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Chemistry 2012

JOHN E. MCMURRY, ROBERT C. FAY, JORDAN FANTINI

Chapter 14

Aqueous Equilibria: Acids and Bases

Educators


Problem 1

Write a balanced equation for the dissociation of each of the following Brønsted–Lowry acids in water:
$\begin{array}{llll}{\text { (a) } \mathrm{H}_{2} \mathrm{SO}_{4}} & {\text { (b) HSO_ - }} & {\text { (c) } \mathrm{H}_{3} \mathrm{O}^{+}} & {\text { (d) } \mathrm{NH}_{4}+}\end{array}$
What is the conjugate base of each acid?

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Problem 2

What is the conjugate acid of each of the following Brønsted–Lowry bases?
$\begin{array}{llll}{\text { (a) } \mathrm{HCO}_{3}^{-}} & {\text { (b) } \mathrm{CO}_{3}^{2-}} & {\text { (c) } \mathrm{OH}^{-}} & {\text { (d) } \mathrm{H}_{2} \mathrm{PO}_{4}^{-}}\end{array}$

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Problem 3

For the following reaction in aqueous solution, identify the Brønsted–Lowry acids, bases, and conjugate acid–base pairs:

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Problem 4

If you mix equal concentrations of reactants and products, which of the following reactions proceed to the right and which proceed to the left?
(a) $\mathrm{HF}(a q)+\mathrm{NO}_{3}^{-}(a q) \rightleftharpoons \mathrm{HNO}_{3}(a q)+\mathrm{F}^{-}(a q)$
(b) $\mathrm{NH}_{4}^{+}(a q)+\mathrm{CO}_{3}^{2-}(a q) \rightleftharpoons \mathrm{HCO}_{3}^{-(a q)}+\mathrm{NH}_{3}(a q)$

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Problem 5

The following pictures represent aqueous solutions of two acids HA or Y); water molecules have been omitted for clarity.
(a) Which is the stronger acid, $\mathrm{HX}$ or HY?
(b) Which is the stronger base, $X^{-}$ or $Y^{-} ?$
(c) If you mix equal concentrations of reactants and products, will the following
reaction proceed to the right or to the left?
$$\mathrm{HX}+\mathrm{Y}^{-} \rightleftharpoons \mathrm{HY}+\mathrm{X}^{-}$$

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Problem 6

Some of the following ions have been detected by mass spectrometry:
$\mathrm{H}_{9} \mathrm{O}_{4}^{+}, \mathrm{H}_{13} \mathrm{O}_{5}^{+}, \mathrm{H}_{19} \mathrm{O}_{9}^{+}, \mathrm{H}_{25} \mathrm{O}_{11}^{+}, \mathrm{H}_{43} \mathrm{O}_{21}^{+}$
(a) Which should be considered as hydrates of the proton?
(b) For the ions that are hydrates, tell how many water molecules are present in addition to the proton.

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Problem 7

The concentration of $\mathrm{H}_{3} \mathrm{O}^{+}$ ions in the runoff from a coal mine is $1.4 \times 10^{-4} \mathrm{M}$ . Calculate the concentration of $\mathrm{OH}^{-}$ ions, and classify the solution as acidic, neutral, or basic.

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Problem 8

The concentration of $\mathrm{OH}^{-}$ in a sample of seawater is $2.0 \times 10^{-6} \mathrm{M} .$ Calculate the concentration of $\mathrm{H}_{3} \mathrm{O}^{+}$ ions, and classify the solution as acidic, neutral, or basic.

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Problem 9

At $50^{\circ} \mathrm{C}$ the value of $K_{\mathrm{w}}$ is $5.5 \times 10^{-14} .$ What are the concentrations of $\mathrm{H}_{3} \mathrm{O}^{+}$ and $\mathrm{OH}^{-}$ in a neutral solution at $50^{\circ} \mathrm{C} ?$

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Problem 10

Calculate the pH of each of the following solutions:
(a) A sample of seawater that has an OH - concentration of 1.58 \times $10^{-6} \mathrm{M}$
(b) A sample of acid rain that has an $\mathrm{H}_{3} \mathrm{O}^{+}$ concentration of $6.0 \times 10^{-5} \mathrm{M}$

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Problem 11

Calculate the concentrations of $\mathrm{H}_{3} \mathrm{O}^{+}$ and $\mathrm{OH}^{-}$ in each of the following solutions:
(a) Human blood (pH 7.40$) \qquad$ (b) A cola beverage (pH 2.8$)$

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Problem 12

Calculate the pH of the following solutions:
$\begin{array}{llll}{\text { (a) } 0.050 \mathrm{MHClO}_{4}} & {\text { (b) } 6.0 \mathrm{MHCl}} & {\text { (c) } 4.0 \mathrm{M} \mathrm{KOH}} & {\text { (d) } 0.010 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}}\end{array}$

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Problem 13

Calculate the $\mathrm{pH}$ of a solution prepared by dissolving 0.25 $\mathrm{g}$ of $\mathrm{BaO}$ in enough water to make 0.500 $\mathrm{L}$ of solution.

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Problem 14

The $\mathrm{pH}$ of 0.10 $\mathrm{M}$ HOCl is 4.23 . Calculate $K_{\mathrm{a}}$ and $\mathrm{p} K_{\mathrm{a}}$ for hypochlorous acid, and check your answers against the values given in Table $14.2 .$

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Problem 15

The following pictures represent aqueous solutions of three acids HA , Y, or Z); water molecules have been omitted for clarity:
(a) Arrange the three acids in order of increasing value of $K_{\mathrm{a}}$ .
(b) Which acid, if any, is a strong acid?
(c) Which solution has the highest pH, and which has the lowest pH?

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Problem 16

Acetic acid, $\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H},$ is the solute that gives vinegar its characteristic odor and sour taste. Calculate the $\mathrm{pH}$ and the concentrations of all species present
$\left(\mathrm{H}_{3} \mathrm{O}^{+}, \mathrm{CH}_{3} \mathrm{CO}_{2}^{-}, \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}, \text { and } \mathrm{OH}^{-}\right)$ in:
(a) 1.00 $\mathrm{M} \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H} \quad$ (b) 0.0100 $\mathrm{M} \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}$

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Problem 17

A vitamin $C$ tablet containing 250 $\mathrm{mg}$ of ascorbic acid $\left(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6},\right.$ $K_{\mathrm{a}}=8.0 \times 10^{-5} )$ is dissolved in a 250 $\mathrm{mL}$ glass of water. What is the pH of the solution?

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Problem 18

Calculate the percent dissociation of $\mathrm{HF}\left(K_{\mathrm{a}}=3.5 \times 10^{-4}\right)$ in:
(a) 0.050 $\mathrm{MHF} \quad$ (b) 0.50 $\mathrm{M} \mathrm{HF}$

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Problem 19

Calculate the pH and the concentrations of all species present in 0.10 $\mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{3} .$ Values of $K_{\mathrm{a}}$ are in Table 14.3

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Problem 20

Like sulfuric acid, selenic acid $\left(\mathrm{H}_{2} \mathrm{SeO}_{4}\right)$ is a diprotic acid that has a very large value of $K_{\text { all }}$ Calculate the $\mathrm{pH}$ and the concentrations of all species present in 0.50 $\mathrm{M} \mathrm{H}_{2} \mathrm{SeO}_{4}\left(K_{\mathrm{a} 2}=1.2 \times 10^{-2}\right) .$

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Problem 21

PROBLEM 14.21 Calculate the $\mathrm{pH}$ and the concentrations of all species present in 0.40 $\mathrm{M} \mathrm{NH}_{3}\left(K_{\mathrm{b}}=1.8 \times 10^{-5}\right)$

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Problem 22

Strychnine $\left(\mathrm{C}_{21} \mathrm{H}_{22} \mathrm{N}_{2} \mathrm{O}_{2}\right),$ a deadly poison used for killing rodents, is a weak base having $K_{\mathrm{b}}=1.8 \times 10^{-6} .$ Calculate the $\mathrm{pH}$ of a saturated solution of strychnine $(16 \mathrm{mg} / 100 \mathrm{mL})$

