16.E: Exercises
- Page ID
- 44931
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)16.2: Brønsted–Lowry Acids and Bases
Conceptual Problems
- Identify the conjugate acid–base pairs in each equilibrium.
- \(HSO^−_{4(aq)}+H_2O_{(l)} \rightleftharpoons SO^{2−}_{4(aq)}+H_3O^+_{(aq)}\)
- \(C_3H_7NO_{2(aq)}+H_3O^+_{(aq)} \rightleftharpoons C_3H_8NO^+_{2(aq)}+H_2O_{(l)} \)
- \(CH_3CO_2H_{(aq)}+NH_{3(aq)} \rightleftharpoons CH_3CO^−_{2(aq)}+NH^+_{4(aq)}\)
- \(SbF_{5(aq)}+2HF_{(aq)} \rightleftharpoons H_2F^+_{(aq)}+SbF^−_{6(aq)}\)
- Identify the conjugate acid–base pairs in each equilibrium.
- \(HF(aq)+H_2O_{(l)} \rightleftharpoons H_3O^+_{(aq)}+F^−_{(aq)} \)
- \(CH_3CH_2NH_{2(aq)}+H_2O_{(l)} \rightleftharpoons CH_3CH_2NH^+_{3(aq)}+OH^−_{(aq)}\)
- \(C_3H_7NO_{2(aq)}+OH^−_{(aq)} \rightleftharpoons C_3H_6NO^−_{2(aq)}+H_2O_{(l)}\)
- \(CH_3CO_2H_{(aq)}+2HF_{(aq)} \rightleftharpoons CH_3C(OH)_2+(aq)+HF^−_{2(aq)}\)
- Salts such as NaH contain the hydride ion (\(H^−\)). When sodium hydride is added to water, it produces hydrogen gas in a highly vigorous reaction. Write a balanced chemical equation for this reaction and identify the conjugate acid–base pairs.
- Write the expression for \(K_a\) for each reaction.
- \(HCO^−_{3(aq)}+H_2O_{(l)} \rightleftharpoons CO^{2−}_{3(aq)}+H_3O^+_{(aq)}\)
- \(formic\; acid_{(aq)}+H_2O_{(l)} \rightleftharpoons formate_{(aq)}+H_3O^+_{(aq)}\)
- \(H_3PO_{4(aq)}+H_2O_{(l)} \rightleftharpoons H_2PO^−_{4(aq)}+H_3O^+_{(aq)}\)
- Write an expression for the ionization constant \(K_b\) for each reaction.
- \(OCH^−_{3(aq)}+H_2O_{(l)} \rightleftharpoons HOCH_{3(aq)}+OH−(aq)\)
- \(NH^−_{2(aq)}+H_2O_{(l)} \rightleftharpoons NH_{3(aq)}+OH^−_{(aq)}\)
- \(S^{2−}_{(aq)}+H_2O_{(l)} \rightleftharpoons HS^−_{(aq)}+OH^−_{(aq)}\)
- Predict whether each equilibrium lies primarily to the left or to the right.
- \(HBr_{(aq)}+H_2O_{(l)} \rightleftharpoons H_3O^+_{(aq)}+Br^−_{(aq)}\)
- \(NaH_{(soln)}+NH_{3(l)} \rightleftharpoons H2(soln)+NaNH_{2(soln)}\)
- \(OCH^−_{3(aq)}+NH_{3(aq)} \rightleftharpoons CH3OH(aq)+NH^−_{2(aq)}\)
- \(NH_{3(aq)}+HCl_{(aq)} \rightleftharpoons NH^+_{4(aq)}+Cl^−_{(aq)}\)
- Species that are strong bases in water, such as \(CH_3^−\), \(NH_2^−\), and \(S^{2−}\), are leveled to the strength of \(OH^−\), the conjugate base of \(H_2O\). Because their relative base strengths are indistinguishable in water, suggest a method for identifying which is the strongest base. How would you distinguish between the strength of the acids \(HIO_3\), \(H_2SO_4\), and \(HClO_4\)?
- Is it accurate to say that a 2.0 M solution of \(H_2SO_4\), which contains two acidic protons per molecule, is 4.0 M in \(H^+\)? Explain your answer.
