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CHEMISTRY: The Molecular Nature of Matter and Change 2016

Martin S. Silberberg, Patricia G. Amateis

Chapter 19

Ionic Equilibria in Aqueous Systems

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Problem 1

What is the purpose of an acid-base buffer?

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Problem 2

How do the acid and base components of a buffer function? Why are they often a conjugate acid-base pair of a weak acid?

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Problem 3

What is the common-ion effect? How is it related to Le Chatelier’s principle? Explain with equations that include HF and NaF.

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Problem 4

The scenes below depict solutions of the same HA/A$^{-}$ buffer (with other ions and water molecules omitted for clarity). (a) Which solution has the greatest buffer capacity? (b) Explain how the pH ranges of the buffers compare. (c) Which solution can react with the largest amount of added strong acid?

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Problem 5

What is the difference between buffers with high and low capacities? Will adding 0.01 mol of $\mathrm{HCl}$ produce a greater pH change in a buffer with a high or a low capacity? Explain.

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Problem 6

Which of these factors influence buffer capacity? How?
(a) Conjugate acid-base pair
(b) pH of the buffer
(c) Concentration of buffer components
(d) Buffer range
(e) $\mathrm{p} K_{\mathrm{a}}$ of the acid component

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Problem 7

What is the relationship between the buffer range and the buffer-component concentration ratio?

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Problem 8

A chemist needs a pH 3.5 buffer. Should she use NaOH with formic acid $\left(K_{a}=1.8 \times 10^{-4}\right)$ or with acetic acid $\left(K_{a}=1.8 \times 10^{-5}\right) ?$ Why? What is the disadvantage of choosing the other acid? What is the role of the NaOH?

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Problem 9

State and explain the relative change in the $\mathrm{pH}$ and in the buffer-component concentration ratio, $[\mathrm{NaA}] /[\mathrm{HA}],$ for each of the following additions:
(a) Add 0.1$M$ NaOH to the buffer
(b) Add 0.1$M \mathrm{HCl}$ to the buffer
(c) Dissolve pure NaA in the buffer
(d) Dissolve pure HA in the buffer

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Problem 10

Does the pH increase or decrease, and does it do so to a large or small extent, with each of the following additions?
(a) 5 drops of 0.1 M NaOH to 100 mL of 0.5 M acetate buffer
(b) 5 drops of 0.1 M HCl to 100 mL of 0.5 M acetate buffer
(c) 5 drops of 0.1 M NaOH to 100 mL of 0.5 M HCl
(d) 5 drops of 0.1 M NaOH to distilled water

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Problem 11

What are the $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ and the $\mathrm{pH}$ of a propanoic acid-propanoate buffer that consists of 0.35$M \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COONa}$ and 0.15$M \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH}\left(K_{\mathrm{a}} \text { of propanoic acid }=1.3 \times 10^{-5}\right) ?$

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Problem 12

What are the $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ and the $\mathrm{pH}$ of a benzoic acid-benzoate buffer that consists of 0.33$M \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}$ and 0.28 $\mathrm{M}$ $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COONa}\left(K_{\mathrm{a}} \text { of benzoic acid }=6.3 \times 10^{-5}\right) ?$

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Problem 13

What are the $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ and the $\mathrm{pH}$ of a buffer that consists of 0.55 $\mathrm{M} \mathrm{HNO}_{2}$ and 0.75 $\mathrm{M} \mathrm{KNO}_{2}\left(K_{\mathrm{a}} \text { of } \mathrm{HNO}_{2}=7.1 \times 10^{-4}\right) ?$

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Problem 14

What are the $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ and the pH of a buffer that consists of 0.20$M \mathrm{HF}$ and 0.25 $\mathrm{M} \mathrm{KF}\left(K_{\mathrm{a}} \text { of } \mathrm{HF}=6.8 \times 10^{-4}\right) ?$

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Problem 15

Find the pH of a buffer that consists of 0.45$M \mathrm{HCOOH}$ and 0.63$M \mathrm{HCOONa}\left(\mathrm{p} K_{\mathrm{a}} \text { of } \mathrm{HCOOH}=3.74\right)$

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Problem 16

Find the $\mathrm{pH}$ of a buffer that consists of 0.95 $\mathrm{M}$ HBrO and 0.68 $\mathrm{M} \mathrm{KBrO}\left(\mathrm{p} K_{\mathrm{a}} \text { of } \mathrm{HBrO}=8.64\right)$

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Problem 17

Find the $\mathrm{pH}$ of a buffer that consists of 1.3 $\mathrm{M}$ sodium phenolate $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{ONa}\right)$ and 1.2 $\mathrm{M}$ phenol $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\left(\mathrm{p} K_{\mathrm{a}} \text { of phenol }=\right.$ 10.00$)$

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Problem 18

Find the $\mathrm{pH}$ of a buffer that consists of 0.12$M$ boric acid $\left(\mathrm{H}_{3} \mathrm{BO}_{3}\right)$ and 0.82 $\mathrm{M}$ sodium borate $\left(\mathrm{NaH}_{2} \mathrm{BO}_{3}\right)\left(\mathrm{p} K_{\mathrm{a}} \text { of boric }\right.$ $\mathrm{acid}=9.24 )$

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Problem 19

Find the pH of a buffer that consists of 0.25$M \mathrm{NH}_{3}$ and 0.15$M \mathrm{NH}_{4} \mathrm{Cl}\left(\mathrm{p} K_{\mathrm{b}} \text { of } \mathrm{NH}_{3}=4.75\right) .$

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Problem 20

Find the pH of a buffer that consists of 0.50$M$ methylamine $\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)$ and 0.60$M \mathrm{CH}_{3} \mathrm{NH}_{3} \mathrm{Cl}\left(\mathrm{p} K_{\mathrm{b}} \text { of } \mathrm{CH}_{3} \mathrm{NH}_{2}=3.35\right)$

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Problem 21

$\mathrm{A}$ buffer consists of 0.22 $\mathrm{M} \mathrm{KHCO}_{3}$ and 0.37 $\mathrm{M} \mathrm{K}_{2} \mathrm{CO}_{3}$ Carbonic acid is a diprotic acid with $K_{\mathrm{al}}=4.5 \times 10^{-7}$ and $K_{\mathrm{a} 2}=$ $4.7 \times 10^{-11} .$ (a) Which $K_{\mathrm{a}}$ value is more important to this buffer? (b) What is the buffer pH?

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Problem 22

$\mathrm{A}$ buffer consists of 0.22 $\mathrm{M} \mathrm{KHCO}_{3}$ and 0.37 $\mathrm{M} \mathrm{K}_{2} \mathrm{CO}_{3}$ $\mathrm{Na}_{2} \mathrm{HPO}_{4} .$ Phosphoric acid is a triprotic acid $\left(K_{\mathrm{al}}=7.2 \times 10^{-3}\right.$ $K_{\mathrm{a} 2}=6.3 \times 10^{-8},$ and $K_{\mathrm{a} 3}=4.2 \times 10^{-13} ) .$ (a) Which $K_{\mathrm{a}}$ value is most important to this buffer? (b) What is the buffer pH?

