Chemistry Principles and Reactions

William L. Masterton, Cecile N. Hurley

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 sulfite
(b) lithium hydroxide
(c) potassium benzoate $\left(\mathrm{KC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}\right)$

Rachel Stegner

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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
5. Calculate $K$ for the reactions in Question $1 .$
6. Calculate $K$ for the reactions in Question 2 .
7. Calculate $K$ for the reactions in Question $3 .$
8. Calculate $K$ for the reactions in Question 4 .

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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) $0.250 \mathrm{M}$
(b) $0.125 \mathrm{M}$
(c) $0.0800 \mathrm{M}$
(d) $0.0500 \mathrm{M}$

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Problem 10

Calculate $\left[\mathrm{OH}^{-}\right]$ and $\mathrm{pH}$ in a solution in which the hydrogen sulfite ion, $\mathrm{HSO}_{3}^{-},$ is $0.429 \mathrm{M}$ and the sulfite ion is
(a) $0.0249 \mathrm{M}$
(b) $0.247 M$
(c) $0.504 \mathrm{M}$
(d) $0.811 \mathrm{M}$
(e) $1.223 \mathrm{M}$

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Problem 11

A buffer is prepared by dissolving $0.0250 \mathrm{~mol}$ 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 $\mathrm{pH}$ of this buffer.

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Problem 12

A buffer is prepared by dissolving $0.062 \mathrm{~mol}$ of sodium fluoride in $127 \mathrm{~mL}$ of $0.0399 \mathrm{M}$ hydrofluoric acid. Assume no volume change after $\mathrm{NaF}$ 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 $0.0188 \mathrm{~mol}$ 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 9.22 is prepared by adding water to $0.413 \mathrm{~mol}$ of KX to make $2.00 \mathrm{~L}$ of solution. What is the $\mathrm{pH}$ of the solution after $0.368 \mathrm{~mol}$ of $\mathrm{HX}$ is added?

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Problem 16

An aqueous solution of $0.057 \mathrm{M}$ 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?

Eileen Sullivan

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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 $295 \mathrm{~mL}$ of $0.380 \mathrm{M} \mathrm{HCl}$ ?
(a) $0.100 \mathrm{~mol}$ of $\mathrm{NH}_{4} \mathrm{Cl}$
(b) $0.033 \mathrm{~mol}$ of $\mathrm{KF}$
(c) $0.167 \mathrm{~mol}$ of $\mathrm{Sr}(\mathrm{OH})_{2}$
(d) $0.279 \mathrm{~mol}$ of $\mathrm{KNO}_{2}$
(e) $0.112 \mathrm{~mol}$ of $\mathrm{KClO}$

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Problem 19

Calculate the pH of a solution prepared by mixing $2.50 \mathrm{~g}$ of hypobromous acid $(\mathrm{HOBr})$ and $0.750 \mathrm{~g}$ of $\mathrm{KOH}$ 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 $1.67 \mathrm{M} \mathrm{HCl} . K_{\mathrm{b}}$ for aniline is $4.3 \times 10^{-10} .$ (Assume volumes are additive.)

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Problem 21

Calculate the $\mathrm{pH}$ of a solution prepared by mixing $49.0 \mathrm{~mL}$ of butyric acid, $\mathrm{HC}_{4} \mathrm{H}_{7} \mathrm{O}_{2},$ with $6.15 \mathrm{~g}$ of $\mathrm{KOH}$ in water. The following data about butyric acid may be helpful:
$$\text { density }=0.9595 \mathrm{~g} / \mathrm{mL} ; K_{\mathrm{a}}=1.54 \times 10^{-5}$$

Eileen Sullivan

Eileen Sullivan

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Problem 22

Calculate the 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 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) 4.5
(b) 9.2
(c) 11.0

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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 pH? (Assume that volumes are additive.)