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Problem 23

(a) Piperidine $\left(\mathrm{C}_{5} \mathrm{H}_{11} \mathrm{N}\right)$ is an amine found in black pepper. Find $K_{\mathrm{b}}$ for piperidine in Appendix $\mathrm{C},$ and then calculate $K_{\mathrm{a}}$ for the $\mathrm{C}_{5} \mathrm{H}_{11} \mathrm{NH}^{+}$ cation.
(b) Find $K_{\mathrm{a}}$ for $\mathrm{HOC}$ lin Appendix $\mathrm{C},$ and then calculate $K_{\mathrm{b}}$ for $\mathrm{OCl}^{-}$
(c) The value of $\mathrm{p} K_{\mathrm{a}}$ for formic acid $\left(\mathrm{HCO}_{2} \mathrm{H}\right)$ is $3.74 .$ What is the value of $\mathrm{p} K_{\mathrm{b}}$ for the
formate ion $\left(\mathrm{HCO}_{2}\right) ?$

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Problem 24

PROBLEM 14.24 Predict whether the following salt solutions are neutral or acidic, and calculate the pH of each:
(a) 0.25 $\mathrm{M} \mathrm{NH}_{4} \mathrm{Br} \quad$ (b) $0.40 \mathrm{M} \mathrm{ZnCl}_{2} ; K_{\mathrm{a}}$ for $\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}$ is $2.5 \times 10^{-10}$

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Problem 25

Calculate the pH of $0.20 \mathrm{M} \mathrm{NaNO}_{2} ; K_{\mathrm{a}}$ for HNO $_{2}$ is $4.6 \times 10^{-4}$

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Problem 26

Calculate $K_{\mathrm{a}}$ for the cation and $K_{\mathrm{b}}$ for the anion in an aqueous
$\mathrm{NH}_{4} \mathrm{CN}$ solution. Is the solution acidic, basic, or neutral?

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Problem 27

Classify each of the following salt solutions as acidic, basic, or neutral:
$\begin{array}{llll}{\text { (a) } \mathrm{KBr}} & {\text { (b) NaNO_ }} & {\text { (c) } \mathrm{NH}_{4} \mathrm{Br}} & {\text { (d) ZnCl_ }} & {\text { (e) } \mathrm{NH}_{4} \mathrm{F}}\end{array}$

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Problem 28

Identify the stronger acid in each of the following pairs:
$\begin{array}{ll}{\text { (a) } \mathrm{H}_{2} \mathrm{S} \text { or } \mathrm{H}_{2} \mathrm{Se}} & {\text { (b) HI or } \mathrm{H}_{2} \mathrm{Te}}\end{array}$
(c) $\mathrm{HNO}_{2}$ or HNO $_{3} \quad$ (d) $\mathrm{H}_{2} \mathrm{SO}_{3}$ or $\mathrm{H}_{2} \mathrm{SeO}_{3}$

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Problem 29

PROBLEM 14.29 For each of the following reactions, identify the Lewis acid and the
Lewis base.
(a) $\mathrm{AlCl}_{3}+\mathrm{Cl}^{-} \longrightarrow \mathrm{AlCl}_{4}^{-} \quad$ (b) $2 \mathrm{NH}_{3}+\mathrm{Ag}^{+} \longrightarrow \mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}^{+}$
(c) $\mathrm{SO}_{2}+\mathrm{OH}^{-} \longrightarrow \mathrm{HSO}_{3}^{-} \quad$ (d) $6 \mathrm{H}_{2} \mathrm{O}+\mathrm{Cr}^{3+} \longrightarrow \mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}$

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Problem 30

For the following Lewis acid–base reaction, draw electron-dot structures for the reactants and products, and use the curved arrow notation to represent the donation of a lone pair of electrons from the Lewis base to the Lewis acid.
$\mathrm{BeCl}_{2}+2 \mathrm{Cl}^{-} \rightarrow \mathrm{BeCl}_{4}^{2-}$

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Problem 31

The reaction of lime (CaO) with $\mathrm{SO}_{2}$ in the scrubber of a power
plant is a Lewis acid-base reaction. Explain.

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Problem 32

What is the $\mathrm{pH}$ of 1.00 $\mathrm{L}$ of rainwater that has dissolved 5.47 $\mathrm{mg}$ of $\mathrm{NO}_{2} ?$ Assume that all of the $\mathrm{NO}_{2}$ has reacted with water to give nitric acid.

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Problem 33

For each of the following reactions, identify the Bronsted-Lowry acids and bases:

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Problem 34

The following pictures represent aqueous solutions of three acids $\mathrm{HA}(\mathrm{A}=\mathrm{X}, \mathrm{Y}, \text { or } \mathrm{Z})$ ; water molecules have been omitted for clarity:
(a) What is the conjugate base of each acid?
(b) Arrange the three acids in order of increasing acid strength.
(c) Which acid, if any, is a strong acid?
(d) Which acid has the smallest value of $K_{\mathrm{a}} ?$
(e) What is the percent dissociation in the solution of HZ?

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Problem 35

Which of the following pictures represents a solution of a weak diprotic acid $\mathrm{H}_{2} \mathrm{A} ?$ (Water molecules are omitted for clarity. Which pictures represent an impossible situation? Explain.

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Problem 36

Which of the following pictures best represents an aqueous solution of sulfuric acid? Explain. (Water molecules have been omitted for clarity.)

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Problem 37

The following pictures represent aqueous solutions of three acids $\mathrm{HA}(\mathrm{A}=\mathrm{X}, \mathrm{Y}, \text { or } \mathrm{Z}) ;$ water molecules have been omitted for clarity:
(a) Which conjugate base $\left(\mathrm{A}^{-}=\mathrm{X}^{-}, \mathrm{Y}^{-}, \text { or } \mathrm{Z}^{-}\right)$ has the largest value of $K_{\mathrm{b}} ?$
(b) Which $\mathrm{A}^{-}$ ion is the weakest base?

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Problem 38

The following pictures represent solutions of three salts NaA $\left(\mathrm{A}^{-}=\mathrm{X}^{-}, \mathrm{Y}^{-}, \text { or } \mathrm{Z}^{-}\right) ;$ water molecules and $\mathrm{Na}^{+}$ ion
have been omitted for clarity:
(a) Arrange the three $\mathrm{A}^{-}$ anions in order of increasing base strength.
(b) Which $\mathrm{A}^{-}$ anion has the strongest conjugate acid?
(c) Which $A^{-}$ anion has the smallest value of $p K_{b} ?$
(d) Why, within each box, is the number of HA molecules and $O H^{-}$ anions the same?

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Problem 39

The following picture represents the hydrated metal cation $\mathrm{M}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{n+},$ where $n=1,2,$ or $3 .$
(a) Write a balanced equation for the reaction of $\mathrm{M}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{n+}$ with water, and write the equilibrium equation for the reaction.
(b) Does the equilibrium constant increase, decrease, or remain the same as the value of $n$ increases? Explain
(c) Which $\mathrm{M}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{n+}$ ion $(n=1,2, \text { or } 3)$ is the stronges acid, and which has the strongest conjugate base?

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Problem 40

Locate sulfur, selenium, chlorine, and bromine in the periodic table:
(a) Which binary acid $\left(\mathrm{H}_{2} \mathrm{S}, \mathrm{H}_{2} \mathrm{Se}, \mathrm{HCl}, \text { or } \mathrm{HBr}\right)$ is the strongest? Which is the weakest? Explain.
(b) Which oxoacid $\left(\mathrm{H}_{2} \mathrm{SO}_{3}, \mathrm{H}_{2} \mathrm{SeO}_{3}, \mathrm{HClO}_{3}, \text { or } \mathrm{HBrO}_{3}\right)$ is the strongest? Which is the weakest? Explain.

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Problem 41

Look at the electron-dot structures of the following molecules and ions:
(a) Which of these molecules and ions can behave as a Brønsted–Lowry acid? Which can behave as a
Brønsted–Lowry base?
(b) Which can behave as a Lewis acid? Which can behave as a Lewis base?

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Problem 42

Boric acid $\left(\mathrm{H}_{3} \mathrm{BO}_{3}\right)$ is a weak monoprotic acid that yields
$\mathrm{H}_{3} \mathrm{O}^{+}$ ions in water. $\mathrm{H}_{3} \mathrm{BO}_{3}$ might behave either as a Brensted-Lowry acid or as a Lewis acid, though it is, in fact, a Lewis acid.
(a) Write a balanced equation for the reaction with water in which $\mathrm{H}_{3} \mathrm{BO}_{3}$ behaves as a Bronsted-Lowry acid.
(b) Write a balanced equation for the reaction with water in which $\mathrm{H}_{3} \mathrm{BO}_{3}$ behaves as a Lewis acid. Hint: One of the reaction products contains a tetrahedral boron atom.