- The alkalinity of soil is defined by the following equation: alkalinity = \([HCO_3^−] + 2[CO_3^{2−}] + [OH^−] − [H^+]\). The source of both \(HCO_3^−\) and \(CO_3^{2−}\) is \(H_2CO_3\). Explain why the basicity of soil is defined in this way.
- Why are aqueous solutions of salts such as \(CaCl_2\) neutral? Why is an aqueous solution of \(NaNH_2\) basic?
- Predict whether aqueous solutions of the following are acidic, basic, or neutral.
- \(Li_3N\)
- \(NaH\)
- \(KBr\)
- \(C_2H_5NH_3^+Cl^−\)
- When each compound is added to water, would you expect the \(pH\) of the solution to increase, decrease, or remain the same?
- \(LiCH_3\)
- \(MgCl_2\)
- \(K_2O\)
- \((CH_3)_2NH_2^+Br^−\)
- Which complex ion would you expect to be more acidic: \(Pb(H_2O)_4^{2+}\) or \(Sn(H_2O)_4^{2+}\)? Why?
- Would you expect \(Sn(H_2O)_4^{2+}\) or \(Sn(H_2O)_6^{4+}\) to be more acidic in aqueous solutions? Why?
- Is it possible to arrange the hydrides \(LiH\), \(RbH\), \(KH\), \(CsH\), and \(NaH\) in order of increasing base strength in aqueous solution? Why or why not?
Conceptual Answer
1.
- \(\overset{\text{acid 1}}{HSO^−_{4(aq)}} + \underset{\text{base 2}}{H_2O_{(l)}} \rightleftharpoons \overset{\text{base 1}}{SO^{2−}_{4(aq)}} + \underset{\text{acid 2}}{H_3O^+_{(aq)}}\)
- \(\underset{\text{base 2}}{C_3H_7NO_{2(aq)}} + \overset{\text{acid 1}}{H_3O^+_{(aq)}} \rightleftharpoons \underset{\text{acid 2}}{C_3H_8NO^+_{2(aq)}} + \overset{\text{base 1}}{H_2O_{(l)}}\)
- \(\overset{\text{acid 1}}{HOAc_{(aq)}} + \underset{\text{base 2}}{NH_{3(aq)}} \rightleftharpoons \overset{\text{base 1}}{CH_3CO^−_{2(aq)}} + \underset{\text{acid 2}}{NH^+_{4(aq)}}\)
- \(\overset{\text{acid 1}}{SbF_{5(aq)}} + \underset{\text{base 2}}{2HF_{(aq)}} \rightleftharpoons \underset{\text{acid 2}}{H_2F^+_{(aq)}} + \overset{\text{base 1}}{SbF_6^−(aq)}\)
Numerical Problems
- Arrange these acids in order of increasing strength.\
- acid A: \(pK_a = 1.52\)
- acid B: \(pK_a = 6.93\)
- acid C: \(pK_a = 3.86\)
Given solutions with the same initial concentration of each acid, which would have the highest percent ionization?
- Arrange these bases in order of increasing strength:
- base A: \(pK_b = 13.10\)
- base B: \(pK_b = 8.74\)
- base C: \(pK_b = 11.87\)
Given solutions with the same initial concentration of each base, which would have the highest percent ionization?
- Calculate the \(K_a\) and the \(pK_a\) of the conjugate acid of a base with each \(pK_b\) value.
- 3.80
- 7.90
- 13.70
- 1.40
- −2.50
- Benzoic acid is a food preservative with a \(pK_a\) of 4.20. Determine the \(K_b\) and the \(pK_b\) for the benzoate ion.
- Determine \(K_a\) and \(pK_a\) of boric acid \([B(OH)_3]\), solutions of which are occasionally used as an eyewash; the \(pK_b\) of its conjugate base is 4.80.
Numerical Answers
1. acid B < acid C < acid A (strongest)
3.
- \(K_a = 6.3 \times 10^{−11}\); \(pK_a = 10.20\)
- \(K_a = 7.9 \times 10^{−7}\); \(pK_a = 6.10\)
- \(K_a = 0.50\); \(pK_a = 0.30\)
- \(K_a = 2.5 \times 10^{−13}\); \(pK_a = 12.60\)
- \(K_a = 3.2 \times 10^{−17}\); \(pK_a = 16.50\)
5. \(K_a = 6.3 \times 10^{−10}\); \(pK_a = 9.20\)
16.3: The Autoionization of Water
Conceptual Problems
- What is the relationship between the value of the equilibrium constant for the autoionization of liquid water and the tabulated value of the ion-product constant of liquid water (\(K_w\))?