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Problem 23

What is the component concentration ratio, $\left[\mathrm{Pr}^{-}\right] /[\mathrm{HPr}],$ of a buffer that has a pH of 5.44$\left(K_{\mathrm{a}} \text { of } \mathrm{HPr}=1.3 \times 10^{-5}\right) ?$

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Problem 24

What is the component concentration ratio $,\left[\mathrm{NO}_{2}^{-}\right] /\left[\mathrm{HNO}_{2}\right]$ of a buffer that has a pH of 2.95$\left(K_{\mathrm{a}} \text { of } \mathrm{HNO}_{2}=7.1 \times 10^{-4}\right) ?$

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Problem 25

What is the component concentration ratio, $\left[\mathrm{BrO}^{-}\right] /[\mathrm{HBrO}]$ of a buffer that has a pH of 7.95$\left(K_{\mathrm{a}} \text { of } \mathrm{HBrO}=2.3 \times 10^{-9}\right) ?$

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Problem 26

What is the component concentration ratio, $\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right] /$ $\left[\mathrm{CH}_{3} \mathrm{COOH}\right],$ of a buffer that has a pH of 4.39$\quad\left(K_{\mathrm{a}} \text { of }\right.$ $\mathrm{CH}_{3} \mathrm{COOH}=1.8 \times 10^{-5} ) ?$

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Problem 27

A buffer containing 0.2000$M$ of acid, HA, and 0.1500$M$ of its conjugate base, $A^{-},$ has a pH of $3.35 .$ What is the pH after 0.0015 mol of $\mathrm{NaOH}$ is added to 0.5000 $\mathrm{L}$ of this solution?

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Problem 28

A buffer that contains 0.40$M$ of a base, $B,$ and 0.25$M$ of its conjugate acid, $B H^{+},$ has a pH of 8.88 . What is the pH after 0.0020 mol of $\mathrm{HCl}$ is added to 0.25 L of this solution?

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Problem 29

A buffer that contains 0.110$M \mathrm{HY}$ and 0.220$M \mathrm{Y}^{-}$ has a $\mathrm{pH}$ of $8.77 .$ What is the pH after 0.0015 $\mathrm{mol}$ of $\mathrm{Ba}(\mathrm{OH})_{2}$ is added to 0.350 $\mathrm{L}$ of this solution?

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Problem 30

A buffer that contains 1.05$M \mathrm{B}$ and 0.750$M \mathrm{BH}^{+}$ has a $\mathrm{pH}$ of $9.50 .$ What is the pH after 0.0050 $\mathrm{mol}$ of $\mathrm{HCl}$ is added to 0.500 $\mathrm{L}$ of this solution?

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Problem 31

A buffer is prepared by mixing 204 $\mathrm{mL}$ of 0.452 $\mathrm{MHCl}$ and 0.500 $\mathrm{L}$ of 0.400 $\mathrm{M}$ sodium acetate. (See Appendix $\mathrm{C}$ ) (a) What is the pH? (b) How many grams of KOH must be added to 0.500 $\mathrm{L}$ of the buffer to change the $\mathrm{pH}$ by 0.15 units?

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Problem 32

A buffer is prepared by mixing 50.0 $\mathrm{mL}$ of 0.050 $\mathrm{M}$ sodium bicarbonate and 10.7 $\mathrm{mL}$ of 0.10 $\mathrm{M} \mathrm{NaOH}$ . (See Appendix C.) (a) What is the $\mathrm{pH}$ ? (b) How many grams of HCl must be added to 25.0 $\mathrm{mL}$ of the buffer to change the pH by 0.07 units?

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Problem 33

Choose specific acid-base conjugate pairs to make the following buffers: (a) $\mathrm{pH} \approx 4.5 ;(\mathrm{b}) \mathrm{pH} \approx 7.0 .$ (See Appendix C.)

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Problem 34

Choose specific acid-base conjugate pairs to make the following buffers: (a) $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right] \approx 1 \times 10^{-9} M ;(\mathrm{b})\left[\mathrm{OH}^{-}\right] \approx 3 \times 10^{-5} \mathrm{M}$ .(See Appendix C.)

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Problem 35

Choose specific acid-base conjugate pairs to make the following buffers: (a) $\mathrm{pH} \approx 3.5 ;(\mathrm{b}) \mathrm{pH} \approx 5.5 .$ (See Appendix C.)

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Problem 36

Choose specific acid-base conjugate pairs to make the following buffers: (a) $\left[\mathrm{OH}^{-}\right] \approx 1 \times 10^{-6} M ;$ (b) $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right] \approx$ $4 \times 10^{-4} M .$ (See Appendix $\mathrm{C} . )$

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Problem 37

An industrial chemist studying bleaching and sterilizing prepares several hypochlorite buffers. Find the $\mathrm{pH}$ of (a) 0.100 $\mathrm{M} \mathrm{HClO}$ and $0.100 \mathrm{M} \mathrm{NaClO} ;(\mathrm{b}) 0.100 \mathrm{M} \mathrm{HClO}$ and $0.150 \mathrm{M} \mathrm{NaClO} ;$ (c) 0.150 $\mathrm{M} \mathrm{HClO}$ and 0.100 $\mathrm{M} \mathrm{NaClO}$ (d) 1.0 $\mathrm{L}$ of the solution in part (a) after 0.0050 $\mathrm{mol}$ of NaOH has been added.

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Problem 38

Oxoanions of phosphorus are buffer components in blood. For a $\mathrm{KH}_{4} \mathrm{PO}_{4} / \mathrm{Na}_{2} \mathrm{HPO}_{4}$ solution with $\mathrm{pH}=7.40(\mathrm{pH} \text { of normal }$ arterial blood), what is the buffer-component concentration ratio?

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Problem 39

How can you estimate the $\mathrm{pH}$ range of an indicator's color change? Why do some indicators have two separate pH ranges?

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Problem 40

Why does the color change of an indicator take place over a range of about 2 pH units?

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Problem 41

Why doesn't the addition of an acid-base indicator affect the pH of the test solution?

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Problem 42

What is the difference between the end point of a titration and the equivalence point? Is the equivalence point always reached first? Explain.

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Problem 43

The scenes below depict the relative concentrations of $\mathrm{H}_{3} \mathrm{PO}_{4}, \mathrm{H}_{2} \mathrm{PO}_{4}^{-},$ and $\mathrm{HPO}_{4}^{2-}$ during a titration with aqueous $\mathrm{NaOH}$ , but they are out of order. (Phosphate groups are purple, hydrogens are blue, and $\mathrm{Na}^{+}$ ions and water molecules are not shown.) (a) List the scenes in the correct order. (b) What is the pH in the correctly ordered second scene (see Appendix $C ) ?(c)$ If it requires 10.00 $\mathrm{mL}$ of the NaOH solution to reach this scene, how much more is needed to reach the last scene?

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Problem 44

Explain how strong acid-strong base, weak acid-strong base, and weak base-strong acid titrations using the same concentrations differ in terms of (a) the initial pH and (b) the pH at the equivalence point. (The component in italics is in the flask.)

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Problem 45

What species are in the buffer region of a weak acid-strong base titration? How are they different from the species at the equivalence point? How are they different from the species in the buffer region of a weak base-strong acid titration?

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Problem 46

Why is the center of the buffer region of a weak acid-strong base titration significant?

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Problem 47

How does the titration curve of a monoprotic acid differ from that of a diprotic acid?

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Problem 48

The indicator cresol red has $K_{\mathrm{a}}=3.5 \times 10^{-9} .$ Over what approximate $\mathrm{pH}$ range does it change color?

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Problem 49

The indicator ethyl red has $K_{\mathrm{a}}=3.8 \times 10^{-6} .$ Over what approximate $\mathrm{pH}$ range does it change color?

