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Chapter 17

Additional Aspects of Aqueous Equilibria

Educators

KC

Problem 1

The following boxes represent aqueous solutions containing a weak acid, HA and its conjugate base, $A^{-} .$ Water molecules, hydronium ions, and cations are not shown. Which solution has the highest pH? Explain. [ Section 17.1$]$

KC
Kevin C.
Numerade Educator

Problem 2

The beaker on the right contains 0.1 Macetic acid solution with methyl orange as an indicator. The beaker on the left contains a mixture of 0.1$M$ acetic acid and 0.1$M$ sodium acetate with methyl orange. (a) Using Figures 16.8 and 16.9, which solution has a higher pH? (b) Which solution is better able to maintain its pH when small amounts of NaOH are added? Explain. [Sections 17.1 and 17.2]

Keenan M.
University of Miami

Problem 3

A buffer contains a weak acid, HA, and its conjugate base. The weak acid has a $\mathrm{pK}_{a}$ of $4.5,$ and the buffer has a $\mathrm{pH}$ of $4.3 .$ Without doing a calculation, state which of these possibilities are correct at $\mathrm{pH} 4.3 .(\mathbf{a})[\mathrm{HA}]=\left[\mathrm{A}^{-}\right]$
$(\mathbf{b})[\mathrm{HA}]>\left[\mathrm{A}^{-}\right], \mathrm{or}(\mathbf{c})[\mathrm{HA}]<\left[\mathrm{A}^{-}\right] .[$ Section 17.2$]$

KC
Kevin C.
Numerade Educator

Problem 4

The following diagram represents a buffer composed of equal concentrations of a weak acid, HA, and its conjugate base, $A^{-} .$ The heights of the columns are proportional to the concentrations of the components of the buffer. (a) Which of the three drawings, $(1),(2),$ or $(3),$ represents the buffer after the addition of a strong acid? (b) Which of the three represents the buffer after the addition of a strong
base? (c) Which of the three represents a situation that cannot arise from the addition of either an acid or a base? $[$ Section 17.2$]$

Keenan M.
University of Miami

Problem 5

The following figure represents solutions at various stages of the titration of a weak acid, HA, with NaOH. (The $\mathrm{Na}^{+}$ ions and water molecules have been omitted for clarity.) To which of the following regions of the titration curve does each drawing correspond: (a) before addition of NaOH, (b) after addition of $\mathrm{NaOH}$ but before the equivalence point, $(\mathbf{c})$ at the equivalence point, $(\mathbf{d})$ after the equivalence point? [ Section 17.3$]$

KC
Kevin C.
Numerade Educator

Problem 6

Match the following descriptions of titration curves with the diagrams: (a) strong acid added to strong base, (b) strong base added to weak acid, (c) strong base added to strong acid, (d) strong base added to polyprotic acid. [Section 17.3]

Keenan M.
University of Miami

Problem 7

Equal volumes of two acids are titrated with 0.10 $\mathrm{M}$ NaOH resulting in the two titration curves shown in the following figure. (a) Which curve corresponds to the more concentrated acid solution? (b) Which corresponds to the acid with the larger $K_{a} ?[$ Section 17.3$]$

KC
Kevin C.
Numerade Educator

Problem 8

A saturated solution of $\mathrm{Cd}(\mathrm{OH})_{2}$ is shown in the middle beaker. If hydrochloric acid solution is added, the solubility of $\mathrm{Cd}(\mathrm{OH})_{2}$ will increase, causing additional solid to dissolve. Which of the two choices, Beaker A or Beaker B, accurately represents the solution after equilibrium is reestablished? (The water molecules and $\mathrm{Cl}^{-}$ ions are omitted
for clarity.) [Sections 17.4 and 17.5]

Keenan M.
University of Miami

Problem 9

The following graphs represent the behavior of $\mathrm{BaCO}_{3}$ under different circumstances. In each case, the vertical axis indicates the solubility of the BaCO $_{3}$ and the horizontal axis represents the concentration of some other reagent. (a) Which graph represents what happens to the solubility
of BaCO $_{3}$ as HNO $_{3}$ is added? (b) Which graph represents what happens to the BaCO $_{3}$ solubility as $\mathrm{Na}_{2} \mathrm{CO}_{3}$ is added? (c) Which represents what happens to the BaCO $_{3}$ solubility as $\mathrm{NaNO}_{3}$ is added? [ Section 17.5$]$

KC
Kevin C.
Numerade Educator

Problem 10

$\mathrm{Ca}(\mathrm{OH})_{2}$ has a $K_{s p}$ of $6.5 \times 10^{-6} .(\mathbf{a})$ If 0.370 $\mathrm{g}$ of $\mathrm{Ca}(\mathrm{OH})_{2}$
is added to 500 $\mathrm{mL}$ of water and the mixture is allowed to come to equilibrium, will the solution be saturated? (b) If 50 mL of the solution from part (a) is added to each of the beakers shown here, in which beakers, if any, will a precipitate form? In those cases where a precipitate forms,
what is its identity? [Section 17.6$]$