Eileen Sullivan

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Problem 26

You want to make a buffer with a pH of 10.00 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 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 pH of the buffer.
(b) the $\mathrm{pH}$ of the buffer after the addition of $0.0500 \mathrm{~mol}$ of 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 $239 \mathrm{~mL}$ of $0.187 \mathrm{M}$ potassium hydrogen tartrate $\left(\mathrm{KHC}_{4} \mathrm{H}_{4} \mathrm{O}_{6}\right)$ and $137 \mathrm{~mL}$ of $0.288 \mathrm{M}$ potassium tartrate $\left(\mathrm{K}_{2} \mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{6}\right) . K_{\mathrm{a}}$ for $\left(\mathrm{H}_{2} \mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{6}\right)$ is $4.55 \times 10^{-5} .$
Assuming volumes are additive, calculate
(a) the $\mathrm{pH}$ of the buffer.
(b) the $\mathrm{pH}$ of the buffer after adding $0.0250 \mathrm{~mol}$ of $\mathrm{HCl}$ to $0.376 \mathrm{~L}$ of the buffer.
(c) the $\mathrm{pH}$ of the buffer after adding $0.0250 \mathrm{~mol}$ of $\mathrm{KOH}$ to $0.376 \mathrm{~L}$ of the buffer.

Susan Hallstrom

Susan Hallstrom

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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 pH of the buffer.
(b) the $\mathrm{pH}$ of the buffer after the addition of $0.0500 \mathrm{~mol}$ of 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 $\mathrm{Na} \mathrm{OH}$ 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 $\mathrm{pH}$ of a buffer and on its buffer capacity.

Eileen Sullivan

Eileen Sullivan

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Problem 32

Enough water is added to the buffer in Question 30 to make the total volume $5.00 \mathrm{~L}$.
(a) Calculate the $\mathrm{pH}$ of the buffer.
(b) Calculate the $\mathrm{pH}$ of the buffer after adding 0.0250 mol of HCl to $0.376 \mathrm{~L}$ of the buffer.
(c) Calculate the pH of the buffer after adding $0.0250 \mathrm{~mol}$ of $\mathrm{KOH}$ to $0.376 \mathrm{~L}$ of the buffer.
(d) Compare your answers to Question $30(\mathrm{a}-\mathrm{c})$ with your answers to $(a-c)$ of this problem.
(e) Comment on the effect of dilution on the pH of a buffer and on its buffer capacity.

Eileen Sullivan

Eileen Sullivan

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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 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?

Eileen Sullivan

Eileen Sullivan

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Problem 34

A buffer is prepared using the butyric acid/butyrate $\left(\mathrm{HC}_{4} \mathrm{H}_{7} \mathrm{O}_{2} / \mathrm{C}_{4} \mathrm{H}_{7} \mathrm{O}_{2}^{-}\right)$ 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)?

Eileen Sullivan

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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?

Eileen Sullivan

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Problem 36

There is a buffer system in blood $\left(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}-\mathrm{HPO}_{4}^{2-}\right)$ that helps keep the blood $\mathrm{pH}$ at $7.40 .\left(\mathrm{K}_{\mathrm{a}} \mathrm{H}_{2} \mathrm{PO}_{4}^{-}=6.2 \times 10^{-8}\right)$
(a) Calculate the $\left[\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\right] /\left[\mathrm{HPO}_{4}^{2-}\right]$ ratio at the normal pH of blood.
(b) What percentage of the $\mathrm{HPO}_{4}^{2-}$ ions are converted to $\mathrm{H}_{2} \mathrm{PO}_{4}^{-}$ when the $\mathrm{pH}$ is $7.00 ?$
(c) What percentage of the $\mathrm{H}_{2} \mathrm{PO}_{4}^{-}$ ions are converted to $\mathrm{HPO}_{4}^{2-}$ when the $\mathrm{pH}$ is 8.00 ?

Eileen Sullivan

Eileen Sullivan

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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

Eileen Sullivan

Eileen Sullivan

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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 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 pH range?
(c) What is the color of a solution with $\mathrm{pH} 9.0$ and a few drops of metacresol purple?