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Problem 50

Use Figure 19.6 to find an indicator for these titrations:
(a) 0.10$M \mathrm{HCl}$ with 0.10$M \mathrm{NaOH}$
(b) 0.10$M$ HCOOH (Appendix $\mathrm{C} )$ with 0.10$M \mathrm{NaOH}$

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Problem 51

Use Figure 19.6 to find an indicator for these titrations:
(a) 0.10$M \mathrm{CH}_{3} \mathrm{NH}_{2}$ ( Appendix $\mathrm{C} )$ with 0.10 $\mathrm{M} \mathrm{HCl}$
(b) 0.50$M$ HI with 0.10$M \mathrm{KOH}$

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Problem 52

Use Figure 19.6 to find an indicator for these titrations:
(a) 0.5$M\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH}(\text { Appendix } \mathrm{C})$ with 0.5$M \mathrm{HBr}$
(b) 0.2 $\mathrm{M} \mathrm{KOH}$ with 0.2 $\mathrm{M} \mathrm{HNO}_{3}$

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Problem 53

Use Figure 19.6 to find an indicator for these titrations:
(a) 0.25$M \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}(\text { Appendix } \mathrm{C})$ with 0.25 $\mathrm{M} \mathrm{KOH}$
(b) 0.50 $\mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}$ (Appendix $\mathrm{C} )$ with 0.50 $\mathrm{M} \mathrm{NaOH}$

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Problem 54

Calculate the pH during the titration of 40.00 $\mathrm{mL}$ of 0.1000 $\mathrm{M} \mathrm{HCl}$ with 0.1000 $\mathrm{M}$ NaOH solution after the following additions of base:
(a) 0 mL (b) 25.00 mL (c) 39.00 mL (d) 39.90 mL
(e) 40.00 mL (f) 40.10 mL (g) 50.00 mL

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Problem 55

Calculate the pH during the titration of 30.00 $\mathrm{mL}$ of 0.1000$M \mathrm{KOH}$ with 0.1000$M \mathrm{HBr}$ solution after the following additions of acid:
(a) 0 mL (b) 15.00 mL (c) 29.00 mL (d) 29.90 mL
(e) 30.00 mL (f) 30.10 mL (g) 40.00 mL

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Problem 56

Find the $\mathrm{pH}$ during the titration of 20.00 $\mathrm{mL}$ of 0.1000 $\mathrm{M}$ butanoic acid, $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COOH}\left(K_{\mathrm{a}}=1.54 \times 10^{-5}\right)$ with 0.1000 $\mathrm{M}$ NaOH solution after the following additions of titrant:
(a) 0 mL (b) 10.00 mL (c) 15.00 mL (d) 19.00 mL
(e) 19.95 mL (f) 20.00 mL (g) 20.05 mL (h) 25.00 mL

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Problem 57

Find the pH during the titration of 20.00 $\mathrm{mL}$ of 0.1000 $\mathrm{M}$ triethylamine, $\left(\mathrm{CH}_{3} \mathrm{CH}_{2}\right)_{3} \mathrm{N}\left(K_{\mathrm{b}}=5.2 \times 10^{-4}\right),$ with 0.1000 $\mathrm{M} \mathrm{HCl}$ solution after the following additions of titrant:
$\begin{array}{ll}{\text { (a) } 0 \mathrm{mL}} & {\text { (b) } 10.00 \mathrm{mL}} & {\text { (c) } 15.00 \mathrm{mL}} & {\text { (d) } 19.00 \mathrm{mL}} \\ {\text { (e) } 19.95 \mathrm{mL}} & {\text { (f) } 20.00 \mathrm{mL}} & {\text { (g) } 20.05 \mathrm{mL}} & {\text { (h) } 25.00 \mathrm{mL}}\end{array}$

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Problem 58

Find the $\mathrm{pH}$ of the equivalence point(s) and the volume $(\mathrm{mL})$ of 0.0372 $\mathrm{M} \mathrm{NaOH}$ needed to reach the point(s) in titrations of
(a) 42.2 $\mathrm{mL}$ of 0.0520 $\mathrm{CH}_{3} \mathrm{COOH}$
(b) 28.9 $\mathrm{mL}$ of 0.0850 $\mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{3}$ (two equivalence points)

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Problem 59

Find the pH of the equivalence point(s) and the volume (mL) of 0.0588 M KOH needed to reach the point(s) in titrations of
(a) 23.4 $\mathrm{mL}$ of 0.0390 $\mathrm{M} \mathrm{HNO}_{2}$
(b) 17.3 $\mathrm{mL}$ of 0.130 $\mathrm{M} \mathrm{H}_{2} \mathrm{CO}_{3}$ (two equivalence points)

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Problem 60

Find the pH of the equivalence point(s) and the volume (mL) of 0.125$M \mathrm{HCl}$ needed to reach the point(s) in titrations of
(a) 65.5 $\mathrm{mL}$ of 0.234 $\mathrm{MNH}_{3}$
(b) 21.8 $\mathrm{mL}$ of 1.11 $\mathrm{M} \mathrm{CH}_{3} \mathrm{NH}_{2}$

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Problem 61

Find the pH of the equivalence point(s) and the volume(mL) of 0.447 $\mathrm{M}$ HNO $_{3}$ needed to reach the point(s) in titrations of
(a) 2.65 $\mathrm{L}$ of 0.0750$M$ pyridine $\left(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{N}\right)$
(b) 0.188 $\mathrm{L}$ of 0.250 $\mathrm{M}$ ethylenediamine $\left(\mathrm{H}_{2} \mathrm{NCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\right)$

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Problem 62

The molar solubility $(S)$ of $\mathrm{M}_{2} \mathrm{X}$ is $5 \times 10^{-5}$ M. Find $S$ of each ion. How do you set up the calculation to find $K_{\mathrm{sp}} ?$ What assumption must you make about the dissociation of $\mathrm{M}_{2} \mathrm{X}$ into ions? Why is the calculated $K_{\mathrm{sp}}$ higher than the actual value?

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Problem 63

Why does pH affect the solubility of $\mathrm{BaF}_{2}$ but not of $\mathrm{BaCl}_{2} ?$

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Problem 64

A list of $K_{\text { sp }}$ values like that in Appendix $C$ can be used to compare the solubility of silver chloride directly with that of silver bromide but not with that of silver chromate. Explain.

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Problem 65

In a gaseous equilibrium, the reverse reaction occurs when $Q_{c}>K_{c}$ . What occurs in aqueous solution when $Q_{\mathrm{sp}}>K_{\mathrm{sp}} ?$

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Problem 66

Write the ion-product expressions for (a) silver carbonate; (b) barium fluoride; (c) copper(I) sulfide.

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Problem 67

Write the ion-product expressions for (a) iron(MI) hydroxide; (b) barium phosphate; (c) tin(II) sulfide.

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Problem 68

Write the ion-product expressions for (a) calcium chromate; (b) silver cyanide; (c) nickel(II) sulfide.

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Problem 69

Write the ion-product expressions for (a) lead(II) iodide; (b) strontium sulfate; (c) cadmium sulfide.

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Problem 70

The solubility of silver carbonate is 0.032$M$ at $20^{\circ} \mathrm{C}$ . Calculate its $K_{\mathrm{sp}} .$

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Problem 71

The solubility of zinc oxalate is $7.9 \times 10^{-3} M$ at $18^{\circ} \mathrm{C}$ . Calculate its $K_{s p^{\prime}}$

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Problem 72

The solubility of silver dichromate at $15^{\circ} \mathrm{C}$ is $8.3 \times 10^{-3} \mathrm{g} / 100 .$ mL solution. Calculate its $K_{\mathrm{sp}}$

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Problem 73

The solubility of calcium sulfate at $30^{\circ} \mathrm{C}$ is 0.209 $\mathrm{g} / 100 . \mathrm{mL}$ solution. Calculate its $K_{\mathrm{sp}}$

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Problem 74

Find the molar solubility of $\mathrm{SrCO}_{3}\left(K_{\mathrm{sp}}=5.4 \times 10^{-10}\right)$ in (a) pure water and (b) 0.13$M \mathrm{Sr}\left(\mathrm{NO}_{3}\right)_{2}$ .

