Chemistry Principles and Reactions

William L Masterton; Cecile N Hurley; Edward J Neth

Chapter 14

Equilibria in Acid-Base Solutions - all with Video Answers

Educators

Chapter Questions

Problem 1

Write a net ionic equation for the reaction between aqueous solutions of
(a) ammonia and hydrofluoric acid.
(b) perchloric acid and rubidium hydroxide.
(c) sodium sulfite and hydriodic acid.
(d) nitric acid and calcium hydroxide.

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Problem 2

Write a net ionic equation for the reaction between aqueous solutions of
(a) sodium acetate $\left(\mathrm{NaC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right)$ and nitric acid.
(b) hydrobromic acid and strontium hydroxide.
(c) hypochlorous acid and sodium cyanide.
(d) sodium hydroxide and nitrous acid.

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Problem 3

Write a balanced net ionic equation for the reaction of each of the following aqueous solutions with $\mathrm{H}^{+}$ ions.
(a) sodium fluoride
(b) barium hydroxide
(c) potassium dihydrogen phosphate $\left(\mathrm{KH}_{2} \mathrm{PO}_{4}\right)$

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Problem 4

Write a balanced net ionic equation for the reaction between the following aqueous solutions and $\mathrm{OH}^{-}$ ions.
(a) $\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}$
(b) sodium hydrogen carbonate
(c) ammonium chloride

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Problem 5

Calculate $K$ for the reactions in Question 1

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Problem 6

Calculate $K$ for the reactions in Question $2 .$

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Problem 7

Calculate $K$ for the reactions in Question 3

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Problem 8

Calculate $K$ for the reactions in Question $4 .$

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Problem 9

Calculate $\left[\mathrm{H}^{+}\right]$ and $\mathrm{pH}$ in a solution in which lactic acid, $\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{3},$ is
$0.250 \mathrm{M}$ and the lactate ion, $\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{O}_{3}^{-},$ is
(a) $0.250 M$
(b) $0.125 M$
(c) $0.0800 M$
(d) $0.0500 M$

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Problem 10

Calculate $\left[\mathrm{OH}^{-}\right]$ and $\mathrm{pH}$ in a solution in which dihydrogen phosphate ion, $\mathrm{H}_{2} \mathrm{PO}_{4}^{-},$ is $0.335 \mathrm{M}$ and hydrogen phosphate ion, $\mathrm{HPO}_{4}^{2-},$ is
(a) $0.335 M$
(b) $0.100 M$
(c) $0.0750 \mathrm{M}$
(d) $0.0300 M$

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Problem 11

A buffer is prepared by dissolving 0.0250 mol of sodium nitrite, $\mathrm{NaNO}_{2}$, in $250.0 \mathrm{~mL}$ of $0.0410 \mathrm{M}$ nitrous acid, $\mathrm{HNO}_{2}$. Assume no volume change after $\mathrm{HNO}_{2}$ is dissolved. Calculate the pH of this buffer.

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Problem 12

A buffer is prepared by dissolving 0.083 mol of sodium hypochlorite in $247 \mathrm{~mL}$ of $0.0692 \mathrm{M}$ hypochlorous acid. Assume no volume change after $\mathrm{NaClO}$ is added. Calculate the $\mathrm{pH}$ of this buffer.

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Problem 13

A buffer solution is prepared by adding $15.00 \mathrm{~g}$ of sodium acetate $\left(\mathrm{NaC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right)$ and $12.50 \mathrm{~g}$ of acetic acid to enough water to make $500 \mathrm{~mL}$ (three significant figures) of solution.
(a) What is the $\mathrm{pH}$ of the buffer?
(b) The buffer is diluted by adding enough water to make $1.50 \mathrm{~L}$ of solution. What is the $\mathrm{pH}$ of the diluted buffer?

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Problem 14

A buffer solution is prepared by adding $5.50 \mathrm{~g}$ of ammonium chloride and 0.0188 mol of ammonia to enough water to make $155 \mathrm{~mL}$ of solution.
(a) What is the pH of the buffer?
(b) If enough water is added to double the volume, what is the $\mathrm{pH}$ of the solution?

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Problem 15

A solution with a pH of 8.73 is prepared by adding water to 0.614 mol of NaX to make $2.50 \mathrm{~L}$ of solution. What is the $\mathrm{pH}$ of the solution after 0.219 mol of $\mathrm{HX}$ is added?

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Problem 16

An aqueous solution of $0.057 M$ weak acid, HX, has a pH of $4.65 .$ What is the $\mathrm{pH}$ of the solution if $0.018 \mathrm{~mol}$ of $\mathrm{KX}$ is dissolved in one liter of the weak acid?