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Problem 43

The reaction of $\mathrm{PCl}_{4}^{+}$ with $\mathrm{Cl}^{-}$ is a Lewis acid-base reaction. Draw electron-dot structures for the reactants and products, and use the curved arrow notation (Section
14.16$)$ to represent the donation of a lone pair of electrons from the Lewis base to the Lewis acid.

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Problem 44

Give three examples of molecules or ions that are Brønsted–Lowry bases but not Arrhenius bases.

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Problem 45

Give an example of an anion that can behave both as a Bronsted-Lowry acid and as a Brensted-Lowry base.

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Problem 46

Give the formula for the conjugate base of each of the following Brensted-Lowry acids:
$\begin{array}{ll}{\text { (a) } \mathrm{HSO}_{4}^{-}} & {\text { (b) } \mathrm{H}_{2} \mathrm{SO}_{3}} & {\text { (c) } \mathrm{H}_{2} \mathrm{PO}_{4}^{-}} \\ {\text { (d) } \mathrm{NH}_{4}^{+}} & {\text { (e) } \mathrm{H}_{2} \mathrm{O}} & {\text { (f) } \mathrm{NH}_{3}}\end{array}$

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Problem 47

Give the formula for the conjugate acid of each of the following Brensted-Lowry bases:
(a) $\mathrm{SO}_{3^2-} \quad$
(b) $\mathrm{H}_{2} \mathrm{O} \quad$
(c) $\mathrm{CH}_{3} \mathrm{NH}_{2}$
(d) $\mathrm{OH}^{-} \quad$
(e) $\mathrm{HCO}_{3}^{-} \quad$
(f) $\mathrm{H}^{-}$

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Problem 48

For each of the following reactions, identify the Brønsted–Lowry acids and bases and the conjugate acid–base pairs:
(a) $\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(a q)+\mathrm{NH}_{3}(a q) \rightleftharpoons \mathrm{NH}_{4}^{+}(a q)+\mathrm{CH}_{3} \mathrm{CO}_{2}^{-}(a q)$
(b) $\mathrm{CO}_{3}^{2-}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{HCO}_{3}(a q)$
(c) $\mathrm{HSO}_{3}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{SO}_{3}^{2-}(a q)$
(d) $\mathrm{HSO}_{3}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{SO}_{3}(a q)+\mathrm{OH}^{-}(a q)$

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Problem 49

For each of the following reactions, identify the Brønsted– Lowry acids and bases and the conjugate acid–base pairs:
(a) $\mathrm{CN}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{OH}^{-}(a q)+\mathrm{HCN}(a q)$
(b) $\mathrm{H}_{2} \mathrm{PO}_{4}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{HPO}_{4}^{2-}(a q)$
(c) $\mathrm{HPO}_{4}^{2-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{OH}^{-}(a q)+\mathrm{H}_{2} \mathrm{PO}_{4}^{-(a q)}$
(d) $\mathrm{NH}_{4}^{+}(a q)+\mathrm{NO}_{2}^{-}(a q) \rightleftharpoons \mathrm{HNO}_{2}(a q)+\mathrm{NH}_{3}(a q)$

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Problem 50

Which of the following species behave as strong acids or as strong bases in aqueous solution? See Table 14.1 to check your answers.
(a) $\mathrm{HNO}_{2}$
(b) $HNO_{3}$
(c) $\mathrm{NH}_{4}^{+} \quad$
(d) $\mathrm{Cl}^{-}$
(e) $\mathrm{H}^{-} \quad$
(f) $\mathrm{O}^{2-} \quad$
(g) $\mathrm{H}_{2} \mathrm{SO}_{4}$

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Problem 51

Which acid in each of the following pairs has the stronger conjugate base? See Table 14.1 for help with parts (c) and (d).
$\begin{array}{ll}{\text { (a) } \mathrm{H}_{2} \mathrm{CO}_{3} \text { or } \mathrm{H}_{2} \mathrm{SO}_{4}} & {\text { (b) HCl or HF }} \\ {\text { (c) HF or NH }_{4}^{+}} & {\text { (d) } \mathrm{HCN} \text { or } \mathrm{HSO}_{4}^{-}}\end{array}$

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Problem 52

Of the conjugate acid-base pairs $\mathrm{HF} / \mathrm{F}^{-}, \mathrm{HCl} / \mathrm{Cl}^{-},$ and
$\mathrm{HCN} / \mathrm{CN}^{-},$ complete the following equation with the
pair that gives an equilibrium constant $K_{\mathrm{c}} >1$
_____ $+\mathrm{H}_{2} \mathrm{PO}_{4}^{-} \longrightarrow$ _____ $+\mathrm{H}_{3} \mathrm{PO}_{4}$

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Problem 53

Of the conjugate acid-base pairs $\mathrm{HSO}_{4}^{-} / \mathrm{SO}_{4}^{2-}, \mathrm{NH}_{4}^{+} /$ $\mathrm{NH}_{3},$ and $\mathrm{HNO}_{3} / \mathrm{NO}_{3}^{-},$ complete the following equation with the pair that gives an equilibrium constant $K_{\mathrm{c}}>1$
_____ $+\mathrm{H}_{2} \mathrm{S} \longrightarrow$ _____ $+\mathrm{HS}^{-}$

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Problem 54

For each of the following solutions, calculate $\left[\mathrm{OH}^{-}\right]$ from
$\left[\mathrm{H}_{3} \mathrm{O}^{+}\right],$ or $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ from $\left[\mathrm{OH}^{-}\right] .$ Classify each solution as acidic, basic, or neutral.
(a) $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=3.4 \times 10^{-9} \mathrm{M} \quad$
(b) $\left[\mathrm{OH}^{-}\right]=0.010 \mathrm{M}$
(c) $\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-10} \mathrm{M}$
(d) $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-7} \mathrm{M}$
(e) $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=8.6 \times 10^{-5} \mathrm{M}$

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Problem 55

For each of the following solutions, calculate $\left[\mathrm{OH}^{-}\right]$ from $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right],$ or $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ from $\left[\mathrm{OH}^{-}\right] .$ Classify each solution as acidic, basic, or neutral.
(a) $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=2.5 \times 10^{-4} \mathrm{M} \quad$ (b) $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=2.0 \mathrm{M}$
(c) $\left[\mathrm{OH}^{-}\right]=5.6 \times 10^{-9} \mathrm{M}$
(e) $\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-7} \mathrm{M}$

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Problem 56

Water superheated under pressure to $200^{\circ} \mathrm{C}$ and 750 $\mathrm{atm}$
has $K_{\mathrm{w}}=1.5 \times 10^{-11}$ . What is $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ and $\left[\mathrm{OH}^{-}\right]$ at $200^{\circ} \mathrm{C} ?$ Is the water acidic, basic, or neutral?

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Problem 57

Water at $500^{\circ} \mathrm{C}$ and 250 atm is a supercritical fluid. Under these conditions, $K_{\mathrm{w}}$ is approximately $1.7 \times 10^{-19} .$ Estimate $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ and $\left[\mathrm{OH}^{-}\right]$ at $500^{\circ} \mathrm{C} .$ Is the water acidic, basic, or neutral?

