm{NNH}_{2},\) hydrazine (Hint: Draw the electron dot structure. (c) the reactants in the reaction \(\mathrm{Ag}^{+}(\mathrm{aq})+2 \mathrm{NH}_{3}(\mathrm{aq}) \rightleftharpoons\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}(\mathrm{aq})\)

Trimethylamine, \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{N},\) is a common reagent. It interacts readily with diborane gas, \(\mathrm{B}_{2} \mathrm{H}_{6}\). The latter dissociates to \(\mathrm{BH}_{3}\), and this forms a complex with the amine, \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{N} \rightarrow \mathrm{BH}_{3} .\) Is the \(\mathrm{BH}_{3}\) fragment a Lewis acid or a Lewis base?

About this time, you may be wishing you had an aspirin. Aspirin is an organic acid with a \(K_{\mathrm{a}}\) of \(3.27 \times 10^{-4}\) for the reaction $$\mathrm{HC}_{3} \mathrm{H}_{7} \mathrm{O}_{4}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons_{\mathrm{C}_{9} \mathrm{H}_{7} \mathrm{O}_{4}^{-}(\mathrm{aq})}+\mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})$$ If you have two tablets, each containing 0.325 g of aspirin (mixed with a neutral "binder" to hold the tablet together), and you dissolve them in a glass of water to give \(225 \mathrm{mL}\) of solution, what is the pH of the solution?

A 2.50 -g sample of a solid that could be \(\mathrm{Ba}(\mathrm{OH})_{2}\) or \(\operatorname{Sr}(\mathrm{OH})_{2}\) was dissolved in enough water to make 1.00 L of solution. If the pH of the solution is \(12.61,\) what is the identity of the solid?

For each of the following reactions, predict whether the equilibrium lies predominantly to the left or to the right. Explain your prediction briefly. (a) \(\mathrm{HCO}_{3}^{-}(\mathrm{aq})+\mathrm{SO}_{4}^{2-}(\mathrm{aq}) \rightleftarrows\) \(\mathrm{CO}_{3}^{2-}(\mathrm{aq})+\mathrm{HSO}_{4}^{-}(\mathrm{aq})\) (b) \(\mathrm{HSO}_{4}^{-}(\mathrm{aq})+\mathrm{CH}_{3} \mathrm{CO}_{2}^{-}(\mathrm{aq}) \rightleftarrows\) \(\mathrm{SO}_{4}^{2-}(\mathrm{aq})+\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\mathrm{aq})\) (c) \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}(\mathrm{aq})+\mathrm{CH}_{3} \mathrm{CO}_{2}^{-}(\mathrm{aq}) \rightleftarrows\) \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}(\mathrm{OH})\right]^{+}(\mathrm{aq})+\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\mathrm{aq})\)

A monoprotic acid HX has \(K_{a}=1.3 \times 10^{-3} .\) Calculate the equilibrium concentrations of HX and \(\mathrm{H}_{3} \mathrm{O}^{+}\) and the \(\mathrm{pH}\) for a \(0.010 \mathrm{M}\) solution of the acid.

Arrange the following \(0.10 \mathrm{M}\) solutions in order of increasing pH. (a) \(\mathrm{NaCl}\) (b) \(\mathrm{NH}_{4} \mathrm{Cl}\) (c) HCl (d) \(\mathrm{NaCH}_{3} \mathrm{CO}_{2}\) (e) KOH

\(m\) -Nitrophenol, a weak acid, can be used as a pH indicator because it is yellow at a pH above 8.6 and colorless at a pH below 6.8. If the pH of a 0.010 M solution of the compound is \(3.44,\) calculate its \(\mathrm{p} K_{\mathrm{a}}\).

The local anesthetic novocaine is the hydrogen chloride salt of an organic base, procaine. $$\begin{array}{cc} \mathrm{C}_{13} \mathrm{H}_{20} \mathrm{N}_{2} \mathrm{O}_{2}(\mathrm{aq})+\mathrm{HCl}(\mathrm{aq}) \longrightarrow & \left.\mathrm{IHC}_{13} \mathrm{H}_{20} \mathrm{N}_{2} \mathrm{O}_{2}\right]^{+} \mathrm{Cl}^{-}(\mathrm{aq}) \\ \text { procaine } & \text { novocaine } \end{array}$$ The \(\mathrm{p} K_{\mathrm{a}}\) for novocaine is \(8.85 .\) What is the \(\mathrm{pH}\) of a \(0.0015 \mathrm{M}\) solution of novocaine?