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Problem 17

Which of the following would form a buffer if added to $250.0 \mathrm{~mL}$ of $0.150 \mathrm{M} \mathrm{SnF}_{2} ?$
(a) $0.100 \mathrm{~mol}$ of $\mathrm{HCl}$
(b) $0.060 \mathrm{~mol}$ of $\mathrm{HCl}$
(c) $0.040 \mathrm{~mol}$ of $\mathrm{HCl}$
(d) $0.040 \mathrm{~mol}$ of $\mathrm{NaOH}$
(e) $0.040 \mathrm{~mol}$ of $\mathrm{HF}$

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Problem 18

Which of the following would form a buffer if added to $650.0 \mathrm{~mL}$ of $0.40 \mathrm{M} \mathrm{Sr}(\mathrm{OH})_{2} ?$
(a) $1.00 \mathrm{~mol}$ of $\mathrm{HF}$
(b) $0.75 \mathrm{~mol}$ of $\mathrm{HF}$
(c) $0.30 \mathrm{~mol}$ of $\mathrm{HF}$
(d) $0.30 \mathrm{~mol}$ of $\mathrm{NaF}$
(e) $0.30 \mathrm{~mol}$ of $\mathrm{HCl}$
Explain your reasoning in each case.

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Problem 19

Calculate the $\mathrm{pH}$ of a solution prepared by mixing $2.50 \mathrm{~g}$ of hypobromous acid (HOBr) and $0.750 \mathrm{~g}$ of KOH in water. $\left(K_{\mathrm{a}} \mathrm{HOBr}=2.5 \times 10^{-9}\right)$

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Problem 20

Calculate the pH of a solution prepared by mixing $20.00 \mathrm{~mL}$ of aniline, $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}(d=1.022 \mathrm{~g} / \mathrm{mL})$, with $35.0 \mathrm{~mL}$ of $1.67 M$ HCl. $K_{\mathrm{b}}$ for aniline is
$4.3 \times 10^{-10} .$ (Assume volumes are additive.)

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Problem 21

Calculate the pH of a solution prepared by mixing $2.00 \mathrm{~g}$ of butyric acid $\left(\mathrm{HC}_{4} \mathrm{H}_{7} \mathrm{O}_{2}\right)$ with $0.50 \mathrm{~g}$ of $\mathrm{NaOH}$ in water $\left(K_{\mathrm{a}}\right.$ butyric acid $\left.=1.5 \times 10^{-5}\right)$

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Problem 22

Calculate the $\mathrm{pH}$ of a solution prepared by mixing $100.0 \mathrm{~mL}$ of $1.20 \mathrm{M}$ ethanolamine, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{ONH}_{2}$, with $50.0 \mathrm{~mL}$ of $1.0 \mathrm{M} \mathrm{HCl} . \mathrm{K}_{\mathrm{a}}$ for $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{ONH}_{3}+$ is $3.6 \times 10^{-10}$.

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Problem 23

Consider the weak acids in Table $13.2 .$ Which acid-base pair would be best for a buffer at a $\mathrm{pH}$ of
(a) 3.0
(b) 6.5
(c) 12.0

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Problem 24

Follow the instructions of Question 23 for a $\mathrm{pH}$ of
(a) 6.6
(b) 9.9
(c) 12.8

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Problem 25

A sodium hydrogen carbonate-sodium carbonate buffer is to be prepared with a pH of 9.40 .
(a) What must the $\left[\mathrm{HCO}_{3}^{-}\right] /\left[\mathrm{CO}_{3}^{2-}\right]$ ratio be?
(b) How many moles of sodium hydrogen carbonate must be added to a liter of $0.225 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3}$ to give this $\mathrm{pH}$ ?
(c) How many grams of sodium carbonate must be added to $475 \mathrm{~mL}$ of $0.336 \mathrm{M} \mathrm{NaHCO}_{3}$ to give this $\mathrm{pH}$ ? (Assume no volume change.)
(d) What volume of $0.200 \mathrm{M} \mathrm{NaHCO}_{3}$ must be added to $735 \mathrm{~mL}$ of a $0.139 \mathrm{M}$ solution of $\mathrm{Na}_{2} \mathrm{CO}_{3}$ to give this $\mathrm{pH}$ ? (Assume that volumes are additive.)

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Problem 26

You want to make a buffer with a pH of $10.00 \mathrm{from} \mathrm{NH}_{4}^{+} / \mathrm{NH}_{3}$
(a) What must the $\left[\mathrm{NH}_{4}^{+}\right] /\left[\mathrm{NH}_{3}\right]$ ratio be?
(b) How many moles of $\mathrm{NH}_{4}$ Cl must be added to $465 \mathrm{~mL}$ of an aqueous solution of $1.24 \mathrm{M} \mathrm{NH}_{3}$ to give this $\mathrm{pH} ?$
(c) How many milliliters of $0.236 \mathrm{M} \mathrm{NH}_{3}$ must be added to $2.08 \mathrm{~g}$ of
$\mathrm{NH}_{4} \mathrm{Cl}$ to give this $\mathrm{pH} ?$
(d) What volume of $0.499 \mathrm{M} \mathrm{NH}_{3}$ must be added to $395 \mathrm{~mL}$ of $0.109 \mathrm{M}$ $\mathrm{NH}_{4} \mathrm{Cl}$ to give this $\mathrm{pH} ?$

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Problem 27

The buffer capacity indicates how much $\mathrm{OH}^{-}$ or $\mathrm{H}^{+}$ ions a buffer can react with. What is the buffer capacity of the buffers in Problem $9 ?$

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Problem 28

The buffer capacity indicates how much $\mathrm{OH}^{-}$ or $\mathrm{H}^{+}$ ions a buffer can react with. What is the buffer capacity of the buffers in Problem $10 ?$