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Problem 58

Calculate the $\mathrm{pH}$ to the correct number of significant figures for solutions with the following concentrations of $\mathrm{H}_{3} \mathrm{O}^{+}$ or $\mathrm{OH}^{-} :$
$\begin{array}{ll}{\text { (a) }\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=2.0 \times 10^{-5} \mathrm{M}} & {\text { (b) }\left[\mathrm{OH}^{-}\right]=4 \times 10^{-3} \mathrm{M}} \\ {\text { (c) }\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=3.56 \times 10^{-9} \mathrm{M}} & {\text { (d) }\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=10^{-3} \mathrm{M}} \\ {\text { (e) }\left[\mathrm{OH}^{-}\right]=12 \mathrm{M}}\end{array}$

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Problem 59

What is the pH to the correct number of significant figures for solutions with the following concentrations of $\mathrm{H}_{3} \mathrm{O}^{+}$ or $\mathrm{OH}^{-} ?$
(a) $\left[\mathrm{OH}^{-}\right]=7.6 \times 10^{-3} \mathrm{M} \quad$
(b) $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=10^{-8} \mathrm{M}$
(c) $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=5.0 \mathrm{M} \quad$
(d) $\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-7} \mathrm{M}$
(e) $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=2.18 \times 10^{-10} \mathrm{M}$

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Problem 60

Calculate the $\mathrm{H}_{3} \mathrm{O}^{+}$ concentration to the correct number of significant figures for solutions with the following $\mathrm{pH}$ values:
$\begin{array}{llll}{\text { (a) } 4.1} & {\text { (b) } 10.82} & {\text { (c) } 0.00}\end{array}$
$\begin{array}{llll}{\text { (d) } 14.25} & {\text { (e) }-1.0} & {\text { (f) } 5.238}\end{array}$

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Problem 61

What is the $\mathrm{H}_{3} \mathrm{O}^{+}$ concentration to the correct number of significant figures for solutions with the following $\mathrm{pH}$ values?
$\begin{array}{ll}{\text { (a) } 9.0} & {\text { (b) } 7.00} & {\text { (c) }-0.3} \\ {\text { (d) } 15.18} & {\text { (e) } 2.63} & {\text { (f) } 10.756}\end{array}$

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Problem 62

Which of the indicators thymol blue, alizarin yellow, chlorphenol red, or methyl orange would be most appropriate to detect a pH change from:
$\begin{array}{llll}{\text { (a) } 7 \text { to } 5 ?} & {\text { (b) } 8 \text { to } 10 ?} & {\text { (c) } 3 \text { to } 5 ?}\end{array}$

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Problem 63

Which of the indicators methyl violet, bromcresol green, phenol red, or thymolphthalein, would be most appropriate to detect a pH change from:
$\begin{array}{llll}{\text { (a) } 4 \text { to } 6 ?} & {\text { (b) } 8 \text { to } 10 ?} & {\text { (c) } 2 \text { to } 0 ?}\end{array}$

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Problem 64

A solution of NaOH has a pH of $10.50 .$ How many grams of CaO should be dissolved in sufficient water to make 1.00 $\mathrm{L}$ of a solution having the same pH?

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Problem 65

A solution of KOH has a pH of $10.00 .$ How many grams of SrO should be dissolved in sufficient water to make 2.00 $\mathrm{L}$ of a solution having the same pH?

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Problem 66

Calculate the pH of solutions prepared by:
(a) Dissolving 4.8 $\mathrm{g}$ of lithium hydroxide in water to give 250 mL of solution
(b) Dissolving 0.93 g of hydrogen chloride in water to give 0.40 $\mathrm{L}$ of solution
(c) Diluting 50.0 $\mathrm{mL}$ of 0.10 $\mathrm{M} \mathrm{HCl}$ to a volume of 1.00 $\mathrm{L}$
(d) Mixing 100.0 $\mathrm{mL}$ of $2.0 \times 10^{-3} \mathrm{M} \mathrm{HCl}$ and 400.0 $\mathrm{mL}$ of
$1.0 \times 10^{-3} \mathrm{M} \mathrm{HClO}_{4}$ (Assume that volumes are additive.)

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Problem 67

Calculate the pH of solutions prepared by:
(a) Dissolving 0.20 $\mathrm{g}$ of sodium oxide in water to give 100.0 $\mathrm{mL}$ of solution
(b) Dissolving 1.26 $\mathrm{g}$ of pure nitric acid in water to give 0.500 Lof solution
(c) Diluting 40.0 $\mathrm{mL}$ of 0.075 $\mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}$ to a volume of
300.0 $\mathrm{mL}$
(d) Mixing equal volumes of 0.20 $\mathrm{M} \mathrm{HCl}$ and 0.50 $\mathrm{M} \mathrm{HNO}_{3}$
(Assume that volumes are additive.)

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Problem 68

Look up the values of $K_{\mathrm{a}}$ in Appendix $\mathrm{C}$ for $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}$ , $\mathrm{HNO}_{3}, \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H},$ and $\mathrm{HOCl},$ and arrange these acids in order of:
(a) Increasing acid strength
(b) Decreasing percent dissociation
Also estimate $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ in a 1.0 $\mathrm{M}$ solution of each acid.

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Problem 69

Look up the values of $K_{\mathrm{a}}$ in Appendix $\mathrm{C}$ for $\mathrm{HCO}_{2} \mathrm{H}, \mathrm{HCN}$ , $\mathrm{HClO}_{4}$ and $\mathrm{HOBr}$ , and arrange these acids in order of:
(a) Increasing acid strength
(b) Decreasing percent dissociation
Also estimate $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ in a 1.0 $\mathrm{M}$ solution of each acid.

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Problem 70

The pH of 0.040 M hypobromous acid (HOBr) is 5.05 . Set up the equilibrium equation for the dissociation of HOBr, and calculate the value of the acid-dissociation constant.

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Problem 71

Lactic acid $\left(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{3}\right),$ which occurs in sour milk and foods such as sauerkraut, is a weak monoprotic acid. The pH of a 0.10 $\mathrm{M}$ solution of lactic acid is $2.43 .$ What are the values of $K_{\mathrm{a}}$ and $\mathrm{p} K_{\mathrm{a}}$ for lactic acid?

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Problem 72

Acrylic acid $\left(\mathrm{HC}_{3} \mathrm{H}_{3} \mathrm{O}_{2}\right)$ is used in the manufacture of paints and plastics. The $\mathrm{p} K_{\mathrm{a}}$ of acrylic acid is $4.25 .$
(a) Calculate the $\mathrm{pH}$ and the concentrations of all species
$\left(\mathrm{H}_{3} \mathrm{O}^{+}, \mathrm{C}_{3} \mathrm{H}_{3} \mathrm{O}_{2}^{-}, \mathrm{HC}_{3} \mathrm{H}_{3} \mathrm{O}_{2}, \text { and } \mathrm{OH}^{-}\right)$ in 0.150 $\mathrm{M}$ acrylic acid.
(b) Calculate the percent dissociation in 0.0500 $\mathrm{M}$ acrylic
acid.

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Problem 73

Hippuric acid $\left(\mathrm{HC}_{9} \mathrm{H}_{8} \mathrm{NO}_{3}\right),$ found in horse urine, has
$\mathrm{p} K_{\mathrm{a}}=3.62$
(a) Calculate the $\mathrm{pH}$ and the concentrations of all species
(H $_{3} \mathrm{O}^{+}, \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{NO}_{3}^{-}, \mathrm{HC}_{9} \mathrm{H}_{8} \mathrm{NO}_{3},$ and $\mathrm{OH}^{-} )$ in 0.100 $\mathrm{M}$
hippuric acid.
(b) Calculate the percent dissociation in 0.0750 $\mathrm{M}$ hippuric
acid.

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Problem 74

Calculate the $\mathrm{pH}$ and the percent dissociation in 1.5 $\mathrm{M}$
$\mathrm{HNO}_{2}\left(K_{\mathrm{a}}=4.5 \times 10^{-4}\right)$

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Problem 75

A typical aspirin tablet contains 324 $\mathrm{mg}$ of aspirin (acetylsalicylic acid, $\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} ),$ a monoprotic acid having $K_{\mathrm{a}}=3.0 \times 10^{-4} .$ If you dissolve two aspirin tablets in a 300 $\mathrm{mL}$ glass of water, what is the pH of the solution and the percent dissociation?