Eileen Sullivan

Eileen Sullivan

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Problem 40

Thymolphthalein is an indicator that changes from colorless to blue at $\mathrm{pH} 9.5$
(a) What is its $K_{\mathrm{a}}$ ?
(b) What is its pH range?
(c) What is the color of a solution with a pH of 10.0 and a few drops of thymolphthalein?

Eileen Sullivan

Eileen Sullivan

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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 $0.218 \mathrm{M}$ 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.)

Eileen Sullivan

Eileen Sullivan

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Problem 42

A solution of $\mathrm{KOH}$ has a $\mathrm{pH}$ of 13.29 . It requires $27.66 \mathrm{~mL}$ of $0.2500 \mathrm{MHCl}$ to reach the equivalence point.
(a) What is the volume of the KOH solution?
(b) What is the $\mathrm{pH}$ at the equivalence point?
(c) What is $\left[\mathrm{K}^{+}\right]$ and $\left[\mathrm{Cl}^{-}\right]$ at the equivalence point? Assume volumes are additive.

Eileen Sullivan

Eileen Sullivan

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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 $\mathrm{KOH}$ 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?

Eileen Sullivan

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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?

Eileen Sullivan

Eileen Sullivan

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Problem 45

A $20.00-\mathrm{mL}$ 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?

Eileen Sullivan

Eileen Sullivan

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Problem 46

A $35.00-\mathrm{mL}$ sample of $0.487 \mathrm{M} \mathrm{KBrO}$ is titrated with $0.264 \mathrm{M} \mathrm{HNO}_{3} \cdot\left(K_{\mathrm{b}} \mathrm{BrO}^{-}=4.0 \times 10^{-6}\right)$
(a) Write a balanced net ionic equation for the reaction.
(b) How many milliliters of $\mathrm{HCl}$ are required to reach the equivalence point?
(c) What is the $\mathrm{pH}$ at the equivalence point?
(d) Calculate $\left[\mathrm{K}^{+}\right],\left[\mathrm{NO}_{3}^{-}\right],\left[\mathrm{H}^{+}\right],\left[\mathrm{BrO}^{-}\right],$ and $[\mathrm{HBrO}]$ at
the equivalence point. (Assume volumes are additive.)

Eileen Sullivan

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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?

Eileen Sullivan

Eileen Sullivan

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Problem 48

A $0.2481 \mathrm{M}$ solution of $\mathrm{KOH}$ is used to titrate $30.00 \mathrm{~mL}$ of $0.269 \mathrm{M}$ hydrobromic acid. 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?
(c) What volume of $\mathrm{KOH}$ is required to reach the equivalence point?
(d) What is the $\mathrm{pH}$ of the solution
1. before any $\mathrm{KOH}$ is added?
2. halfway to the equivalence point?
3. at the equivalence point?

Eileen Sullivan

Eileen Sullivan

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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 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 pH of the solution at the equivalence point?

Eileen Sullivan

Eileen Sullivan

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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 $0.1500 \mathrm{M}$ solution 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 $\mathrm{pH}$ 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 $\mathrm{pH}$ of the solution at the equivalence point?

Eileen Sullivan

Eileen Sullivan

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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.

Eileen Sullivan

Eileen Sullivan

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Problem 52

A solution is prepared by dissolving $0.350 \mathrm{~g}$ of benzoic acid, $\mathrm{HC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}$, in water to make $100.0 \mathrm{~mL}$ of solution. A $30.00-\mathrm{mL}$ sample of the solution is titrated with $0.272 \mathrm{M}$ KOH. Calculate the $\mathrm{pH}$ of the solution
(a) before titration.
(b) halfway to the equivalence point.
(c) at the equivalence point.