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Problem 75

Find the molar solubility of $\mathrm{BaCrO}_{4}\left(K_{\mathrm{sp}}=2.1 \times 10^{-10}\right)$ in (a) pure water and (b) $1.5 \times 10^{-3} \mathrm{M} \mathrm{Na}_{2} \mathrm{CrO}_{4}$

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Problem 76

Calculate the molar solubility of $\mathrm{Ca}\left(\mathrm{IO}_{3}\right)_{2}$ in (a) 0.060 $\mathrm{M}$ $\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}$ and (b) 0.060 $\mathrm{M} \mathrm{NaIO}_{3} .$ (See Appendix $\mathrm{C} . )$

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Problem 77

Calculate the molar solubility of $\mathrm{Ag}_{2} \mathrm{SO}_{4}$ in (a) 0.22 $\mathrm{M}$ $\mathrm{AgNO}_{3}$ and (b) 0.22 $\mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4} .(\text { See Appendix } \mathrm{C})$

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Problem 78

Which compound in each pair is more soluble in water?
(a) Magnesium hydroxide or nickel(I) hydroxide
(b) Lead(II) sulfide or copper(Il) sulfide
(c) Silver sulfate or magnesium fluoride

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Problem 79

Which compound in each pair is more soluble in water?
(a) Strontium sulfate or barium chromate
(b) Calcium carbonate or copper(Il) carbonate
(c) Barium iodate or silver chromate

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Problem 80

Which compound in each pair is more soluble in water?
(a) Barium sulfate or calcium sulfate
(b) Calcium phosphate or magnesium phosphate
(c) Silver chloride or lead(II) sulfate

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Problem 81

Which compound in each pair is more soluble in water?
(a) Manganese(Il) hydroxide or calcium iodate
(b) Strontium carbonate or cadmium sulfide
(c) Silver cyanide or copper(I) iodide

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Problem 82

Write equations to show whether the solubility of either of the following is affected by pH: (a) AgCl; (b) $\mathrm{SrCO}_{3}$ .

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Problem 83

Write equations to show whether the solubility of either of the following is affected by pH: (a) CuBr; (b) $\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}$ .

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Problem 84

Write equations to show whether the solubility of either of the following is affected by pH: (a) $\mathrm{Fe}(\mathrm{OH})_{2} ;(\mathrm{b}) \mathrm{CuS}$ .

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Problem 85

Write equations to show whether the solubility of either of the following is affected by pH: (a) $\mathrm{PbI}_{2} ;(\mathrm{b}) \mathrm{Hg}_{2}(\mathrm{CN})_{2}$ .

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Problem 86

Does any solid $\mathrm{Cu}(\mathrm{OH})_{2}$ form when 0.075 $\mathrm{g}$ of KOH is dissolved in 1.0 $\mathrm{L}$ of $1.0 \times 10^{-3} \mathrm{M} \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2} ?$

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Problem 87

Does any solid $\mathrm{PbCl}_{2}$ form when 3.5 $\mathrm{mg}$ of $\mathrm{NaCl}$ is dissolved in 0.250 $\mathrm{L}$ of 0.12 $\mathrm{M} \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2} ?$

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Problem 88

Does any solid $\mathrm{Ba}\left(\mathrm{IO}_{3}\right)_{2}$ form when 7.5 $\mathrm{mg}$ of $\mathrm{BaCl}_{2}$ is dissolved in $500 . \mathrm{mL}$ of 0.023 $\mathrm{M} \mathrm{NaIO}_{3} ?$

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Problem 89

Does any solid $\mathrm{Ag}_{2} \mathrm{CrO}_{4}$ form when $2.7 \times 10^{-5} \mathrm{g}$ of AgNO $_{3}$ is dissolved in 15.0 $\mathrm{mL}$ of $4.0 \times 10^{-4} \mathrm{M} \mathrm{K}_{2} \mathrm{CrO}_{4} ?$

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Problem 90

When blood is donated, sodium oxalate solution is used to precipitate $\mathrm{Ca}^{2+},$ which triggers clotting. A $104-\mathrm{mL}$ sample of blood contains $9.7 \times 10^{-5} \mathrm{g} \mathrm{Ca}^{2+} / \mathrm{mL}$ . A technologist treats the sample with 100.0 $\mathrm{mL}$ of 0.1550 $\mathrm{M} \mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}$ . Calculate $\left[\mathrm{Ca}^{2+}\right]$ after the treatment. (See Appendix $\mathrm{C}$ for $K_{\mathrm{sp}}$ of $\mathrm{CaC}_{2} \mathrm{O}_{4} \cdot \mathrm{H}_{2} \mathrm{O} . )$

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Problem 91

A 50.0 -mL volume of 0.50$M$ Fe(NO $_{3},$ is mixed with 125 $\mathrm{mL}$ of 0.25$M \mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2}$
(a) If aqueous NaOH is added, which ion precipitates first? (See Appendix C.)
(b) Describe how the metal ions can be separated using NaOH.
(c) Calculate the $\left[\mathrm{OH}^{-}\right]$ that will accomplish the separation.

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Problem 92

How can a metal cation be at the center of a complex anion?

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Problem 93

Write equations to demonstrate the stepwise reaction of $\mathrm{Cd}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}^{2+}$ in an aqueous solution of $\mathrm{KI}$ to form $\mathrm{CdI}_{4}^{-2} .$ Show $\mathrm{Cd}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}^{2+}$ in an aqueous solution of $\mathrm{KI}$ to form $\mathrm{CdI}_{4}^{-2} .$ Show that $K_{\text { f(overall } )}=$ $K_{\mathrm{fl}} \times K_{\mathrm{f}_{2}} \times K_{\mathrm{f} 3} \times K_{\mathrm{f} 4}$

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Problem 94

Consider the dissolution of PbS in water:
$$
\operatorname{PbS}(s)+\mathrm{H}_{2} \mathrm{O}(l)=\mathrm{Pb}^{2+}(a q)+\mathrm{HS}^{-}(a q)+\mathrm{OH}^{-}(a q)
$$
Adding aqueous NaOH causes more PbS to dissolve. Does this violate Le Châtelier's principle? Explain.

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Problem 95

Write a balanced equation for the reaction of $\mathrm{Hg}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}^{2+}$ in aqueous $\mathrm{KCN}$ .

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Problem 96

Write a balanced equation for the reaction of $\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}^{2+}$ in aqueous NaCN.

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Problem 97

Write a balanced equation for the reaction of $\mathrm{Ag}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}+\mathrm{in}$ aqueous $\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}$ .

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Problem 98

Write a balanced equation for the reaction of $\mathrm{Al}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}$ in aqueous $\mathrm{KF}$ .

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Problem 99

Write a balanced equation for the reaction of $\mathrm{Al}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}$ in aqueous $\mathrm{KF}$ .

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Problem 100

Potassium thiocyanate, $\mathrm{KSCN}$ , is often used to detect the presence of $\mathrm{Fe}^{3+}$ ions in solution through the formation of the red $\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{SCN}^{2+}$ (or, more simply, FeSCN $^{2+} ; K_{\mathrm{f}}=8.9 \times 10^{2} )$ What is $\left[\mathrm{Fe}^{3+}\right]$ when 0.50 $\mathrm{L}$ each of 0.0015 $\mathrm{M} \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}$ and 0.20$M \mathrm{KSCN}$ are mixed?