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Problem 76

Write balanced net ionic equations and the corresponding equilibrium equations for the stepwise dissociation of the diprotic acid $\mathrm{H}_{2} \mathrm{SeO}_{4}$

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Problem 77

Write balanced net ionic equations and the corresponding equilibrium equations for the stepwise dissociation of the triprotic acid $\mathrm{H}_{3} \mathrm{PO}_{4}$

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Problem 78

Calculate the $\mathrm{pH}$ and the concentrations of all species present $\left(\mathrm{H}_{2} \mathrm{CO}_{3}, \mathrm{HCO}_{3}^{-}, \mathrm{CO}_{3}^{2-}, \mathrm{H}_{3} \mathrm{O}^{+}, \text { and } \mathrm{OH} \text { ) in }\right.$ 0.010 $\mathrm{M} \mathrm{H}_{2} \mathrm{CO}_{3}\left(K_{\mathrm{al}}=4.3 \times 10^{-7} ; K_{\mathrm{a} 2}=5.6 \times 10^{-11}\right)$

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Problem 79

Calculate the $\mathrm{pH}$ and the concentrations of $\mathrm{H}_{2} \mathrm{SO}_{3}$
$\mathrm{HSO}_{3}^{-}, \mathrm{SO}_{3}^{2-}, \mathrm{H}_{3} \mathrm{O}^{+},$ and $\mathrm{OH}^{-}$ in 0.025 $\mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{3}$
$\left(K_{\mathrm{al}}=1.5 \times 10^{-2} ; K_{\mathrm{a} 2}=6.3 \times 10^{-8}\right)$

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Problem 80

Oxalic acid $\left(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)$ is a diprotic acid that occurs
in plants such as rhubarb and spinach. Calculate the $\mathrm{pH}$ and the concentration of $\mathrm{C}_{2} \mathrm{O}_{4}^{2-}$ ions in 0.20 $\mathrm{M} \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}$ $\left(K_{\mathrm{a} 1}=5.9 \times 10^{-2} ; K_{\mathrm{a} 2}=6.4 \times 10^{-5}\right)$

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Problem 81

Calculate the concentrations of $\mathrm{H}_{3} \mathrm{O}^{+}$ and $\mathrm{SO}_{4}^{2-}$ in a solution prepared by mixing equal volumes of 0.2 $\mathrm{M} \mathrm{HCl}$ and 0.6 $\mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\left(K_{\mathrm{a} 2} \text { for } \mathrm{H}_{2} \mathrm{SO}_{4} \text { is } 1.2 \times 10^{-2}\right)$

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Problem 82

Write a balanced net ionic equation and the corresponding equilibrium equation for the reaction of the following weak bases with water:
(a) Dimethylamine, $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH} \quad$
(b) Aniline, $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}$
(c) Cyanide ion, CN $^{-}$

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Problem 83

Write a balanced net ionic equation and the corresponding equilibrium equation for the reaction of the following weak bases with water:
(a) Pyridine, $\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{N}$
(b) Ethylamine, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}$
(c) Acetate ion, $\mathrm{CH}_{3} \mathrm{CO}_{2}^{-}$

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Problem 84

Morphine $\left(\mathrm{C}_{17} \mathrm{H}_{19} \mathrm{NO}_{3}\right),$ a narcotic used in painkillers, is a weak organic base. If the $\mathrm{pH}$ of a $7.0 \times 10^{-4} \mathrm{M}$ solution of morphine is $9.50,$ what are the values of $K_{\mathrm{b}}$ and $\mathrm{p} K_{\mathrm{b}} ?$

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Problem 85

A $1.00 \times 10^{-3} \mathrm{M}$ solution of quinine, a drug used in treating malaria, has a pH of $9.75 .$ What are the values of $K_{\mathrm{b}}$ and $\mathrm{p} K_{\mathrm{b}} ?$

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Problem 86

Oxycodone $\left(\mathrm{C}_{18} \mathrm{H}_{21} \mathrm{NO}_{4}\right),$ a narcotic analgesic, is a weak base with $\mathrm{pK}_{\mathrm{b}}=5.47$ . Calculate the $\mathrm{pH}$ and the concentra-
tions of all species present $\left(\mathrm{C}_{18} \mathrm{H}_{21} \mathrm{NO}_{4}, \mathrm{HC}_{18} \mathrm{H}_{21} \mathrm{NO}_{4}^{+}\right.$
$\mathrm{H}_{3} \mathrm{O}^{+},$ and $\mathrm{OH}^{-} )$ in a 0.00250 $\mathrm{M}$ oxycodone solution.

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Problem 87

Morpholine $\left(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{NO}\right)$ is a weak organic base with
$\mathrm{p} K_{\mathrm{b}}=5.68$ . Calculate the $\mathrm{pH}$ and the concentrations of all
species present $\left(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{NO}, \mathrm{HC}_{4} \mathrm{H}_{9} \mathrm{NO}^{+}, \mathrm{H}_{3} \mathrm{O}^{+}, \text { and } \mathrm{OH}^{-}\right)$ in
a 0.0100 $\mathrm{M}$ morpholine solution.

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Problem 88

Using values of $K_{\mathrm{b}}$ in Appendix $\mathrm{C},$ calculate values of $K_{\mathrm{a}}$
for each of the following ions:
(a) Propylammonium ion, $\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{NH}_{3}+$
(b) Hydroxylammonium ion, $\mathrm{NH}_{3} \mathrm{OH}^{+}$
(c) Anilinium ion, $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}$
(d) Pyridinium ion, $\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{NH}^{+}$

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Problem 89

Using values of $K_{\mathrm{a}}$ in Appendix $\mathrm{C},$ calculate values of $K_{\mathrm{b}}$
for each of the following ions:
(a) Fluoride ion, $\mathrm{F}^{-}$
(b) Hypobromite ion, OBr $^{-}$
(c) Hydrogen sulfide ion, HS -
(d) Sulfide ion, $\mathrm{S}^{2-}$

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Problem 90

Write a balanced net ionic equation for the reaction of each of the following ions with water. In each case, identify the Bronsted-Lowry acids and bases and the conjugate acid-base pairs.
$\begin{array}{ll}{\text { (a) } \mathrm{CH}_{3} \mathrm{NH}_{3}^{+}} & {\text { (b) } \mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}} \\ {\text { (c) } \mathrm{CH}_{3} \mathrm{CO}_{2}^{-}} & {\text { (d) } \mathrm{PO}_{4}^{3-}}\end{array}$

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Problem 91

Write a balanced net ionic equation for the principal reaction in solutions of each of the following salts. In each case, identify the Bronsted-Lowry acids and bases and the conjugate acid-base pairs.
$\begin{array}{llll}{\text { (a) } \mathrm{Na}_{2} \mathrm{CO}_{3}} & {\text { (b) } \mathrm{NH}_{4} \mathrm{NO}_{3}} & {\text { (c) NaCl }} & {\text { (d) } \mathrm{ZnCl}_{2}}\end{array}$

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Problem 92

Classify each of the following ions according to whether they react with water to give a neutral, acidic, or basic solution:
$\begin{array}{ll}{\text { (a) } \mathrm{F}^{-}} & {\text { (b) Br }^{-}} & {\text { (c) } \mathrm{NH}_{4}^{+}} \\ {\text { (d) } \mathrm{K}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{+}} & {\text { (e) } \mathrm{SO}_{3}^{2-}} & {\text { (f) } \mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}}\end{array}$

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Problem 93

Classify each of the following salt solutions as neutral, acidic, or basic. See Appendix C for values of equilibrium constants.
(a) $\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}$
(b) $\operatorname{Ba}\left(\mathrm{NO}_{3}\right)_{2}$
(c) NaOCl
(d) $\mathrm{NH}_{4} \mathrm{I}$
(e) $\mathrm{NH}_{4} \mathrm{NO}_{2}$
(f) $\left(\mathrm{CH}_{3} \mathrm{NH}_{3}\right) \mathrm{Cl}$

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Problem 94

Calculate the concentrations of all species present and the $\mathrm{pH}$ in 0.10 $\mathrm{M}$ solutions of the following substances. See Appendix $\mathrm{C}$ for values of equilibrium constants.
(a) Ethylammonium nitrate, $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}\right) \mathrm{NO}_{3}$
(b) Sodium acetate, $\mathrm{Na}\left(\mathrm{CH}_{3} \mathrm{CO}_{2}\right)$
(c) Sodium nitrate, $NaNO_{3}$

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Problem 95

Calculate the $\mathrm{pH}$ and the percent dissociation of the hydrated cation in 0.020 $\mathrm{M}$ solutions of the following substances. See Appendix $\mathrm{C}$ for values of equilibrium constants.
(a) $\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{2} \quad$
(b) $\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}$

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Problem 96

Arrange each group of compounds in order of increasing acid strength. Explain your reasoning.
$\begin{array}{ll}{\text { (a) } \mathrm{HCl}, \mathrm{H}_{2} \mathrm{S}, \mathrm{PH}_{3}} & {\text { (b) } \mathrm{NH}_{3}, \mathrm{PH}_{3}, \mathrm{AsH}_{3}} \\ {\text { (c) } \mathrm{HBrO}, \mathrm{HBrO}_{3}, \mathrm{HBrO}_{4}}\end{array}$