Eileen Sullivan

Eileen Sullivan

Numerade Educator

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 pH of $4.50 ?$

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 54

Ammonia gas is bubbled into $275 \mathrm{~mL}$ of water to make an aqueous solution of ammonia. To prepare a buffer with a $\mathrm{pH}$ of $9.56,15.0 \mathrm{~g}$ of $\mathrm{NH}_{4} \mathrm{Cl}$ are added. How many liters of $\mathrm{NH}_{3}$ at $25^{\circ} \mathrm{C}$ and 0.981 atm should be used to prepare the buffer? Assume no volume changes 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 point. 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 $0.925 \mathrm{M}$ HCl. The pH after the 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 pH 4.12 . The equivalence point is reached after a total of $32.62 \mathrm{~mL}$ of $\mathrm{KOH}$ are added.
$$\mathrm{HUric}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{Uric}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}$$
(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 $6.00 \mathrm{M}$ HCl. A $75.00-\mathrm{mL}$ 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 base (nonelectrolyte) at $25^{\circ} \mathrm{C}$ has an osmotic pressure of 1.287 atm and a $\mathrm{pH}$ of 8.94 . (Assume that, in the equation for $\pi[$ Chapter 10$], i \approx 1 .)$ What is $K_{\mathrm{a}}$ for its conjugate acid?

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 60

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

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 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 (a) the addition of $2 \mathrm{~mol}$ of $\mathrm{OH}^{-}(2 \Delta)$.
(b) the addition of $5 \mathrm{~mol}$ of $\mathrm{OH}^{-}(5 \Delta)$.
(c) the addition of $10 \mathrm{~mol}$ of $\mathrm{OH}^{-}(10 \Delta)$.
(d) the addition of $12 \mathrm{~mol}$ of $\mathrm{OH}^{-}(12 \Delta)$. Which addition (a)-(d) represents neutralization halfway to the equivalence point?

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 62

Use the same symbols as in Question 61 $(O=$ anion, $\left.\Delta=\mathrm{OH}^{-}\right)$ for the box below. (a) Fill in a similar box (representing one liter of the same solution) after $2 \mathrm{~mol}$ of $\mathrm{H}^{+}(2 \square)$ have been added. Indicate whether the resulting solution is an acid, base, or buffer.
(b) Follow the directions of part (a) for the resulting solution after $2 \mathrm{~mol}$ of $\mathrm{OH}^{-}(2 \Delta)$ have been added.
(c) Follow the directions of part (a) for the resulting solution after $5 \mathrm{~mol}$ of $\mathrm{OH}^{-}(5 \Delta)$ have been added.

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 $0.100 \mathrm{~mol}$ HA and $0.100 \mathrm{~mol} \mathrm{NaA}$ in $100 \mathrm{~mL}$ of solution. Beaker $\mathrm{B}$ has $0.100 \mathrm{~mol} \mathrm{HA}$ and $0.100 \mathrm{~mol} \mathrm{NaA}$ in
$200 \mathrm{~mL}$ of solution. Beaker $\mathrm{C}$ has $0.100 \mathrm{~mol}$ HA, $0.100 \mathrm{~mol} \mathrm{NaA},$ and 0.0500 mol HCl in $100 \mathrm{~mL}$ of solution. Beaker $\mathrm{D}$ has $0.100 \mathrm{~mol} \mathrm{HA}, 0.100 \mathrm{~mol} \mathrm{NaA},$ 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.
Answer the questions below, using LT (for is less than), GT (for is greater than), EQ (for is equal to), or MI (for more information required).
(a) The $\mathrm{pH}$ in beaker $\mathrm{A}$ ___________ the $\mathrm{pH}$ in beaker $\mathrm{B}$.
(b) The $\mathrm{pH}$ in beaker $\mathrm{A}$ ___________ the $\mathrm{pH}$ in beaker $\mathrm{C}$.
(c) The pH in beaker D ___________ the $\mathrm{pH}$ in beaker $\mathrm{E}$.
(d) The $\mathrm{pH}$ in beaker $\mathrm{A}$ ___________ the $\mathrm{pH}$ in beaker $\mathrm{E}$.
(e) The $\mathrm{pH}$ in beaker $\mathrm{A}$ ___________ the $\mathrm{pH}$ in beaker $\mathrm{D}$.