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Problem 29

A buffer is made up of $0.300 \mathrm{~L}$ each of $0.500 \mathrm{M} \mathrm{KH}_{2} \mathrm{PO}_{4}$ and $0.317 \mathrm{M}$ $\mathrm{K}_{2} \mathrm{HPO}_{4}$. Assuming that volumes are additive, calculate
(a) the $\mathrm{pH}$ of the buffer.
(b) the $\mathrm{pH}$ of the buffer after the addition of $0.0500 \mathrm{~mol}$ of $\mathrm{HCl}$ to $0.600 \mathrm{~L}$ of buffer.
(c) the $\mathrm{pH}$ of the buffer after the addition of $0.0500 \mathrm{~mol}$ of $\mathrm{NaOH}$ to $0.600 \mathrm{~L}$ of buffer.

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Problem 30

A buffer is made up of $355 \mathrm{~mL}$ each of $0.200 \mathrm{M} \mathrm{NaHCO}_{3}$ and $0.134 \mathrm{M}$ $\mathrm{Na}_{2} \mathrm{CO}_{3}$. Assuming that volumes are additive, calculate
(a) the $\mathrm{pH}$ of the buffer.
(b) the $\mathrm{pH}$ of the buffer after the addition of $0.0300 \mathrm{~mol}$ of $\mathrm{HCl}$ to $0.710 \mathrm{~L}$ of buffer.
(c) the $\mathrm{pH}$ of the buffer after the addition of $0.0300 \mathrm{~mol}$ of $\mathrm{KOH}$ to $0.710 \mathrm{~L}$ of buffer.

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Problem 31

Enough water is added to the buffer in Question 29 to make the total volume $10.0 \mathrm{~L}$. Calculate
(a) the $\mathrm{pH}$ of the buffer.
(b) the $\mathrm{pH}$ of the buffer after the addition of $0.0500 \mathrm{~mol}$ of $\mathrm{HCl}$ to
$0.600 \mathrm{~L}$ of diluted buffer.
(c) the $\mathrm{pH}$ of the buffer after the addition of $0.0500 \mathrm{~mol}$ of $\mathrm{NaOH}$ to $0.600 \mathrm{~L}$ of diluted buffer.
(d) Compare your answers to Question $29(\mathrm{a})-(\mathrm{c})$ with your answers to
(a)-(c) in this problem.
(e) Comment on the effect of dilution on the pH of a buffer and on its buffer capacity.

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Problem 32

Enough water is added to the buffer in Question 30 to make the total volume 10.0 L. Calculate
(a) the $\mathrm{pH}$ of the buffer.
(b) the $\mathrm{pH}$ of the buffer after the addition of $0.0300 \mathrm{~mol}$ of $\mathrm{HCl}$ to $0.710 \mathrm{~L}$ of diluted buffer.
(c) the $\mathrm{pH}$ of the buffer after the addition of $0.0300 \mathrm{~mol}$ of $\mathrm{NaOH}$ to $0.710 \mathrm{~L}$ of diluted buffer.
(d) Compare your answers to Question $30(\mathrm{a})-(\mathrm{c})$ with your answers to
(a)-(c) in this problem.
(e) Comment on the effect of dilution on the pH of a buffer and on its buffer capacity.

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Problem 33

A buffer is prepared in which the ratio $\left[\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\right] /\left[\mathrm{HPO}_{4}^{2-}\right]$ is 3.0
(a) What is the pH of this buffer?
(b) Enough strong acid is added to convert $15 \%$ of $\mathrm{HPO}_{4}{ }^{2-}$ to $\mathrm{H}_{2} \mathrm{PO}_{4}^{-}$. What is the $\mathrm{pH}$ of the resulting solution?
(c) Enough strong base is added to make the $\mathrm{pH} 7.00$. What is the ratio of $\left[\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\right]$ to $\left[\mathrm{HPO}_{4}^{2-}\right]$ at this point?

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Problem 34

A buffer is prepared using the butyric acid/butyrate $\left(\mathrm{HC}_{4} \mathrm{H}_{7} \mathrm{O}_{2} /\right.$ $\left.\mathrm{C}_{4} \mathrm{H}_{7} \mathrm{O}_{2}^{-}\right)$ acid-base pair. The ratio of acid to base is 2.2 and $K_{\mathrm{a}}$ for butyric acid is $1.54 \times 10^{-5}$
(a) What is the $\mathrm{pH}$ of this buffer?
(b) Enough strong base is added to convert $15 \%$ of butyric acid to the butyrate ion. What is the $\mathrm{pH}$ of the resulting solution?
(c) Strong acid is added to the buffer to increase its $\mathrm{pH}$. What must the acid/base ratio be so that the pH increases by exactly one unit (e.g., from 2 to 3 ) from the answer in (a)?