The base ethylamine \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{NH}_{2}\right)\) has a \(K_{\mathrm{b}}\) of \(4.3 \times 10^{-4} .\) A closely related base, ethanolamine \(\left(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\right),\) has a \(K_{\mathrm{b}}\) of \(3.2 \times 10^{-5}\) (a) Which of the two bases is stronger? (b) Calculate the \(\mathrm{pH}\) of a \(0.10 \mathrm{M}\) solution of the stronger base.

Chloroacetic acid, \(\mathrm{ClCH}_{2} \mathrm{CO}_{2} \mathrm{H},\) is a moderately weak acid \(\left(K_{\mathrm{a}}=1.40 \times 10^{-3}\right) .\) If you dissolve \(94.5 \mathrm{mg}\) of the acid in water to give \(125 \mathrm{mL}\) of solution, what is the pH of the solution?

Saccharin (HC \(_{7} \mathrm{H}_{4} \mathrm{NO}_{3} \mathrm{S}\) ) is a weak acid with \(\mathrm{p} K_{\mathrm{a}}=2.32\) at \(25^{\circ} \mathrm{C} .\) It is used in the form of sodium saccharide, \(\mathrm{NaC}_{7} \mathrm{H}_{4} \mathrm{NO}_{3} \mathrm{S}\). What is the \(\mathrm{pH}\) of a 0.10 M solution of sodium saccharide at \(25^{\circ} \mathrm{C} ?\)

Given the following solutions: (a) \(0.1 \mathrm{M} \mathrm{NH}_{3}\) (b) \(0.1 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3}\) (c) \(0.1 \mathrm{M} \mathrm{NaCl}\) (d) \(0.1 \mathrm{M} \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\) (e) \(0.1 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}\) (f) \(0.1 \mathrm{M} \mathrm{NaCH}_{3} \mathrm{CO}_{2}\) (g) \(0.1 \mathrm{M} \mathrm{NH}_{4} \mathrm{CH}_{3} \mathrm{CO}_{2}\) (i) Which of the solutions are acidic? (ii) Which of the solutions are basic? (iii) Which of the solutions is most acidic?

For each of the following salts, predict whether a \(0.10 \mathrm{M}\) solution has a pH less than, equal to, or greater than 7 (a) \(\mathrm{NaHSO}_{4}\) (b) \(\mathrm{NH}_{4} \mathrm{Br}\) (c) \(\mathrm{KClO}_{4}\) (d) \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) (e) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{S}\) (f) \(\mathrm{NaNO}_{3}\) (g) \(\mathrm{Na}_{2} \mathrm{HPO}_{4}\) (h) LiBr (i) \(\mathrm{FeCl}_{3}\) Which solution has the highest pH? The lowest pH?

Nicotine, \(\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{N}_{2}\), has two basic nitrogen atoms (Figure \(16.12),\) and both can react with water. $$\begin{array}{c} \text { Nic(aq) }+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{NicH}^{+}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq}) \\ \mathrm{NicH}^{+}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{NicH}_{2^{2+}}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq}) \end{array}$$ \(K_{\mathrm{b} 1}\) is \(7.0 \times 10^{-7}\) and \(K_{\mathrm{b} 2}\) is \(1.1 \times 10^{-10} .\) Calculate the approximate \(\mathrm{pH}\) of a \(0.020 \mathrm{M}\) solution.

The hydrogen phthalate ion, \(\mathrm{C}_{8} \mathrm{H}_{5} \mathrm{O}_{4}^{-},\) is a weak acid with \(K_{\mathrm{a}}=3.91 \times 10^{-6}\). $$\mathrm{C}_{8} \mathrm{H}_{5} \mathrm{O}_{4}^{-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{C}_{8} \mathrm{H}_{4} \mathrm{O}_{4}^{2-}(\mathrm{aq})+\mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})$$ What is the pH of a 0.050 M solution of potassium hydrogen phthalate, \(\mathrm{KC}_{8} \mathrm{H}_{5} \mathrm{O}_{4}\) ? Note: To find the pH for a solution of the anion, we must take into account that the ion is amphiprotic. It can be shown that, for most cases of amphiprotic ions, the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration is $$\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=\sqrt{K_{\mathrm{al}} \times K_{\mathrm{a} 2}}$$ For phthalic acid, \(\mathrm{C}_{8} \mathrm{H}_{6} \mathrm{O}_{4}, K_{\mathrm{a} 1}\) is \(1.12 \times 10^{-3},\) and \(K_{\mathrm{a} 2}\) is \(3.91 \times 10^{-6}\).