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Problem 97

Arrange each group of compounds in order of decreasing acid strength. Explain your reasoning.
$\begin{array}{ll}{\text { (a) } \mathrm{H}_{2} \mathrm{O}, \mathrm{H}_{2} \mathrm{S}, \mathrm{H}_{2} \mathrm{Se}} & {\text { (b) } \mathrm{HClO}_{3}, \mathrm{HBrO}_{3}, \mathrm{HIO}_{3}} \\ {\text { (c) } \mathrm{PH}_{3}, \mathrm{H}_{2} \mathrm{S}, \mathrm{HCl}}\end{array}$

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Problem 98

Identify the strongest acid in each of the following sets. Explain your reasoning.
$\begin{array}{ll}{\text { (a) } \mathrm{H}_{2} \mathrm{O}, \mathrm{HF}, \text { or } \mathrm{HCl}} & {\text { (b) } \mathrm{HClO}_{2}, \mathrm{HClO}_{3}, \text { or } \mathrm{HBrO}_{3}} \\ {\text { (c) } \mathrm{HBr}, \mathrm{H}_{2} \mathrm{S}, \text { or } \mathrm{H}_{2} \mathrm{Se}}\end{array}$

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Problem 99

Identify the weakest acid in each of the following sets. Explain your reasoning.
(a) $\mathrm{H}_{2} \mathrm{SO}_{3}, \mathrm{HClO}_{3}, \mathrm{HClO}_{4} \quad(\mathrm{b}) \mathrm{NH}_{3}, \mathrm{H}_{2} \mathrm{O}, \mathrm{H}_{2} \mathrm{S}$
(c) $\mathrm{B}(\mathrm{OH})_{3}, \mathrm{Al}(\mathrm{OH})_{3}, \mathrm{Ga}(\mathrm{OH})_{3}$

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Problem 100

Identify the stronger acid in each of the following pairs. Explain your reasoning.
$\begin{array}{ll}{\text { (a) } \mathrm{H}_{2} \mathrm{Se} \text { or } \mathrm{H}_{2} \mathrm{Te}} & {\text { (b) } \mathrm{H}_{3} \mathrm{PO}_{4} \text { or } \mathrm{H}_{3} \mathrm{AsO}_{4}} \\ {\text { (c) } \mathrm{H}_{2} \mathrm{PO}_{4}^{-} \text { or } \mathrm{HPO}_{4}^{2-}} & {\text { (d) } \mathrm{CH}_{4} \text { or } \mathrm{NH}_{4}^{+}}\end{array}$

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Problem 101

Identify the stronger base in each of the following pairs. Explain your reasoning.
$\begin{array}{ll}{\text { (a) } \mathrm{ClO}_{2}^{-} \text { or } \mathrm{ClO}_{3}^{-}} & {\text { (b) } \mathrm{HSO}_{4}^{-} \text { or HSeO }_{4}^{-}} \\ {\text { (c) } \mathrm{HS}^{-}} {\text { or } \mathrm{OH}^{-}} {\text { (d) } \mathrm{HS}^{-} \text { or Br }^{-}}\end{array}$

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Problem 102

For each of the following reactions, identify the Lewis acid and the Lewis base:
(a) $\mathrm{SiF}_{4}+2 \mathrm{F}^{-} \longrightarrow \mathrm{SiF}_{6^2-}$
(b) $4 \mathrm{NH}_{3}+\mathrm{Zn}^{2+} \longrightarrow \mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4^2+}$
(c) $2 \mathrm{Cl}^{-}+\mathrm{HgCl}_{2} \longrightarrow \mathrm{HgCl}_{4^2-}$
(d) $\mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{H}_{2} \mathrm{CO}_{3}$

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Problem 103

For each of the following reactions, identify the Lewis acid and the Lewis base:
(a) $2 \mathrm{Cl}^{-}+\mathrm{BeCl}_{2} \longrightarrow \mathrm{BeCl}_{4^2-}$
(b) $\mathrm{Mg}^{2+}+6 \mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{Mg}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6^2+}$
(c) $\mathrm{SO}_{3}+\mathrm{OH}^{-} \longrightarrow \mathrm{HSO}_{4}^{-} \quad$ (d) $\mathrm{F}^{-}+\mathrm{BF}_{3} \longrightarrow \mathrm{BF}_{4}^{-}$

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Problem 104

For each of the Lewis acid-base reactions in Problem $14.102,$ draw electron-dot structures for the reactants and products, and use the curved arrow notation (Section 14.16$)$ to represent the donation of a lone pair of electrons from the Lewis base to the Lewis acid.

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Problem 105

For each of the Lewis acid-base reactions in Problem $14.103,$ draw electron-dot structures for the reactants and products, and use the curved arrow notation (Section 14.16$)$ to represent the donation of a lone pair of electrons from the Lewis base to the Lewis acid.

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Problem 106

Classify each of the following as a Lewis acid or a Lewis base:
$\begin{array}{ll}{\text { (a) } \mathrm{CN}^{-}} & {\text { (b) } \mathrm{H}^{+}} & {\text { (c) } \mathrm{H}_{2} \mathrm{O}} \\ {\text { (d) Fe }^{3+}} & {\text { (e) } \mathrm{OH}^{-}} & {\text { (f) } \mathrm{CO}_{2}} \\ {\text { (g) } \mathrm{P}\left(\mathrm{CH}_{3}\right)_{3}} & {\text { (h) } \mathrm{B}\left(\mathrm{CH}_{3}\right)_{3}}\end{array}$

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Problem 107

Which would you expect to be the stronger Lewis acid in each of the following pairs? Explain.
$\begin{array}{ll}{\text { (a) } \mathrm{BF}_{3} \text { or } \mathrm{BH}_{3}} & {\text { (b) } \mathrm{SO}_{2} \text { or } \mathrm{SO}_{3}} \\ {\text { (c) } \mathrm{Sn}^{2+} \text { or } \mathrm{Sn}^{4+}} & {\text { (d) } \mathrm{CH}_{3}^{+} \text { or } \mathrm{CH}_{4}}\end{array}$

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Problem 108

Aqueous solutions of hydrogen sulfide contain $\mathrm{H}_{2} \mathrm{S}, \mathrm{HS}^{-}$
$\mathrm{S}^{2-}, \mathrm{H}_{3} \mathrm{O}^{+}, \mathrm{OH}^{-},$ and $\mathrm{H}_{2} \mathrm{O}$ in varying concentrations. Which of these species can act only as an acid? Which can
act only as a base? Which can act both as an acid and as a base?

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Problem 109

The hydronium ion $\mathrm{H}_{3} \mathrm{O}^{+}$ is the strongest acid that can exist in aqueous solution because stronger acids dissociate by transferring a proton to water. What is the strongest
base that can exist in aqueous solution?

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Problem 110

Baking powder contains baking soda $(NaHCO_{3})$ and an acidic substance such as sodium alum, $\mathrm{NaAl}\left(\mathrm{SO}_{4}\right)_{2}$$\cdot 12 \mathrm{H}_{2} \mathrm{O}$ These components react in an aqueous medium to produce $\mathrm{CO}_{2}$ gas, which "raises" the dough. Write a balanced netionic equation for the reaction.

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Problem 111

Arrange the following substances in order of increasing $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ for a 0.10 $\mathrm{M}$ solution of each:
$\begin{array}{ll}{\text { (a) } \mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}} & {\text { (b) } \mathrm{Na}_{2} \mathrm{O}} \\ {\text { (d) } \mathrm{NaClO}_{4}} & {\text { (e) } \mathrm{HClO}_{4}}\end{array}$

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Problem 112

At $0^{\circ} \mathrm{C},$ the density of liquid water is 0.9998 $\mathrm{g} / \mathrm{mL}$ and
the value of $K_{\mathrm{w}}$ is $1.14 \times 10^{-15}$ . What fraction of the molecules in liquid water are dissociated at $0^{\circ} \mathrm{C} ?$ What is the percent dissociation at $0^{\circ} \mathrm{C} ?$ What is the $\mathrm{pH}$ of a neutral solution at $0^{\circ} \mathrm{C} ?$

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Problem 113

Use the conjugate acid-base pair $\mathrm{HCN}$ and $\mathrm{CN}^{-}$ to derive the relationship between $K_{\mathrm{a}}$ and $K_{\mathrm{b}}$ .