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Problem 101

Find the solubility of $\mathrm{Cr}(\mathrm{OH})_{3}$ in a buffer of $\mathrm{pH} 13.0\left[K_{\mathrm{sp}}\right.$ of $\mathrm{Cr}(\mathrm{OH})_{3}=6.3 \times 10^{-31} ; K_{\mathrm{f}}$ of $\mathrm{Cr} \mathrm{r} \mathrm{OH} )_{4}^{-}=8.0 \times 10^{99} ]$

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Problem 102

Find the solubility of $\mathrm{AgI}$ in 2.5 $\mathrm{NH}_{3}\left[K_{\mathrm{sp}} \text { of AgI }=\right.$ $8.3 \times 10^{-17} ; K_{\mathrm{f}}$ of $\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}^{+}=1.7 \times 10^{7} ]$

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Problem 103

When 0.84 $\mathrm{g}$ of $\mathrm{ZnCl}_{2}$ is dissolved in 245 $\mathrm{mL}$ of 0.150 $\mathrm{M}$ $\mathrm{NaCN},$ what are $\left[\mathrm{Zn}^{2+}\right],\left[\mathrm{Zn}(\mathrm{CN})_{4}^{2-}\right],$ and $\left[\mathrm{CN}^{-}\right]\left[K_{\mathrm{f}} \text { of }\right.$
$\mathrm{Zn}(\mathrm{CN})_{4}^{2-}=4.2 \times 10^{19} ] ?$

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Problem 104

When 2.4 g of $\mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2}$ is dissolved in 0.350 $\mathrm{L}$ of
$0.22 \mathrm{M} \mathrm{KOH},$ what are $\left[\mathrm{Co}^{2+}\right],\left[\mathrm{Co}(\mathrm{OH})_{4}^{2-}\right],$ and $\left[\mathrm{OH}^{-}\right]\left[K_{\mathrm{f}} \text { of }\right.$
$\mathrm{Co}(\mathrm{OH})_{4}^{2-}=5 \times 10^{9} ] ?$

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Problem 105

What volumes of 0.200$M \mathrm{HCOOH}$ and 2.00$M \mathrm{NaOH}$ would make $500 . \mathrm{mL}$ of a buffer with the same pH as one made from 475 $\mathrm{mL}$ of 0.200$M$ benzoic acid and 25 $\mathrm{mL}$ of 2.00 $\mathrm{M}$ $\mathrm{NaOH} ?$

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Problem 106

A microbiologist is preparing a medium on which to culture $E$ . coli bacteria. She buffers the medium at pH 7.00 to minimize the effect of acid-producing fermentation. What volumes of equimolar aqueous solutions of $\mathrm{K}_{2} \mathrm{HPO}_{4}$ and $\mathrm{KH}_{2} \mathrm{PO}_{4}$ must she
combine to make $100 . \mathrm{mL}$ of the pH 7.00 buffer?

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Problem 107

As an FDA physiologist, you need 0.700 $\mathrm{L}$ of formic acid-formate buffer with a pH of 3.74 . (a) What is the required buffer-component concentration ratio? (b) How do you prepare this solution from stock solutions of 1.0 $\mathrm{M}$ HCOOH and 1.0 $\mathrm{M}$ NaOH? (c) What is the final concentration of HCOOH in this solution?

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Problem 108

Tris(hydroxymethyl)aminomethane $\left[\left(\mathrm{HOCH}_{2}\right)_{3} \mathrm{CNH}_{2}\right]$ ,
known as TRIS, is a weak base used in biochemical experiments to make buffer solutions in the pH range of 7 to $9 .$ A certain TRIS buffer has a pH of 8.10 at $25^{\circ} \mathrm{C}$ and a pH of 7.80 at $37^{\circ} \mathrm{C}$ . Why does the pH change with temperature?

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Problem 109

Water flowing through pipes of carbon steel must be kept at pH 5 or greater to limit corrosion. If an $8.0 \times 10^{3} \mathrm{lbh}$ water stream contains 10 ppm sulfuric acid and 0.015$\%$ acetic acid, how many pounds per hour of sodium acetate trihydrate must be added to maintain that pH?

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Problem 110

Gout is caused by an error in metabolism that leads to a buildup of uric acid in body fluids, which is deposited as slightly soluble sodium urate $\left(\mathrm{C}_{5} \mathrm{H}_{3} \mathrm{N}_{4} \mathrm{O}_{3} \mathrm{Na}\right)$ in the joints. If the extracellular $\left[\mathrm{Na}^{+}\right]$ is 0.15$M$ and the solubility of sodium urate is 0.085 $\mathrm{g} / 100 . \mathrm{mL}$ , what is the minimum urate ion concentration (abbreviated $\left[\mathrm{Ur}^{\mathrm{r}}\right] )$ that will cause a deposit of sodium urate?

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Problem 111

In the process of cave formation (p. 853 ), the dissolution of $\mathrm{CO}_{2}$ (equation 1$)$ has a $K_{\mathrm{cq}}$ of $3.1 \times 10^{-2},$ and the formation of aqueous $\mathrm{Ca}\left(\mathrm{HCO}_{3}\right)_{2}$ (equation 2 ) has a $K_{\mathrm{cq}}$ of $1 \times 10^{-12}$ . The fraction by volume of atmospheric $\mathrm{CO}_{2}$ is $4 \times 10^{-4} .(\mathrm{a})$ Find $\left[\mathrm{CO}_{2}(a q)\right]$ in equilibrium with atmospheric $\mathrm{CO}_{2}$ . (b) Determine $\left[\mathrm{Ca}^{2+}\right]$ arising from (equation 2$)$ given current levels of atmospheric $\mathrm{CO}_{2}$ (c) Calculate $\left[\mathrm{Ca}^{2+}\right]$ if atmospheric $\mathrm{CO}_{2}$ doubles.

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Problem 112

Phosphate systems form essential buffers in organisms. Calculate the $\mathrm{pH}$ of a buffer made by dissolving 0.80 $\mathrm{mol}$ of $\mathrm{NaOH}$ in 0.50 $\mathrm{L}$ of 1.0$M \mathrm{H}_{3} \mathrm{PO}_{4}$ .

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Problem 113

The solubility of $\mathrm{KCl}$ is 3.7 $\mathrm{at} 20^{\circ} \mathrm{C}$ . Two beakers contain $100 .$ mL of saturated $\mathrm{KCl}$ solution: $100 . \mathrm{mL}$ of 6.0 $\mathrm{MHCl}$ is added to the first beaker and $100 . \mathrm{mL}$ of 12$M \mathrm{HCl}$ to the second.(a) Find the ion-product constant of $\mathrm{KCl}$ at $20^{\circ} \mathrm{C} .$ (b) What mass, if any, of $\mathrm{KCl}$ will precipitate from each beaker?

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Problem 114

It is possible to detect $N H_{3}$ gas over $10^{-2} M \mathrm{NH}_{3}$ . To what pH must 0.15$M \mathrm{NH}_{4} \mathrm{Cl}$ be raised to form detectable $\mathrm{NH}_{3} ?$

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Problem 115

Manganese(II) sulfide is one of the compounds found in the nodules on the ocean floor that may eventually be a primary source of many transition metals. The solubility of MnS is $4.7 \times 10^{-4}$ g/100. mL solution. Estimate the $K_{\mathrm{sp}}$ of MnS.

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Problem 116

The normal pH of blood is $7.40 \pm 0.05$ and is controlled in part by the $\mathrm{H}_{3} \mathrm{CO}_{3} / \mathrm{HCO}_{3}^{-}$ buffer system. (a) Assuming that the $K_{\mathrm{a}}$ value for carbonic acid at $25^{\circ} \mathrm{C}$ applies to blood, what is the $\left[\mathrm{H}_{2} \mathrm{CO}_{3}\right] /\left[\mathrm{HCO}_{3}-\right]$ ratio in normal blood? (b) In a condition called acidosis, the blood is too acidic. What is the $\left[\mathrm{H}_{2} \mathrm{CO}_{3}\right] /\left[\mathrm{HCO}_{3}-\right]$ ratio in a patient whose blood $\mathrm{pH}$ is 7.20$?$

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Problem 117

A bioengineer preparing cells for cloning bathes a small piece of rat epithelial tissue in a TRIS buffer (see Problem 19.108 ). The buffer is made by dissolving 43.0 $\mathrm{g}$ of TRIS $\left(\mathrm{p} K_{\mathrm{b}}=5.91\right)$ in enough 0.095$M \mathrm{HCl}$ to make 1.00 $\mathrm{L}$ of solution.
What is the molarity of TRIS and the pH of the buffer?