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Problem 35

Blood is buffered mainly by the $\mathrm{HCO}_{3}^{-}-\mathrm{H}_{2} \mathrm{CO}_{3}$ buffer system. The normal $\mathrm{pH}$ of blood is 7.40 .
(a) Calculate the $\left[\mathrm{H}_{2} \mathrm{CO}_{3}\right] /\left[\mathrm{HCO}_{3}^{-}\right]$ ratio.
(b) What does the $\mathrm{pH}$ become if $15 \%$ of the $\mathrm{HCO}_{3}^{-}$ ions are converted to $\mathrm{H}_{2} \mathrm{CO}_{3} ?$
(c) What does the pH become if $15 \%$ of the $\mathrm{H}_{2} \mathrm{CO}_{3}$ molecules are converted to $\mathrm{HCO}_{3}^{-}$ ions?

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Problem 36

There is a buffer system $\left(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}-\mathrm{HPO}_{4}{ }^{2-}\right)$ in blood that helps keep the blood $\mathrm{pH}$ at about $7.40 .\left(\mathrm{K}_{\mathrm{a}} \mathrm{H}_{2} \mathrm{PO}_{4}^{-}=6.2 \times 10^{-8}\right)$
(a) Calculate the $\left[\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\right] /\left[\mathrm{HPO}_{4}^{2-}\right]$ ratio at the normal $\mathrm{pH}$ of blood.
(b) What percentage of the $\mathrm{HPO}_{4}{ }^{2-}$ ions are converted to $\mathrm{H}_{2} \mathrm{PO}_{4}^{-}$ when the $\mathrm{pH}$ goes down to $6.80 ?$
(c) What percentage of $\mathrm{H}_{2} \mathrm{PO}_{4}^{-}$ ions are converted to $\mathrm{HPO}_{4}{ }^{2-}$ when the $\mathrm{pH}$ goes up to $7.80 ?$

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Problem 37

Given three acid-base indicators-methyl orange (end point at $\mathrm{pH} 4$ ), bromthymol blue (end point at $\mathrm{pH} 7$ ), and phenolphthalein (end point at $\mathrm{pH}$ 9)-which would you select for the following acid-base titrations?
(a) perchloric acid with an aqueous solution of ammonia
(b) nitrous acid with lithium hydroxide
(c) hydrobromic acid with strontium hydroxide
(d) sodium fluoride with nitric acid

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Problem 38

Given the acid-base indicators in Question $37,$ select a suitable indicator for the following titrations.
(a) sodium formate $\left(\mathrm{NaCHO}_{2}\right)$ with $\mathrm{HNO}_{3}$
(b) hypochlorous acid with barium hydroxide
(c) nitric acid with $\mathrm{HI}$
(d) hydrochloric acid with ammonia

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Problem 39

Metacresol purple is an indicator that changes from yellow to purple at $\mathrm{pH} 8.2$
(a) What is $K_{\mathrm{a}}$ for this indicator?
(b) What is its $\mathrm{pH}$ range?
(c) What is the color of a solution with $\mathrm{pH} 9.0$ and a few drops of metacresol purple?

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Problem 40

An indicator has a $\mathrm{p} K_{\mathrm{a}}$ of $5.7 .$ It is colorless in acid solution and deep green in alkaline solution.
(a) What is its $K_{\mathrm{a}}$ ?
(b) What is its pH range?
(c) What would its color be at pH $5.7 ?$

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Problem 41

When $25.00 \mathrm{~mL}$ of $\mathrm{HNO}_{3}$ are titrated with $\mathrm{Sr}(\mathrm{OH})_{2}, 58.4 \mathrm{~mL}$ of a $0.218 M$ solution are required.
(a) What is the $\mathrm{pH}$ of $\mathrm{HNO}_{3}$ before titration?
(b) What is the $\mathrm{pH}$ at the equivalence point?
(c) Calculate $\left[\mathrm{NO}_{3}^{-}\right]$ and $\left[\mathrm{Sr}^{2+}\right]$ at the equivalence point. (Assume that volumes are additive.)

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Problem 42

A solution of $\mathrm{NaOH}$ with $\mathrm{pH} 13.68$ requires $35.00 \mathrm{~mL}$ of $0.128 \mathrm{M} \mathrm{HClO}_{4}$ to reach the equivalence point.
(a) What is the volume of the NaOH solution?
(b) What is the $\mathrm{pH}$ at the equivalence point?
(c) Calculate $\left[\mathrm{Na}^{+}\right]$ and $\left[\mathrm{ClO}_{4}^{-}\right]$ at the equivalence point. (Assume that volumes are additive.)

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Problem 43

A solution consisting of $25.00 \mathrm{~g} \mathrm{NH}_{4} \mathrm{Cl}$ in $178 \mathrm{~mL}$ of water is titrated with $0.114 \mathrm{M} \mathrm{KOH}$.
(a) How many milliliters of KOH are required to reach the equivalence point?
(b) Calculate $\left[\mathrm{Cl}^{-}\right],\left[\mathrm{K}^{+}\right],\left[\mathrm{NH}_{3}\right],$ and $\left[\mathrm{OH}^{-}\right]$ at the equivalence point. (Assume that volumes are additive.)
(c) What is the $\mathrm{pH}$ at the equivalence point?