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Problem 114

The pH of 0.050 M gallic acid, an acid found in tea leaves, is $2.86 .$ Calculate $K_{\mathrm{a}}$ and $\mathrm{p} K_{\mathrm{a}}$ for gallic acid.

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Problem 115

The pH of 0.040 M pyruvic acid, a compound involved in metabolic pathways, is 1.96 . Calculate $K_{\text { a }}$ and $\mathrm{pK}_{\text { a }}$ for pyruvic acid.

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Problem 116

Nicotine $\left(\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{N}_{2}\right)$ can accept two protons because it has two basic $\mathrm{N}$ atoms $\left(K_{\mathrm{b} 1}=1.0 \times 10^{-6} ; K_{\mathrm{b} 2}=1.3 \times 10^{-11}\right)$ Calculate the values of $K_{\mathrm{a}}$ for the conjugate acids $\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{N}_{2} \mathrm{H}^{+}$ and $\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{N}_{2} \mathrm{H}_{2}^{2+}$

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Problem 117

Sodium benzoate $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{Na}\right)$ is used as a food preservative. Calculate the $\mathrm{pH}$ and the concentrations of all species present $\left(\mathrm{Na}^{+}, \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2}^{-}, \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H}, \mathrm{H}_{3} \mathrm{O}^{+}, \text { and } \mathrm{OH}\right)$ in 0.050 $\mathrm{M}$ sodium benzoate; $K_{\mathrm{a}}$ for benzoic acid $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H}\right)$ is $6.5 \times 10^{-5} .$

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Problem 118

The hydrated cation $\mathrm{M}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}$ has $K_{\mathrm{a}}=10^{-4},$ and the acid HA has $K_{\mathrm{a}}=10^{-5} .$ Identify the principal reaction in an aqueous solution of each of the following salts, and classify each solution as acidic, basic, or neutral:
(a) NaA $\quad$ (b) $\mathrm{M}\left(\mathrm{NO}_{3}\right)_{3} \quad$ (c) NaNO_ $_{3} \quad$ (d) $\mathrm{MA}_{3}$

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Problem 119

Calculate the $\mathrm{pH}$ and the concentrations of all species present $\left(\mathrm{H}_{3} \mathrm{O}^{+}, \mathrm{F}^{-}, \mathrm{HF}, \mathrm{Cl}^{-}, \text { and } \mathrm{OH}^{-4}\right)$ in a solution that contains 0.10 $\mathrm{M} \mathrm{HF}\left(K_{\mathrm{a}}=3.5 \times 10^{-4}\right)$ and 0.10 $\mathrm{M} \mathrm{MCl}$

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Problem 120

Calculate the $\mathrm{pH}$ and the concentrations of all species present $\left(\mathrm{H}_{3} \mathrm{O}^{+}, \mathrm{OH}^{-}, \mathrm{HIO}_{3}, \text { and } \mathrm{IO}_{3}-\right)$ in 0.0500 $\mathrm{M} \mathrm{HIO}_{3} . K_{\mathrm{a}}$ for $\mathrm{HIO}_{3}$ is $1.7 \times 10^{-1} .$

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Problem 121

Quinolinic acid, $\mathrm{H}_{2} \mathrm{C}_{7} \mathrm{H}_{3} \mathrm{NO}_{4}\left(\mathrm{pK}_{\mathrm{a} 1}=2.43 ; \mathrm{p} K_{\mathrm{a} 2}=4.78\right)$
has been implicated in the progression of Alzheimer's dis-
ease. Calculate the $\mathrm{pH}$ and the concentrations of all species present $\left(\mathrm{H}_{2} \mathrm{C}_{7} \mathrm{H}_{3} \mathrm{NO}_{4}, \mathrm{HC}_{7} \mathrm{H}_{3} \mathrm{NO}_{4}^{-}, \mathrm{C}_{7} \mathrm{H}_{3} \mathrm{NO}_{4}^{2-}, \mathrm{H}_{3} \mathrm{O}^{+}\right.$
and $\mathrm{OH}^{-} )$ in a 0.050 $\mathrm{M}$ solution of quinolinic acid.

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Problem 122

Calculate the $\mathrm{pH}$ and the concentrations of all species present
$\left(\mathrm{H}_{2} \mathrm{C}_{8} \mathrm{H}_{4} \mathrm{O}_{4}, \mathrm{HC}_{8} \mathrm{H}_{4} \mathrm{O}_{4}^{-}, \mathrm{C}_{8} \mathrm{H}_{4} \mathrm{O}_{4}^{2-}, \mathrm{H}_{3} \mathrm{O}^{+}, \text { and } \mathrm{OH}^{-}\right)$ in a 0.0250 $\mathrm{M}$ solution of phthalic acid, $\mathrm{H}_{2} \mathrm{C}_{8} \mathrm{H}_{4} \mathrm{O}_{4}\left(\mathrm{p} K_{\mathrm{a} 1}=2.89\right.$
$\mathrm{p} K_{\mathrm{a} 2}=5.51 )$

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Problem 123

Sulfur dioxide is quite soluble in water:
$$\mathrm{SO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{SO}_{3}(a q) \quad K=1.33$$
The $\mathrm{H}_{2} \mathrm{SO}_{3}$ produced is a weak diprotic acid $\left(K_{\mathrm{a} 1}=\right.$ $1.5 \times 10^{-2} ; K_{\mathrm{a} 2}=6.3 \times 10^{-8} ) .$ Calculate the $\mathrm{pH}$ and the concentrations of $\mathrm{H}_{2} \mathrm{SO}_{3}, \mathrm{HSO}_{3}^{-},$ and $\mathrm{SO}_{3}^{2-}$ in a solution prepared by continuously bubbling $\mathrm{SO}_{2}$ at a pressure of 1.00 $\mathrm{atm}$ into pure water.

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Problem 124

Classify each of the following salt solutions as neutral, acidic, or basic. See Appendix C for values of equilibrium constants.
(a) $\mathrm{NH}_{4} \mathrm{F}$
(b) $\mathrm{NH}_{4} )_{2} \mathrm{SO}_{3}$

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Problem 125

Calculate the $\mathrm{pH}$ and the percent dissociation of the hydrated cation in the following solutions. See Appendix $\mathrm{C}$ for the value of the equilibrium constant.
(a) 0.010 $\mathrm{M} \mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}$
(b) 0.0050 $\mathrm{M} \mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}$
(c) 0.0010 $\mathrm{M} \mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}$

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Problem 126

Beginning with the equilibrium equation for the dissociation of a weak acid HA, show that the percent dissociation varies directly as the square root of $K_{\mathrm{a}}$ and inversely as the square root of the initial concentration of HA when the concentration of HA that dissociates is negligible compared
with its initial concentration.

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Problem 127

Calculate the pH and the concentrations of all species present in 0.25 $\mathrm{M}$ solutions of each of the salts in Problem $14.124 .$ Hint: The principal reaction is proton transfer from the cation to the anion.)

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Problem 128

For a solution of two weak acids with comparable values of $K_{a},$ there is no single principal reaction. The two acid-dissociation equilibrium equations must therefore be solved simultaneously. Calculate the $\mathrm{pH}$ in a solution that is 0.10 $\mathrm{M}$ in acetic acid $\left(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}, K_{\mathrm{a}}=1.8 \times 10^{-5}\right)$ and 0.10 $\mathrm{M}$ in benzoic acid $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H}, \quad K_{\mathrm{a}}=6.5 \times 10^{-5}\right)$ (Hint: Let $x=\left[\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\right]$ that dissociates and $y=\left[\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H}\right]$ that dissociates; then $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=x+y . )$

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Problem 129

What is the $\mathrm{pH}$ and the principal source of $\mathrm{H}_{3} \mathrm{O}^{+}$ ions in
$1.0 \times 10^{-10} \mathrm{M} \mathrm{HCl} ?(\text { Hint: The } \mathrm{pH} \text { of an acid solution can't }$ exceed $7 .$ What is the pH of $1.0 \times 10^{-7} \mathrm{M} \mathrm{HCl} ?$

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Problem 130

When $\mathrm{NO}_{2}$ is bubbled into water, it is completely converted to $\mathrm{HNO}_{3}$ and $\mathrm{HNO}_{2}$ :

$$2 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{HNO}_{3}(a q)+\mathrm{HNO}_{2}(a q)$$
Calculate the pH and the concentrations of all species present $\left(\mathrm{H}_{3} \mathrm{O}^{+}, \mathrm{OH}^{-}, \mathrm{HNO}_{2}, \mathrm{NO}_{2}^{-}, \text { and } \mathrm{NO}_{3}^{-}\right)$ in a solution prepared by dissolving 0.0500 $\mathrm{mol}$ of $\mathrm{NO}_{2}$ in 1.00 $\mathrm{L}$ of water. $K_{\mathrm{a}}$ for $\mathrm{HNO}_{2}$ is $4.5 \times 10^{-4}$ .