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Problem 118

Sketch a qualitative curve for the titration of ethylene-diamine, $\mathrm{H}_{2} \mathrm{NCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2},$ with 0.1 $\mathrm{MCl} .$

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Problem 119

A solution contains 0.10$M \mathrm{ZnCl}_{2}$ and 0.020 $\mathrm{M} \mathrm{MnCl}_{2}$ Given the following information, how would you adjust the pH to separate the ions as their sulfides $\left(\left[\mathrm{H}_{2} \mathrm{S}\right] \text { of a saturated aqueous }\right.$ solution at $25^{\circ} \mathrm{C}=0.10 M ; K_{\mathrm{w}}=1.0 \times 10^{-14} \mathrm{at} 25^{\circ} \mathrm{C} ) ?$
$$
\begin{array}{lll}{\mathrm{MnS}+\mathrm{H}_{2} \mathrm{O}} & {\rightleftharpoons \mathrm{Mn}^{2+}+\mathrm{HS}^{-}+\mathrm{OH}^{-}} & {K_{\mathrm{sp}}=3 \times 10^{-11}} \\ {\mathrm{ZnS}+\mathrm{H}_{2} \mathrm{O}} & {=\mathrm{Zn}^{2+}+\mathrm{HS}^{-}+\mathrm{OH}^{-}} & {K_{\mathrm{sp}}=2 \times 10^{-22}} \\ {\mathrm{H}_{2} \mathrm{S}+\mathrm{H}_{2} \mathrm{O}} & {\rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{HS}^{-}} & {K_{\mathrm{al}}=9 \times 10^{-8}}\end{array}
$$

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Problem 120

Amino acids [general formula $\mathrm{NH}_{2} \mathrm{CH}(\mathrm{R}) \mathrm{COOH} ]$ can be
considered polyprotic acids. In many cases, the R group contains additional amine and carboxyl groups.
(a) Can an amino acid dissolved in pure water have a protonated COOH group and an unprotonated $\mathrm{NH}_{2}$ group $\left(K_{\mathrm{a}} \text { of } \mathrm{COOH}\right.$ group $=4.47 \times 10^{-3} ; K_{\mathrm{b}}$ of $\mathrm{NH}_{2}$ group $=6.03 \times 10^{-5} ) ?$ Use glycine, $\mathrm{NH}_{2} \mathrm{CH}_{2} \mathrm{COOH}$ , to explain why.
(b) Calculate $\left[^{+} \mathrm{NH}_{3} \mathrm{CH}_{2} \mathrm{COO}^{-}\right] /\left[\mathrm{NH}_{3} \mathrm{CH}_{2} \mathrm{COOH}\right]$ at pH 5.5
(c) The R group of lysine is $-\mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\left(\mathrm{p} K_{\mathrm{b}}=3.47\right)$ Draw the structure of lysine at pH 1 , physiological pH $(\sim 7),$ and $\mathrm{pH} 13$
(d) The R group of glutamic acid is $-\mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COOH}\left(\mathrm{p} K_{\mathrm{a}}=\right.$ 4.07$) .$ Of the forms of glutamic acid that are shown below, which predominates at $(1) \mathrm{pH} 1,(2)$ physiological pH $(\sim 7),$ and (3) $\mathrm{pH} 13 ?$

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Problem 121

The scene at right depicts a saturated solution of $\mathrm{MCl}_{2}(s)$ in the presence of dilute aqueous NaCl; each sphere represents $1.0 \times 10^{-6} \mathrm{mol}$ of ion, and the volume is 250.0 $\mathrm{mL}$ (solid $\mathrm{MCl}_{2}$ is shown as green chunks, $\mathrm{M}^{2+}$ is blue, and $\mathrm{Cl}^{-}$ is yellow; Nat ions and water molecules are not shown). (a) Calculate the $K_{\mathrm{sp}}$ of $\mathrm{MCl}_{2}$ . ( b) If $\mathrm{M}\left(\mathrm{NO}_{3}\right)_{2}(s)$ is added, is there an increase, decrease, or no change in the number of $\mathrm{Cl}^{-}$ particles? In $K_{\mathrm{sp}} ?$ In the mass of $\mathrm{MCl}_{2}(s) ?$

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Problem 122

Tooth enamel consists of hydroxyapatite, $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH}$ $\left(K_{\mathrm{sp}}=6.8 \times 10^{-37}\right) .$ Fluoride ion added to drinking water
reacts with $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH}$ to form the more tooth decay-resistant fluorapatite, $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{F}\left(K_{\mathrm{sp}}=1.0 \times 10^{-60}\right) .$ Fluoridated water has dramatically decreased cavities among children. Calculate the solubility of $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH}$ and of $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{F}$ in water.

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Problem 123

The acid-base indicator ethyl orange turns from red to yellow over the pH range 3.4 to $4.8 .$ Estimate $K_{\mathrm{a}}$ for ethyl orange.

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Problem 124

Use the values obtained in Problem 19.54 to sketch a curve of $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ vs. $\mathrm{mL}$ of added titrant. Are there advantages or disadvantages to viewing the results in this form? Explain.

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Problem 125

Instrumental acid-base titrations use a pH meter to monitor the changes in $\mathrm{pH}$ and volume. The equivalence point is found from the volume at which the curve has the steepest slope. (a) Use the data in Figure 19.8$(\mathrm{p} .838)$ to calculate the slope $(\Delta \mathrm{pH} / \Delta V)$ for all pairs of adjacent points and to calculate the average volume $\left(V_{\text { avg }}\right)$ for each interval. (b) Plot $\Delta \mathrm{pH} / \Delta V$ vs. $V_{\text { avg }}$ to find the steepest slope, and thus the volume at the equivalence point. (For example, the first pair of points gives $\Delta \mathrm{pH}=0.22, \Delta V=10.00 \mathrm{mL} ;$ hence, $\Delta \mathrm{pH} / \Delta V=$ $0.022 \mathrm{mL}^{-1},$ and $V_{\mathrm{avg}}=5.00 \mathrm{mL} . )$

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Problem 126

What is the pH of a solution of $6.5 \times 10^{-9} \mathrm{mol}$ of $\mathrm{Ca}(\mathrm{OH})_{2}$
in 10.0 $\mathrm{L}$ of water $\left[K_{\mathrm{sp}} \text { of } \mathrm{Ca}(\mathrm{OH})_{2}=6.5 \times 10^{-6}\right] ?$

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Problem 127

Muscle physiologists study the accumulation of lactic acid $\left[\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{COOH}\right]$ during exercise. Food chemists study its occurrence in sour milk, beer, wine, and fruit. Industrial microbiologists study its formation by various bacterial species from carbohydrates. A biochemist prepares a lactic acid-lactate buffer by mixing 225 $\mathrm{mL}$ of 0.85$M$ lactic acid $\left(K_{\mathrm{a}}=1.38 \times 10^{-4}\right)$ with 435 $\mathrm{mL}$ of 0.68 $\mathrm{M}$ sodium lactate. What is the buffer pH?

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Problem 128

A student wants to dissolve the maximum amount of $\mathrm{CaF}_{2}$ $\left(K_{\mathrm{sp}}=3.2 \times 10^{-11}\right)$ to make 1 $\mathrm{L}$ of aqueous solution. (a) Into which of the following solvents should she dissolve the salt?
(I) Pure water (II) 0.01 M HF
(III) 0.01 M NaOH (IV) 0.01 M HCl
(V) 0.01$M \mathrm{Ca}(\mathrm{OH})_{2}$
(b) Which would dissolve the least amount of salt?

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Problem 129

$\mathrm{A} 500 .$ -mL solution consists of 0.050 $\mathrm{mol}$ of solid $\mathrm{NaOH}$ and 0.13 $\mathrm{mol}$ of hypochlorous acid $\left(\mathrm{HClO} ; K_{\mathrm{a}}=3.0 \times 10^{-8}\right)$ dissolved in water.
(a) Aside from water, what is the concentration of each species that is present?
(b) What is the pH of the solution?
(c) What is the pH after adding 0.0050 mol of HCl to the flask?