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Problem 44

A $50.0-\mathrm{mL}$ sample of $\mathrm{NaHSO}_{3}$ is titrated with $22.94 \mathrm{~mL}$ of $0.238 \mathrm{M}$ $\mathrm{KOH}$
(a) Write a balanced net ionic equation for the reaction.
(b) What is $\left[\mathrm{HSO}_{3}^{-}\right]$ before the titration?
(c) Find $\left[\mathrm{HSO}_{3}^{-}\right],\left[\mathrm{SO}_{3}^{2-}\right],\left[\mathrm{OH}^{-}\right],\left[\mathrm{K}^{+}\right],$ and $\left[\mathrm{Na}^{+}\right]$ at the equivalence point.
(d) What is the $\mathrm{pH}$ at the equivalence point?

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Problem 45

A 20.00 -mL sample of $0.220 \mathrm{M}$ triethylamine, $\left(\mathrm{CH}_{3} \mathrm{CH}_{2}\right)_{3} \mathrm{~N},$ is titrated with $0.544 \mathrm{M} \mathrm{HCl} .\left(\mathrm{K}_{\mathrm{b}}\left(\mathrm{CH}_{3} \mathrm{CH}_{2}\right)_{3} \mathrm{~N}=5.2 \times 10^{-4}\right)$
(a) Write a balanced net ionic equation for the titration.
(b) How many milliliters of $\mathrm{HCl}$ are required to reach the equivalence
point?
(c) Calculate $\left[\left(\mathrm{CH}_{3} \mathrm{CH}_{2}\right)_{3} \mathrm{~N}\right],\left[\left(\mathrm{CH}_{3} \mathrm{CH}_{2}\right)_{3} \mathrm{NH}^{+}\right],\left[\mathrm{H}^{+}\right],$ and $\left[\mathrm{Cl}^{-}\right]$ at the
equivalence point. (Assume that volumes are additive.)
(d) What is the $\mathrm{pH}$ at the equivalence point?

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Problem 46

Pyridine, $\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N},$ has $K_{\mathrm{b}}$ of $1.7 \times 10^{-9} .$ A $38.00-\mathrm{mL}$ sample of pyridine requires $29.20 \mathrm{~mL}$ of $0.332 \mathrm{M}$ HBr to reach the equivalence point.
(a) Write a balanced net ionic equation for the titration.
(b) How many grams of pyridine are in the sample?
(c) Calculate $\left[\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N}\right],\left[\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{NH}^{+}\right],\left[\mathrm{H}^{+}\right]$ and $\left[\mathrm{Br}^{-}\right]$ at the equivalence
point. (Assume that volumes are additive.)
(d) What is the $\mathrm{pH}$ at the equivalence point?

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Problem 47

A $0.4000 \mathrm{M}$ solution of nitric acid is used to titrate $50.00 \mathrm{~mL}$ of $0.237 \mathrm{M}$ barium hydroxide. (Assume that volumes are additive.)
(a) Write a balanced net ionic equation for the reaction that takes place during titration.
(b) What are the species present at the equivalence point?
(c) What volume of nitric acid is required to reach the equivalence point?
(d) What is the $\mathrm{pH}$ of the solution before any $\mathrm{HNO}_{3}$ is added?
(e) What is the $\mathrm{pH}$ of the solution halfway to the equivalence point?
(f) What is the $\mathrm{pH}$ of the solution at the equivalence point?

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Problem 48

A $0.2128 M$ solution of $\mathrm{NaOH}$ is used to titrate $37.00 \mathrm{~mL}$ of $0.1988 \mathrm{M}$ HI.
(Assume that volumes are additive.)
(a) Write a balanced net ionic equation for the reaction that takes place during the titration.
(b) What are the species present at the equivalence point besides $\mathrm{H}_{2} \mathrm{O}$ and the $\mathrm{H}^{+}$ and $\mathrm{OH}^{-}$ that result from the ionization of water?
(c) What volume of $\mathrm{NaOH}$ is required to reach the equivalence point?
(d) What is the $\mathrm{pH}$ of the solution before any $\mathrm{NaOH}$ is added?
(e) What is the $\mathrm{pH}$ of the solution halfway to the equivalence point (half-neutralization)?
(f) What is the pH of the solution at the equivalence point?

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Problem 49

Consider the titration of butyric acid (HBut) with sodium hydroxide. In an experiment, $50.00 \mathrm{~mL}$ of $0.350 \mathrm{M}$ butyric acid is titrated with $0.225 \mathrm{M}$ $\mathrm{NaOH} . K_{\mathrm{a}}$ HBut $=1.5 \times 10^{-5}$
(a) Write a balanced net ionic equation for the reaction that takes place during titration.
(b) What are the species present at the equivalence point?
(c) What volume of sodium hydroxide is required to reach the equivalence point?
(d) What is the $\mathrm{pH}$ of the solution before any $\mathrm{NaOH}$ is added?
(e) What is the pH of the solution halfway to the equivalence point?
(f) What is the $\mathrm{pH}$ of the solution at the equivalence point?

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Problem 50

Morphine, $\mathrm{C}_{17} \mathrm{H}_{19} \mathrm{O}_{3} \mathrm{~N},$ is a weak base $\left(K_{\mathrm{b}}=7.4 \times 10^{-7}\right)$. Consider its
titration with hydrochloric acid. In the titration, $50.0 \mathrm{~mL}$ of a $0.1500 \mathrm{M}$ solu-
tion of morphine is titrated with $0.1045 \mathrm{M} \mathrm{HCl}$.
(a) Write a balanced net ionic equation for the reaction that takes place during titration.
(b) What are the species present at the equivalence point?
(c) What volume of hydrochloric acid is required to reach the equivalence point?
(d) What is the pH of the solution before any $\mathrm{HCl}$ is added?
(e) What is the $\mathrm{pH}$ of the solution halfway to the equivalence point?
(f) What is the pH of the solution at the equivalence point?