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.
The volume and molarity of each acid in the beakers are the same. Both acids are to be titrated with a $0.1 \mathrm{M}$ solution of $\mathrm{NaOH}$
(a) Before titration starts (at zero time), the pH of the solution in Beaker $A$ is _________ the $p H$ of the solution in Beaker B.
(b) At half-neutralization (halfway to the equivalence point), the $\mathrm{pH}$ of the solution in Beaker $\mathrm{A}$ __________ the $\mathrm{pH}$ of the solution in Beaker $\mathrm{B}$.
(c) When each solution has reached its equivalence point, the $\mathrm{pH}$ of the solution in Beaker $\mathrm{A} $ _________ the $\mathrm{pH}$ of the solution in Beaker B.
(d) At the equivalence point, the volume of $\mathrm{NaOH}$ used to titrate HCl in Beaker B ________ the volume of $\mathrm{NaOH}$ used to titrate the weak acid in Beaker A.

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 66

Which statements are true about the titration represented by the following equation?
$$\mathrm{H}^{+}(a q)+\mathrm{F}^{-}(a q) \rightleftharpoons \mathrm{HF}(a q)$$
(a) The net ionic equation could represent the titration of $\mathrm{NaF}$ by $\mathrm{H}_{2} \mathrm{SO}_{4}$
(b) The reaction could be considered to be that of a strong acid with a strong base.
(c) At the equivalence point, the resulting solution can act as a buffer.
(d) Diluting the solution obtained at half-neutralization with water does not change the $\mathrm{pH}$ of the solution.
(e) Phenolphthalein (pH range: 9-11) would be an effective indicator in this titration.

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 $4.7 \times 10^{-11}, \mathrm{~K}_{\mathrm{b}}$ 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 $\mathrm{A}, \mathrm{B}$, and $\mathrm{C}$ 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 $0.1 \mathrm{M}$. 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 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 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 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 $\mathrm{pH}$ of 6.50 by mixing $\mathrm{NH}_{3}$ and $\mathrm{NH}_{4} \mathrm{Cl}$.

Eileen Sullivan

Eileen Sullivan

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 $\mathrm{NaOH}$ 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 $14.10(\mathrm{pH}$ versus volume $\mathrm{NaOH}$ added).

Thomas Harr

Numerade Educator

Problem 75

A diprotic acid, $\mathrm{H}_{2} \mathrm{~B}(\mathrm{MM}=126 \mathrm{~g} / \mathrm{mol})$, is determined to be a hydrate, $\mathrm{H}_{2} \mathrm{~B} \cdot x \mathrm{H}_{2} \mathrm{O} .$ A $10.00-\mathrm{g}$ sample of this hydrate is dissolved in enough water to make $150.0 \mathrm{~mL}$ of solution. Twenty-five milliliters of this solution requires $48.5 \mathrm{~mL}$ of $0.425 \mathrm{M} \mathrm{NaOH}$ to reach the equivalence point. What is $x$ ?

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 $\left.1.1 \times 10^{-2} .\right)$

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 77

Two students were asked to determine the $K_{b}$ 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 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

How many grams of NaF must be added to $70.00 \mathrm{~mL}$ of $0.150 \mathrm{M} \mathrm{HNO}_{3}$ to obtain a buffer with a pH of $4.68 ?$

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 80

A student is asked to determine the molarity of $25.00 \mathrm{~mL}$ of a solution of $\mathrm{HClO}_{4}$. He uses $0.731 \mathrm{M} \mathrm{KOH}$. After adding $42.35 \mathrm{~mL}$ of $\mathrm{KOH}$, he realizes that he forgot to add an indicator. His TA suggests he take the $\mathrm{pH}$ of the solution. The $\mathrm{pH}$ is 12.39
(a) Did the student go beyond the equivalence point?
(b) What is the molarity of the strong acid?
(c) If he did, how many milliliters of $\mathrm{KOH}$ did he add in excess? If he did not, how much more (in mL) KOH should he add?

Eileen Sullivan

Eileen Sullivan

Numerade Educator