- The density of liquid water decreases as the temperature increases from 25°C to 50°C. Will this effect cause \(K_w\) to increase or decrease? Why?
- Show that water is amphiprotic by writing balanced chemical equations for the reactions of water with \(HNO_3\) and \(NH_3\). In which reaction does water act as the acid? In which does it act as the base?
- Write a chemical equation for each of the following.
- Nitric acid is added to water.
- Potassium hydroxide is added to water.
- Calcium hydroxide is added to water.
- Sulfuric acid is added to water.
- Show that \(K\) for the sum of the following reactions is equal to \(K_w\).
Conceptual Answers
1.
\[K_{auto} = \dfrac{[H_3O^+][OH^−]}{[H_2O]^2}\]
\[K_w = [H_3O^+][OH^−] = K_{auto}[H_2O]^2\]
Numerical Problems
- The autoionization of sulfuric acid can be described by the following chemical equation:
\[H_2SO_{4(l)}+H_2SO_{4(l)} \rightleftharpoons H_3SO^+_{4(soln)}+H_SO^−_{4(soln)}\] At 25°C, K = 3 × 10−4. Write an equilibrium constant expression for\(KH_2SO_4\) that is analogous to \(K_w\). The density of \(H_2SO_4\) is 1.8 g/cm3 at 25°C. What is the concentration of H3SO4+? What fraction of \(H_2SO_4\) is ionized? - An aqueous solution of a substance is found to have \([H_3O]^+ = 2.48 \times 10^{−8}\; M\). Is the solution acidic, neutral, or basic?
- The pH of a solution is 5.63. What is its pOH? What is the [OH−]? Is the solution acidic or basic?
- State whether each solution is acidic, neutral, or basic.
- \([H_3O^+] = 8.6 \times 10^{−3}\; M\)
- \([H_3O^+] = 3.7 \times 10^{−9}\; M\)
- \([H_3O^+] = 2.1 \times 10^{−7}\; M\)
- \([H_3O^+] = 1.4 \times 10^{−6}\; M\)
- Calculate the pH and the pOH of each solution.
- 0.15 M HBr
- 0.03 M KOH
- \(2.3 \times 10^{−3}\; M\; HNO_3\)
- \(9.78 \times 10^{−2} \;M\; NaOH\)
- 0.00017 M HCl
- 5.78 M HI
- Calculate the pH and the pOH of each solution.
- 25.0 mL of \(2.3 \times 10^{−2}\; M\; HCl\), diluted to 100 mL
- 5.0 mL of 1.87 M NaOH, diluted to 125 mL
- 5.0 mL of 5.98 M HCl added to 100 mL of water
- 25.0 mL of 3.7 M \(HNO_3\) added to 250 mL of water
- 35.0 mL of 0.046 M HI added to 500 mL of water
- 15.0 mL of 0.0087 M KOH added to 250 mL of water.
- The pH of stomach acid is approximately 1.5. What is the \([H^+]\)?
- Given the pH values in parentheses, what is the \([H^+]\) of each solution?
- household bleach (11.4)
- milk (6.5)
- orange juice (3.5)
- seawater (8.5)
- tomato juice (4.2)
- A reaction requires the addition of 250.0 mL of a solution with a pH of 3.50. What mass of HCl (in milligrams) must be dissolved in 250 mL of water to produce a solution with this pH?
- If you require 333 mL of a pH 12.50 solution, how would you prepare it using a 0.500 M sodium hydroxide stock solution?
Numerical Answers
1.
\[[H_3SO_4^+] = 0.3 M\]
So the fraction ionized is 0.02.
3. \(pOH = 8.37\); \([OH^−] = 4.3 \times 10^{−9}\; M\); acidic
5.
- pH = 0.82; pOH = 13.18
- pH = 12.5; pOH = 1.5
- pH = 2.64; pOH = 11.36
- pH = 12.990; pOH = 1.010
- pH = 3.77; pOH = 10.23
- pH = −0.762; pOH = 14.762
9. 2.9 mg HCl