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Problem 51

Consider a $10.0 \%$ (by mass) solution of hypochlorous acid. Assume the density of the solution to be $1.00 \mathrm{~g} \mathrm{mL}$. A $30.0-\mathrm{mL}$ sample of the solution is titrated with $0.419 \mathrm{M} \mathrm{KOH}$. Calculate the $\mathrm{pH}$ of the solution
(a) before titration.
(b) halfway to the equivalence point.
(c) at the equivalence point.

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Problem 52

At $25^{\circ} \mathrm{C}$ and $0.925 \mathrm{~atm},$ one liter of ammonia is bubbled into $815 \mathrm{~mL}$ of water. Assume that all the ammonia dissolves and the volume of the resulting solution is $815 \mathrm{~mL}$. A $25.00-\mathrm{mL}$ portion of the prepared solution is titrated with $0.149 \mathrm{M} \mathrm{HCl}$. Calculate the $\mathrm{pH}$ of the solution
(a) before titration.
(b) halfway to the equivalence point.
(c) at the equivalence point.

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Problem 53

A student is given $250.0 \mathrm{~g}$ of sodium lactate, $\mathrm{NaC}_{3} \mathrm{H}_{5} \mathrm{O}_{3}$, and a bottle of lactic acid marked " $73.0 \%$ by mass $\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{3}, d=1.20 \mathrm{~g} / \mathrm{mL}$." How many milliliters of $73.0 \%$ lactic acid should the student add to the sodium lactate to produce a buffer with a $\mathrm{pH}$ of $4.50 ?$

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Numerade Educator

Problem 54

Methylamine, $\mathrm{CH}_{3} \mathrm{NH}_{2},$ is a gas at room temperature and very soluble in water. An aqueous solution of methylamine has $K_{\mathrm{b}}=4.2 \times 10^{-4}$. How many liters of methylamine at $27^{\circ} \mathrm{C}$ and a pressure of 1.2 atm should be bubbled into $0.750 \mathrm{~L}$ of a solution that is $0.588 \mathrm{M}$ in the methylammonium ion, $\mathrm{CH}_{3} \mathrm{NH}_{3}^{+},$ so that a buffer of $\mathrm{pH} 9.80$ is obtained? Assume no volume changes after methylamine is bubbled into the solution and ignore the vapor pressure of water.

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 55

For an aqueous solution of acetic acid to be called "distilled white vinegar" it must contain $5.0 \%$ acetic acid by mass. A solution with a density of $1.05 \mathrm{~g} / \mathrm{mL}$ has a $\mathrm{pH}$ of $2.95 .$ Can the solution be called "distilled white vinegar"?

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 56

Consider an unknown base, RNH. One experiment titrates a $50.0-\mathrm{mL}$ aqueous solution containing $2.500 \mathrm{~g}$ of the base. This titration requires $59.90 \mathrm{~mL}$ of $0.925 \mathrm{M} \mathrm{HCl}$ to reach the equivalence poinl. A second experiment uses a $50.0-\mathrm{mL}$ solution of the unknown base identical to what was used in the first experiment. To this solution is added $29.95 \mathrm{~mL}$ of $0.925 \mathrm{M} \mathrm{HCl}$. The $\mathrm{pH}$ after the $\mathrm{HCl}$ addition is 10.77
(a) What is the molar mass of the unknown base?
(b) What is $K_{\mathrm{b}}$ for the unknown base?
(c) What is $K_{\mathrm{a}}$ for $\mathrm{RNH}_{2}+?$

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 57

A painful arthritic condition known as gout is caused by an excess of uric acid, HUric, in the blood. An aqueous solution contains $4.00 \mathrm{~g}$ of uric acid. A $0.730 \mathrm{M}$ solution of $\mathrm{KOH}$ is used for titration. After $12.00 \mathrm{~mL}$ of $\mathrm{KOH}$
are added, the resulting solution has $\mathrm{pH} 4.12 .$ The equivalence point is reached after a total of $32.62 \mathrm{~mL}$ of $\mathrm{KOH}$ are added.
$$
\operatorname{HUric}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{Uric}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}
$$
(a) What is the molar mass of uric acid?
(b) What is its $K_{\mathrm{a}}$ ?

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 58

Water is accidentally added to $350.00 \mathrm{~mL}$ of a stock solution of $6.00 \mathrm{M} \mathrm{HCl}$. A 75.00-mL sample of the diluted solution is titrated to $\mathrm{pH} 7.00$ with $78.8 \mathrm{~mL}$ of $4.85 \mathrm{M} \mathrm{NaOH}$. How much water was accidentally added? (Assume that volumes are additive.)

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 59

A solution of an unknown weak acid at $25^{\circ} \mathrm{C}$ has an osmotic pressure of 0.878 atm and a $\mathrm{pH}$ of $6.76 .$ What is $K_{\mathrm{b}}$ for its conjugate base? (Assume that, in the equation for $\pi$ [Chapter 10$], i \approx 1$.)