You prepare a 0.10 M solution of oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} .\) What molecules and ions exist in this solution? List them in order of decreasing concentration.

You mix 30.0 mL of 0.15 M NaOH with \(30.0 \mathrm{mL}\) of \(0.15 \mathrm{M}\) acetic acid. What molecules and ions exist in this solution? List them in order of decreasing concentration.

Describe an experiment that will allow you to place the following three bases in order of increasing base strength: \(\mathrm{NaCN}, \mathrm{CH}_{3} \mathrm{NH}_{2}, \mathrm{Na}_{2} \mathrm{CO}_{3}\).

You have three solutions labeled \(A, B\), and \(C\). You know only that each contains a different cation \(-\mathrm{Na}^{+}, \mathrm{NH}_{4}^{+},\) or \(\mathrm{H}_{3} \mathrm{O}^{+} .\) Each has an anion that does not contribute to the solution \(\mathrm{pH}\) (eg. \(\mathrm{Cl}^{-}\) ). You also have two other solutions, Y and \(\mathrm{Z}\) each containing a different anion, \(\mathrm{Cl}^{-}\) or \(\mathrm{OH}^{-}\) with a cation that does not influence solution \(\mathrm{pH}\) \(\left(\mathrm{e} \cdot \mathrm{g} \cdot, \mathrm{K}^{+}\right) .\) If equal amounts of \(\mathrm{B}\) and \(\mathrm{Y}\) are mixed, the result is an acidic solution. Mixing A and Z gives a neutral solution, whereas \(\mathrm{B}\) and Z give a basic solution. Identify the five unknown solutions. (Adapted from D. H. Barouch: Voyages in Conceptual Chemistry, Boston, Jones and Bartlett, \(1997 .)\)

Nicotinic acid, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NO}_{2}\), is found in minute amounts in all living cells, but appreciable amounts occur in liver, yeast, milk, adrenal glands, white meat, and corn. Whole-wheat flour contains about \(60 . \mu g\) per gram of flour. One gram (1.00 g) of the acid dissolves in water to give \(60 .\) mL of solution having a pH of \(2.70 .\) What is the approximate value of \(K_{\mathrm{a}}\) for the acid?

Sulfanilic acid, which is used in making dyes, is made by reacting aniline with sulfuric acid. (a) Is aniline a Bronsted base, a Lewis base, or both? Explain, using its possible reactions with HCl, BF \(_{3}\) or other acid. (b) Sulfanilic acid has a \(\mathrm{p} K_{\mathrm{a}}\) value of \(3.23 .\) The sodium salt of the acid, \(\mathrm{Na}\left(\mathrm{H}_{2} \mathrm{NC}_{6} \mathrm{H}_{4} \mathrm{SO}_{3}\right),\) is quite soluble in water. If you dissolve \(1.25 \mathrm{g}\) of the salt in water to give \(125 \mathrm{mL}\) of solution, what is the pH of the solution?

How can water be both a Bronsted base and a Lewis base? Can water be a Bronsted acid? A Lewis acid?

The nickel(II) ion exists as \(\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) in aqueous solution. Why is this solution acidic? As part of your answer, include a balanced equation depicting what happens when \(\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) interacts with water.

The halogens form three stable, weak acids, HOX. (a) Which is the strongest of these acids? (b) Explain why the acid strength changes as the halogen atom is changed.

Perchloric acid behaves as an acid, even when it is dissolved in sulfuric acid. (a) Write a balanced equation showing how perchloric acid can transfer a proton to sulfuric acid. (b) Draw a Lewis electron dot structure for sulfuric acid. How can sulfuric acid function as a base?

You purchase a bottle of water. On checking its \(\mathrm{pH},\) you find that it is not neutral, as you might have expected. Instead, it is slightly acidic. Why?

Iodine, \(\mathrm{I}_{2}\), is much more soluble in an aqueous solution of potassium iodide, KI, than it is in pure water. The anion found in solution is \(\mathrm{I}_{3}^{-}\) (a) Draw an electron dot structure for \(\mathrm{I}_{3}^{-}\) (b) Write an equation for this reaction, indicating the Lewis acid and the Lewis base.