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Problem 130

Calcium ion present in water supplies is easily precipitated as calcite $\left(\mathrm{CaCO}_{3}\right)$ :
$$
\mathrm{Ca}^{2+}(a q)+\mathrm{CO}_{3}^{2-}(a q) \rightleftharpoons \mathrm{CaCO}_{3}(s)
$$
Because the $K_{\mathrm{sp}}$ decreases with temperature, heating hard water forms a calcite "scale," which clogs pipes and water heaters. Find the solubility of calcite in water (a) at $10^{\circ} \mathrm{C}\left(K_{\mathrm{sp}}=4.4 \times 10^{-9}\right)$ and (b) at $30^{\circ} \mathrm{C}\left(K_{\mathrm{sp}}=3.1 \times 10^{-9}\right)$

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Problem 131

Calculate the molar solubility of $\mathrm{Hg}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \quad\left(K_{\mathrm{sp}}=\right.$ $1.75 \times 10^{-13} )$ in 0.13$M \mathrm{Hg}_{2}\left(\mathrm{NO}_{3}\right)_{2}$

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Problem 132

Environmental engineers use alkalinity as a measure of the capacity of carbonate buffering systems in water samples: Alkalinity $(\mathrm{mol} / \mathrm{L})=\left[\mathrm{HCO}_{3}^{-}\right]+2\left[\mathrm{CO}_{3}^{2-}\right]+\left[\mathrm{OH}^{-}\right]-\left[\mathrm{H}^{+}\right]$ Find the alkalinity of a water sample that has a pH of 9.5
$26.0 \mathrm{mg} / \mathrm{L} \mathrm{L} \mathrm{O}_{3}^{2-},$ and 65.0 $\mathrm{mg} / \mathrm{L} \mathrm{HCO}_{3}^{-}$

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Problem 133

Human blood contains one buffer system based on phosphate species and one based on carbonate species. Assuming that blood has a normal pH of $7.4,$ what are the principal phosphate and carbonate species present? What is the ratio of the two phosphate species? (In the presence of the dissolved ions
and other species in blood, $K_{\mathrm{al}}$ of $\mathrm{H}_{3} \mathrm{PO}_{4}=1.3 \times 10^{-2}, K_{\mathrm{a} 2}=$ $2.3 \times 10^{-7},$ and $K_{33}=6 \times 10^{-12} ; K_{\mathrm{al}}$ of $\mathrm{H}_{2} \mathrm{CO}_{3}=8 \times 10^{-7} \mathrm{and}$ $K_{\mathrm{a} 2}=1.6 \times 10^{-10} . )$

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Problem 134

$\mathrm{A} 0.050 \mathrm{M} \mathrm{H}_{2} \mathrm{S}$ solution contains 0.15 $\mathrm{M} \mathrm{NiCl}_{2}$ and 0.35 $\mathrm{M} \mathrm{Hg}\left(\mathrm{NO}_{3}\right)_{2} .$ What $\mathrm{pH}$ is required to precipitate the maximum amount of HgS but none of the NiS? (See Appendix C.)

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Problem 135

Quantitative analysis of $\mathrm{Cl}^{-}$ ion is often performed by a titration with silver nitrate, using sodium chromate as an indicator. As standardized AgNO, is added, both white AgCl and red $\mathrm{Ag}_{2} \mathrm{CrO}_{4}$ precipitate, but so long as some $\mathrm{Cl}^{-}$ remains, the $\mathrm{Ag}_{2} \mathrm{CrO}_{4}$ redissolves as the mixture is stirred. When the red color is permanent, the equivalence point has been reached. (a) Calculate the equilibrium constant for the reaction
$$
2 \mathrm{AgCl}(s)+\mathrm{CrO}_{4}^{2-}(a q) \rightleftharpoons \mathrm{Ag}_{2} \mathrm{CrO}_{4}(s)+2 \mathrm{Cl}^{-}(a q)
$$
(b) Explain why the silver chromate redissolves.
(c) If 25.00 $\mathrm{cm}^{3}$ of 0.1000$M \mathrm{NaCl}$ is mixed with 25.00 $\mathrm{cm}^{3}$ of $0.1000 \mathrm{M} \mathrm{AgNO}_{3},$ what is the concentration of Ag' remaining in solution? Is this sufficient to precipitate any silver chromate?

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Problem 136

If the $E_{\text { cell }}$ of the following cell is $0.915 \mathrm{V},$ what is the pH in the anode compartment?
$$
\operatorname{Pt}(s)\left|\mathrm{H}_{2}(1.00 \mathrm{atm})\right| \mathrm{H}^{+}(a q) \| \mathrm{Ag}^{+}(0.100 M) | \mathrm{Ag}(s)
$$

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Problem 137

From the skeleton equations below, create a list of balanced half-reactions in which the strongest oxidizing agent is on top and the weakest is on the bottom:
$$
\begin{array}{c}{\mathrm{U}^{3+}(a q)+\mathrm{Cr}^{3+}(a q) \longrightarrow \mathrm{Cr}^{2+}(a q)+\mathrm{U}^{4+}(a q)} \\ {\mathrm{Fe}(s)+\mathrm{Sn}^{2+}(a q) \longrightarrow \operatorname{Sn}(s)+\mathrm{Fe}^{2+}(a q)} \\ {\mathrm{Fe}(s)+\mathrm{U}^{4+}(a q) \longrightarrow \text { no reaction }}\end{array}
$$
$$
\begin{array}{c}{\mathrm{Cr}^{3+}(a q)+\mathrm{Fe}(s) \longrightarrow \mathrm{Cr}^{2+}(a q)+\mathrm{Fe}^{2+}(a q)} \\ {\mathrm{Cr}^{2+}(a q)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Sn}(s)+\mathrm{Cr}^{3+}(a q)}\end{array}
$$

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Problem 138

You are given the following three half-reactions:
$$
\begin{array}{l}{\text { (1) } \mathrm{Fe}^{3+}(a q)+\mathrm{e}^{-} \Longrightarrow \mathrm{Fe}^{2+}(a q)} \\ {\text { (2) } \mathrm{Fe}^{2+}(a q)+2 \mathrm{e}^{-} \Longrightarrow \mathrm{Fe}(s)} \\ {\text { (3) } \mathrm{Fe}^{3+}(a q)+3 \mathrm{e}^{-} \rightleftharpoons \mathrm{Fe}(s)}\end{array}
$$
(a) Use $E_{\text { half-cell values for }}(1)$ and $(2)$ to find $E_{\text { half-cell }}^{\circ}$ for $(3)$
(b) Calculate $\Delta G^{\circ}$ for $(1)$ and $(2)$ from their $E_{\text { half-cell values. }}^{\circ}$
(c) Calculate $\Delta G^{\circ}$ for $(3)$ from $(1)$ and $(2)$
(d) Calculate $E_{\text { half cell }}^{\circ}$ for $(3)$ from its $\Delta G^{\circ} .$
(e) What is the relationship between the $E_{\text { half-cell values for }}(1)$ and (2) and the $E_{\text { half-cell }}^{\circ}$ value for $(3) ?$

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Problem 139

Use the half-reaction method to balance the equation for the conversion of ethanol to acetic acid in acid solution:
$$
\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} \rightarrow \mathrm{CH}_{3} \mathrm{COOH}+\mathrm{Cr}^{3+}
$$

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Problem 140

When zinc is refined by electrolysis, the desired half-reaction at the cathode is
$$
\mathrm{Zn}^{2+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Zn}(s)
$$
A competing reaction, which lowers the yield, is the formation of hydrogen gas:
$$
2 \mathrm{H}^{+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{H}_{2}(g)
$$
If 91.50$\%$ of the current flowing results in zinc being deposited, while 8.50$\%$ produces hydrogen gas, how many liters of $\mathrm{H}_{2}$ , measured at STP, form per kilogram of zinc?