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Problem 131

Acid and base behavior can be observed in solvents other than water. One commonly used solvent is dimethyl sulfoxide (DMSO), which can be treated as a monoprotic acid "HSol." Just as water can behave either as an acid or a base, so HSol can behave either as a Bronsted-Lowry acid or base.
(a) The equilibrium constant for self-dissociation of HSol (call it $K_{\text { HSol }} )$ is $1 \times 10^{-35} .$ Write the chemical equation for the self-dissociation reaction and the corresponding equilibrium equation. (Hint: The equilibrium equation is analogous to the equilibrium equation for $K_{\mathrm{w}}$ in the case of water.)
(b) The weak acid HCN has an acid dissociation constant $K_{\mathrm{a}}=1.3 \times 10^{-13} \mathrm{in}$ the solvent HSol. If 0.010 $\mathrm{mol}$ of $\mathrm{NaCN}$ is dissolved in 1.00 $\mathrm{L}$ of HSol, what is the equilibrium concentration of $\mathrm{H}_{2} \mathrm{Sol}^{+} ?$

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Problem 132

A 7.0 mass $\%$ solution of $\mathrm{H}_{3} \mathrm{PO}_{4}$ in water has a density of 1.0353 $\mathrm{g} / \mathrm{mL}$ . Calculate the $\mathrm{pH}$ and the molar concentrations of all species present $\left(\mathrm{H}_{3} \mathrm{PO}_{4}, \mathrm{H}_{2} \mathrm{PO}_{4}^{-}, \mathrm{HPO}_{4}^{2-}\right.$ $\mathrm{PO}_{4}^{3-}, \mathrm{H}_{3} \mathrm{O}^{+},$ and $\mathrm{OH}^{-}$ ) in the solution. Values of equilibrium constants are listed in Appendix C.

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Problem 133

In the case of very weak acids, $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ from the dissociation of water is significant compared with $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ from the dissociation of the weak acid. The sugar substitute saccharin $\left(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{NO}_{3} \mathrm{S}\right)$ , for example, is a very weak acid having $K_{\mathrm{a}}=2.1 \times 10^{-12}$ and a solubility in water of 348 $\mathrm{mg} / 100 \mathrm{mL}$ . Calculate $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ in a saturated solution of saccharin. (Hint: Equilibrium equations for the dissociation of saccharin and water must be solved simultaneously.)

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Problem 134

In aqueous solution, sodium acetate behaves as a strong electrolyte, yielding Nat cations and $\mathrm{CH}_{3} \mathrm{CO}_{2}^{-}$ anions. A particular solution of sodium acetate has a pH of 9.07 and a density of 1.0085 $\mathrm{g} / \mathrm{mL}$ . What is the molality of this solution, and what is its freezing point?

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Problem 135

During a certain time period, 4.0 million tons of $\mathrm{SO}_{2}$ was released into the atmosphere and was subsequently oxidized to $\mathrm{SO}_{3}$ . As explained in the Inquiry, the acid rain produced when the $\mathrm{SO}_{3}$ dissolves in water can damage marble statues:
$\mathrm{CaCO}_{3}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{CaSO}_{4}(a q)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)$
(a) How many 500 pound marble statues could be damaged by the acid rain? (Assume that the statues are pure $\mathrm{CaCO}_{3}$ and that a statue is damaged when 3.0$\%$ of its mass is dissolved.)
(b) How many liters of $\mathrm{CO}_{2}$ gas at $20^{\circ} \mathrm{C}$ and 735 $\mathrm{mm}$ Hg is produced as a byproduct?
(c) The cation in aqueous $\mathrm{H}_{2} \mathrm{SO}_{4}$ is trigonal pyramidal rather than trigonal planar. Explain.

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Problem 136

Neutralization reactions involving either a strong acid or a strong base go essentially to completion, and therefore we must take such neutralizations into account before calculating concentrations in mixtures of acids and bases. Consider a mixture of 3.28 $\mathrm{g}$ of $\mathrm{Na}_{3} \mathrm{PO}_{4}$ and 300.0 $\mathrm{mL}$ of 0.180 $\mathrm{M} \mathrm{HCl}$ . Write balanced net ionic equations for the neutralization reactions, and calculate the pH of the solution.

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Problem 137

We've said that alkali metal cations do not react appreciably with water to produce $\mathrm{H}_{3} \mathrm{O}^{+}$ ions, but in fact, all cations are acidic to some extent. The most acidic alkali metal cation is the smallest one, Lit, which has $K_{\mathrm{a}}=2.5 \times 10^{-14}$ for the reaction
$\mathrm{Li}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}^{+}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{Li}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3}(\mathrm{OH})(a q)$
This reaction and the dissociation of water must be considered simultaneously in calculating the pH of Li' solutions, which nevertheless have $\mathrm{pH} \approx 7 .$ Check this by calculating the pH of 0.10 $\mathrm{M} \mathrm{LiCl} .$

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Problem 138

A 1.000 L sample of HF gas at $20.0^{\circ} \mathrm{C}$ and 0.601 atm pressure was dissolved in enough water to make 50.0 $\mathrm{mL}$ of hydrofluoric acid.
(a) What is the pH of the solution?
(b) To what volume must you dilute the solution to triple the percent dissociation. Why can't you solve this problem by using the result obtained in Problem 14.126$?$

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Problem 139

A 200.0 mL sample of 0.350 M acetic acid $\left(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\right)$ was allowed to react with 2.000 $\mathrm{L}$ of gaseous ammonia at $25^{\circ} \mathrm{C}$
and a pressure of 650.8 $\mathrm{mm}$ Hg. Assuming no change in the volume of the solution, calculate the $\mathrm{pH}$ and the equilibrium concentrations of all species present $\left(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H},\right.$
$\mathrm{CH}_{3} \mathrm{CO}_{2}^{-}, \mathrm{NH}_{3}, \mathrm{NH}_{4}^{+}, \mathrm{H}_{3} \mathrm{O}^{+},$ and $\mathrm{OH}^{-} ) .$ Values of equilibrium constants are listed in Appendix C.

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Problem 140

You may have been told not to mix bleach and ammonia. The reason is that bleach (sodium hypochlorite) reacts with ammonia to produce toxic chloramines, such as $\mathrm{NH}_{2} \mathrm{Cl}$ . For example, in basic solution:

$$\mathrm{OCl}^{-}(a q)+\mathrm{NH}_{3}(a q) \longrightarrow \mathrm{OH}^{-}(a q)+\mathrm{NH}_{2} \mathrm{Cl}(a q)$$
(a) The following initial rate data for this reaction were obtained in basic solution at $25^{\circ} \mathrm{C} :$ What is the rate law for the reaction? What is the numerical value of the rate constant $k$ , including the correct units?
(b) The following mechanism has been proposed for this reaction in basic solution:
$\mathrm{H}_{2} \mathrm{O}+\mathrm{OCl}^{-} \rightleftharpoons \mathrm{HOCl}+\mathrm{OH}^{-} \quad$ Fast, equilibrium constant $K_{1}$
$\mathrm{HOCl}+\mathrm{NH}_{3} \longrightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{NH}_{2} \mathrm{Cl}$ Slow, rate constant $k_{2}$
Assuming that the first step is in equilibrium and the second step is rate-determining, calculate the value of the rate constant $k_{2}$ for the second step. $K_{\mathrm{a}}$ for $\mathrm{HOCl}$ is $3.5 \times 10^{-8} .$

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