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 60

Consider an aqueous solution of HF. The molar heat of formation for aqueous HF is $-320.1 \mathrm{~kJ} / \mathrm{mol}$.
(a) What is the $\mathrm{pH}$ of a $0.100 \mathrm{M}$ solution of $\mathrm{HF}$ at $100^{\circ} \mathrm{C} ?$
(b) Compare with the $\mathrm{pH}$ of a $0.100 \mathrm{M}$ solution of $\mathrm{HF}$ at $25^{\circ} \mathrm{C}$.

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 61

61. Each symbol in the box below represents a mole of a component in one liter of a buffer solution; $\bigcirc$ represents the anion $\left(\mathrm{X}^{-}\right), \square 0=$ the weak acid $(\mathrm{HX}), \square=\mathrm{H}^{+},$ and $\Delta=\mathrm{OH}^{-}$. Water molecules and the few $\mathrm{H}^{+}$ and $\mathrm{OH}^{-}$ ions from the dissociation of $\mathrm{HX}$ and $\mathrm{X}^{-}$ are not shown. The box contains $10 \mathrm{~mol}$ of a weak acid, $\square 0,$ in a liter of solution. Show what happens upon

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 62

Use the same symbols as in Question $61\left(\bigcirc=\right.$ anion, $\left.\Delta=\mathrm{OH}^{-}\right)$ for the box below.

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 63

The following is the titration curve for the titration of $50.00 \mathrm{~mL}$ of a $0.100 \mathrm{M}$ acid with $0.100 \mathrm{M} \mathrm{KOH}$.
(a) Is the acid strong or weak?
(b) If the acid is weak, what is its $K_{\mathrm{a}} ?$
(c) Estimate the $\mathrm{pH}$ at the equivalence point.

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 64

Consider the following five beakers:
Beaker A has $0.100 \mathrm{~mol} \mathrm{HA}$ and $0.100 \mathrm{~mol} \mathrm{NaA}$ in $100 \mathrm{~mL}$ of solution.
Beaker B has $0.100 \mathrm{~mol} \mathrm{HA}$ and $0.100 \mathrm{~mol} \mathrm{NaA}$ in $200 \mathrm{~mL}$ of solution.
Beaker $\mathrm{C}$ has $0.100 \mathrm{~mol} \mathrm{HA}, 0.100 \mathrm{~mol} \mathrm{NaA},$ and $0.0500 \mathrm{~mol} \mathrm{HCl}$ in
$100 \mathrm{~mL}$ of solution. Beaker $\mathrm{D}$ has $0.100 \mathrm{~mol} \mathrm{HA}, 0.100 \mathrm{~mol} \mathrm{Na} \mathrm{A},$ and $0.100 \mathrm{~mol} \mathrm{NaOH}$ in
$100 \mathrm{~mL}$ of solution. Beaker $\mathrm{E}$ has $0.100 \mathrm{~mol} \mathrm{HCl}$ and $0.100 \mathrm{~mol} \mathrm{NaOH}$ in $100 \mathrm{~mL}$ of
solution.

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 65

Follow the directions of Question 64. Consider two beakers:
Beaker A has a weak acid $\left(K_{\mathrm{a}}=1 \times 10^{-5}\right)$ Beaker B has HCl.

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 66

Explain why
(a) the $\mathrm{pH}$ decreases when lactic acid is added to a sodium lactate solution.
(b) the $\mathrm{pH}$ of $0.1 \mathrm{M} \mathrm{NH}_{3}$ is less than 13.0 .
(c) a buffer resists changes in $\mathrm{pH}$ caused by the addition of $\mathrm{H}^{+}$ or $\mathrm{OH}^{-}$.
(d) a solution with a low $\mathrm{pH}$ is not necessarily a strong acid solution.

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 67

Indicate whether each of the following statements is true or false. If the statement is false, restate it to make it true.
(a) The formate ion $\left(\mathrm{CHO}_{2}^{-}\right)$ concentration in $0.10 \mathrm{M} \mathrm{HCHO}_{2}$ is the same as in $0.10 \mathrm{M} \mathrm{NaCHO}_{2}$
(b) A buffer can be destroyed by adding too much strong acid.
(c) A buffer can be made up by any combination of weak acid and weak base.
(d) Because $K_{\mathrm{a}}$ for $\mathrm{HCO}_{3}^{-}$ is $4.7 \times 10^{-11}, K_{\mathrm{b}}$ for $\mathrm{HCO}_{3}^{-}$ is $2.1 \times 10^{-4}$.

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 68

The solutions in three test tubes labeled $A, B,$ and $C$ all have the same $\mathrm{pH}$. The test tubes are known to contain $1.0 \times 10^{-3} \mathrm{M} \mathrm{HCl}, 6.0 \times 10^{-3} \mathrm{M}$ $\mathrm{HCHO}_{2},$ and $4 \times 10^{-2} \mathrm{M} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}^{+} .$ Describe a procedure for identifying the solutions.