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Problem 141

A chemist designs an ion-specific probe for measuring $\left[\mathrm{Ag}^{+}\right]$ in an NaCl solution saturated with AgCl. One half-cell has an Ag-wire electrode immersed in the unknown AgCl-saturated NaCl solution. It is connected through a salt bridge to the other half-cell, which has a calomel reference electrode [a platinum wire immersed in a paste of mercury and calomel $\left(\mathrm{Hg}_{2} \mathrm{Cl}_{2}\right) ]$ in a saturated $\mathrm{KCl}$ solution. The measured $E_{\text { cell }}$ is
0.060 $\mathrm{V}$ .
(a) Given the following standard half-reactions, calculate $\left[\mathrm{Ag}^{+}\right] .$ Calomel:
$$
\mathrm{Hg}_{2} \mathrm{Cl}_{2}(s)+2 \mathrm{e}^{-} \longrightarrow_{2 \mathrm{Hg}(l)}+2 \mathrm{Cl}^{-(a q)} \quad E^{\circ}=0.24 \mathrm{V}
$$
$$
\operatorname{Ag}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \operatorname{Ag}(s) \quad E^{\circ}=0.80 \mathrm{V}
$$
(Hint: Assume that $\left[\mathrm{Cl}^{-}\right]$ is so high that it is essentially constant.)
(b) A mining engineer wants an ore sample analyzed with the Ag'- -selective probe. After pretreating the ore sample, the chemist measures the cell voltage as 0.53 $\mathrm{V} .$ What is $\left[\mathrm{Ag}^{+}\right] ?$

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Problem 142

Use Appendix D to calculate the $K_{\mathrm{sp}}$ of AgCl.

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Problem 143

Black-and-white photographic film is coated with silver halides. Because silver is expensive, the manufacturer monitors the $\mathrm{Ag}^{+}$ content of the waste stream, $\left[\mathrm{Ag}^{+}\right]_{\text { waste }},$ from the plant with an Ag$^{+}$ -selective electrode at $25^{\circ} \mathrm{C}$ . A stream of known Ag$^{+}$ concentration, $\left[\mathrm{Ag}^{+}\right]_{\text { standard }},$ is passed over the electrode in turn with the waste stream and the data recorded by a computer.
(a) Write the equations relating the nonstandard cell potential to the standard cell potential and $\left[\mathrm{Ag}^{+}\right]$ for each solution.
(b) Combine these into a single equation to find [Ag $^{+} ]_{\text { waste }}$
(c) Rewrite the equation from part (b) to find [Ag' $]_{\text { waste }}$ in ng/L.
(d) If $E_{\text { waste is }} 0.003$ V higher than $E_{\text { standard }},$ and the standard solution contains 1000 . ng/L, what is $\left[\mathrm{Ag}^{+}\right]_{\text { waste }} ?$
(e) Rewrite the equation from part (b) to find $\left[\mathrm{Ag}^{+}\right]_{\text { waste for a }}$ system in which $T$ changes and $T_{\text { waste }}$ and $T_{\text { standard }}$ may be different.

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Problem 144

Calculate the $K_{\mathrm{f}}$ of $\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}+\mathrm{from}$
$$
\mathrm{Ag}^{+}(a q)+\mathrm{e}^{-} \rightleftharpoons \mathrm{Ag}(s) \quad E^{\circ}=0.80 \mathrm{V}
$$
$$
\operatorname{Ag}\left(\mathrm{NH}_{3}\right)_{2}^{+}(a q)+\mathrm{e}^{-} \rightleftharpoons \mathrm{Ag}(s)+2 \mathrm{NH}_{3}(a q) \qquad E^{\circ}=0.37 \mathrm{V}
$$

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Problem 145

Even though the toxicity of cadmium has become a concern, nickel-cadmium (nicad) batteries are still used commonly in many devices. The overall cell reaction is
$$
\mathrm{Cd}(s)+2 \mathrm{NiO}(\mathrm{OH})(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow
$$
$$
2 \mathrm{Ni}(\mathrm{OH})(s)+\mathrm{Cd}(\mathrm{OH})_{2}(s)
$$
A certain nicad battery weighs 18.3 $\mathrm{g}$ and has a capacity of $300 . \mathrm{mA} \cdot \mathrm{h}$ (that is, the cell can store charge equivalent to a current of $300 .$ mA flowing for 1 $\mathrm{h} )$
(a) What is the capacity of this cell in coulombs?
(b) What mass of reactants is needed to deliver $300 . \mathrm{mA}$ -h?
(c) What percentage of the cell mass consists of reactants?

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Problem 146

The zinc-air battery is a less expensive alternative to silver batteries for use in hearing aids. The cell reaction is
$$
2 \mathrm{Zn}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{ZnO}(s)
$$
A new battery weighs 0.275 g. The zinc accounts for exactly $\frac{1}{10}$ of the mass, and the oxygen does not contribute to the mass because it is supplied by the air.
(a) How much electricity (in $\mathrm{C} )$ can the battery deliver?
(b) How much free energy (in $\mathrm{J} )$ is released if $E_{\text { cell }}$ is 1.3 $\mathrm{V} ?$

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Problem 147

Use Appendix $D$ to create an activity series of Mn, Fe, Ag, Sn, Cr, Cu, Ba, Al, Na, Hg, Ni, Li, Au, Zn, and Pb. Rank these metals in order of decreasing reducing strength, and divide them into three groups: those that displace $\mathrm{H}_{2}$ from water, those that displace $\mathrm{H}_{2}$ from acid, and those that cannot displace $\mathrm{H}_{2} .$

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Problem 148

Both Ti and $V$ are reactive enough to displace $H_{2}$ from water. The difference in their $E_{\text { half-cell values is } 0.43}$ V.Given
$$
\mathrm{V}(s)+\mathrm{Cu}^{2+}(a q) \longrightarrow \mathrm{V}^{2+}(a q)+\mathrm{Cu}(s) \quad \Delta G^{\circ}=-298 \mathrm{kJ} / \mathrm{mol}
$$
use Appendix D to calculate the $E_{\text { half-cell values for }} V$ and Ti.

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Problem 149

For the reaction
$$
\mathrm{S}_{4} \mathrm{O}_{6}^{2-}(a q)+2 \mathrm{I}^{-}(a q) \longrightarrow \mathrm{I}_{2}(s)+\mathrm{S}_{2} \mathrm{O}_{3}^{2-}(a q)
$$
$$
\Delta G^{\circ}=87.8 \mathrm{kJ} / \mathrm{mol}
$$
(a) Identify the oxidizing and reducing agents. (b) Calculate $E_{\text { celve }}^{\circ}$ (c) For the reduction half-reaction, write a balanced equation, give the oxidation number of each element, and calculate $E_{\text { half-cell. }}^{\circ} .$

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Problem 150

Two concentration cells are prepared, both with 90.0 $\mathrm{mL}$ of 0.0100 $\mathrm{M} \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}$ and a Cu bar in each half-cell.
(a) In the first concentration cell, 10.0 $\mathrm{mL}$ of 0.500 $\mathrm{M} \mathrm{NH}_{3}$ is added to one half-cell; the complex ion $\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}$ forms, and $E_{\mathrm{cell}}$ is 0.129 $\mathrm{V}$ . Calculate $K_{\mathrm{f}}$ for the formation of the complex ion.
(b) Calculate $E_{\text_{cell}$ when an additional $10.0 \mathrm{mL}}$ of 0.500 $\mathrm{M} \mathrm{NH}_{3}$ is added.
(c) In the second concentration cell, 10.0 $\mathrm{mL}$ of 0.500 $\mathrm{M} \mathrm{NaOH}$ is added to one half-cell; the precipitate $\mathrm{Cu}(\mathrm{OH})_{2}$ forms $\left(K_{\mathrm{sp}}=\right.$ $2.2 \times 10^{-20}$ ). Calculate $E_{\mathrm{cell}}^{\circ}$
(d) What would the molarity of NaOH have to be for the addition of 10.0 $\mathrm{mL}$ to result in an $E_{\mathrm{cell}}^{\circ}$ of 0.340 $\mathrm{V}$ ?

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