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 69

Consider the following titration curves. The solution in the buret is 0.1 $M$. The solution in the beaker has a volume of $50.0 \mathrm{~mL}$. Answer the following questions.
(a) Is the titrating agent (solution in the buret) an acid or a base?
(b) Which curve shows the titration of the weakest base?
(c) What is the $K_{\mathrm{a}}$ of the conjugate acid of the base titrated in curve $\mathrm{B}$ ?
(d) What is the molarity of the solution in the beaker for curve $\mathrm{C} ?$
(e) What is the $\mathrm{pH}$ at the equivalence point for curve $\mathrm{A?}$

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 70

Consider the titration of $\mathrm{HF}\left(K_{\mathrm{a}}=6.7 \times 10^{-4}\right)$ with $\mathrm{NaOH}$. What is the $\mathrm{pH}$ when a third of the acid has been neutralized?

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 71

The species called glacial acetic acid is $98 \%$ acetic acid by mass $(d=1.0542 \mathrm{~g} / \mathrm{mL}) .$ What volume of glacial acetic acid must be added to $100.0 \mathrm{~mL}$ of $1.25 \mathrm{M} \mathrm{NaOH}$ to give a buffer with a $\mathrm{pH}$ of $4.20 ?$

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 72

Four grams of a monoprotic weak acid are dissolved in water to make $250.0 \mathrm{~mL}$ of solution with a $\mathrm{pH}$ of $2.56 .$ The solution is divided into two equal parts, $A$ and $B$. Solution $A$ is titrated with strong base to its equivalence point. Solution $\mathrm{B}$ is added to solution $\mathrm{A}$ after solution $\mathrm{A}$ is neutralized. The $\mathrm{pH}$ of the resulting solution is $4.26 .$ What is the molar mass of the acid?

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 73

Explain why it is not possible to prepare a buffer with a pH of 6.50 by mixing $\mathrm{NH}_{3}$ and $\mathrm{NH}_{4} \mathrm{Cl}$.

Sima Sarker

Numerade Educator

Problem 74

Fifty $\mathrm{cm}^{3}$ of $1.000 \mathrm{M}$ nitrous acid is titrated with $0.850 \mathrm{M} \mathrm{NaOH}$. What
is the $\mathrm{pH}$ of the solution
(a) before any $\mathrm{Na} \mathrm{OH}$ is added?
(b) at half-neutralization?
(c) at the equivalence point?
(d) when $0.10 \mathrm{~mL}$ less than the volume of $\mathrm{NaOH}$ to reach the equivalence point is added?
(e) when $0.10 \mathrm{~mL}$ more than the volume of $\mathrm{NaOH}$ to reach the equivalence point is added?
(f) Use your data to construct a plot similar to that shown in Figure 14.6 (pH versus volume $\mathrm{Na} \mathrm{OH}$ added $)$

Thomas Harr

Numerade Educator

Problem 75

In a titration of $50.00 \mathrm{~mL}$ of $1.00 \mathrm{M} \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}$ with $1.00 \mathrm{M} \mathrm{NaOH},$ a student used bromcresol green as an indicator $\left(K_{\mathrm{a}}=1.0 \times 10^{-5}\right) .$ About how many milliliters of $\mathrm{NaOH}$ would it take to reach the end point with this indicator? Is there a better indicator that she could have used for this titration?

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 76

What is the $\mathrm{pH}$ of a $0.1500 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}$ solution if
(a) the ionization of $\mathrm{HSO}_{4}^{-}$ is ignored?
(b) the ionization of $\mathrm{HSO}_{4}^{-}$ is taken into account? $\left(K_{\mathrm{a}}\right.$ for $\mathrm{HSO}_{4}^{-}$ is $1.1 \times 10^{-2} .$

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 77

Two students were asked to determine the $K_{\mathrm{b}}$ of an unknown base. They were given a bottle with a solution in it. The bottle was labeled "aqueous solution of a monoprotic strong acid." They were also given a pH meter, a buret, and an appropriate indicator. They reported the following data: volume of acid required for neutralization $=21.0 \mathrm{~mL}$ $\mathrm{pH}$ after $7.00 \mathrm{~mL}$ of strong acid added $=8.95$ Use the students' data to determine the $K_{\mathrm{b}}$ of the unknown base.

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 78

How many grams of $\mathrm{NaOH}$ must be added to $1.00 \mathrm{~L}$ of a buffer made from $0.150 \mathrm{M} \mathrm{NH}_{3}$ and $10.0 \mathrm{~g}$ of $\mathrm{NH}_{4} \mathrm{Cl}$ so that the $\mathrm{pH}$ increases by one unit (e.g., from 5 to 6 )? $K_{\mathrm{a}}$ for $\mathrm{NH}_{4}{ }^{+}$ is $5.6 \times 10^{-10}$.

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 79

Starting with the relation
$$
\left[\mathrm{H}^{+}\right]=K_{\mathrm{a}} \frac{[\mathrm{HB}]}{\left[\mathrm{B}^{-}\right]}
$$
derive the Henderson-Hasselbalch equation
$$
\mathrm{pH}=\mathrm{p} K_{\mathrm{a}}+\log _{10} \frac{\left[\mathrm{B}^{-}\right]}{[\mathrm{HB}]}
$$

Sima Sarker

Numerade Educator