Keenan M.
University of Miami

Problem 11

The graph below shows the solubility of a salt as a function of pH. Which of the following choices explain the shape of this graph? (a) None; this behavior is not possible. (b) A soluble salt reacts with acid to form a precipitate, and additional acid reacts with this product to dissolve it. (c) A soluble salt forms an insoluble hydroxide, then additional base reacts with this product to dissolve it. (d) The
solubility of the salt increases with pH, then decreases be- cause of the heat generated from the neutralization reac-
tions. [Section 17.5]

KC
Kevin C.
Numerade Educator

Problem 12

Three cations, $\mathrm{Ni}^{2+}, \mathrm{Cu}^{2+},$ and $\mathrm{Ag}^{+},$ are separated using
two different precipitating agents. Based on Figure $17.23,$ what two precipitating agents could be used? Using these agents, indicate which of the cations is $\mathrm{A},$ which is $\mathrm{B},$ and
which is C. [ Section 17.7$]$

Keenan M.
University of Miami

Problem 13

Which of these statements about the common-ion effect is most correct? (a) The solubility of a salt MA is decreased in a solution that already contains either M $^{+}$ or $A^{-} .(\mathbf{b})$ Common ions alter the equilibrium constant for the reaction of an ionic solid with water. (c) The common-ion effect does not apply to unusual ions like $\mathrm{SO}_{3}^{2-}$ . (d) The solubility of a salt MA is affected equally by the addition of either $\mathrm{A}^{-}$ or a noncommon ion.

KC
Kevin C.
Numerade Educator

Problem 14

Consider the equilibrium
$$\mathrm{B}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{HB}^{+}(a q)+\mathrm{OH}^{-}(a q)$$
Suppose that a salt of $\mathrm{HB}^{+}(a q)$ is added to a solution of $\mathrm{B}(a q)$ at equilibrium. (a) Will the equilibrium constant for the reaction increase, decrease, or stay the same? (b) Will the concentration of $\mathrm{B}(a q)$ increase, decrease, or stay the same? (c) Will the $\mathrm{pH}$ of the solution increase, decrease, or stay the same?

Keenan M.
University of Miami

Problem 15

Use information from Appendix D to calculate the pH of (a) a solution that is 0.060$M$ in potassium propionate $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOK}$ or $\mathrm{KC}_{3} \mathrm{H}_{5} \mathrm{O}_{2}\right)$ and 0.085 $\mathrm{M}$ in propionic acid $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOH}$ or $\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{2}\right) ;(\mathbf{b})$ a solution that is 0.075 $\mathrm{M}$ in trimethylamine, $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{N},$ and 0.10 $\mathrm{M}$ in trimethylammonium chloride, $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{NHCl} ;(\mathbf{c})$ a solution that is made by mixing 50.0 $\mathrm{mL}$ of 0.15 $\mathrm{M}$ acetic acid and 50.0 $\mathrm{mL}$ of 0.20 $\mathrm{M}$
sodium acetate.

KC
Kevin C.
Numerade Educator

Problem 16

Use information from Appendix D to calculate the pH of (a) a solution that is 0.250$M$ in sodium formate (HCOONa) and 0.100$M$ in formic acid (HCOOH), (b) a solution that is 0.510$M$ in pyridine $\left(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{N}\right)$ and 0.450 $\mathrm{M}$ in pyridinium
chloride $\left(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{NHCl}\right),(\mathbf{c})$ a solution that is made by combining 55 $\mathrm{mL}$ of 0.050 $\mathrm{M}$ hydrofluoric acid with 125 $\mathrm{mL}$ of 0.10 $\mathrm{M}$ sodium fluoride.

Keenan M.
University of Miami

Problem 17

(a) Calculate the percent ionization of 0.0075$M$ butanoic acid $\left(K_{a}=1.5 \times 10^{-5}\right) .$ (b) Calculate the percent ionization of 0.0075$M$ butanoic acid in a solution containing 0.085$M$ sodium butanoate.

KC
Kevin C.
Numerade Educator

Problem 18

(a) Calculate the percent ionization of 0.125$M$ lactic acid $\left(K_{a}=1.4 \times 10^{-4}\right) .($ b) Calculate the percent ionization of 0.125$M$ lactic acid in a solution containing 0.0075$M$ sodium lactate.

Keenan M.
University of Miami

Problem 19

Which of the following solutions is a buffer? (a) 0.10$M$
$\mathrm{CH}_{3} \mathrm{COOH}$ and $0.10 \mathrm{MCH}_{3} \mathrm{CONa},(\mathbf{b}) 0.10 \mathrm{MCH}_{3} \mathrm{COOH}$ (c) 0.10 $\mathrm{M} \mathrm{HCl}$ and $0.10 \mathrm{M} \mathrm{NaCl},(\mathbf{d})$ both a and $\mathrm{c},(\mathbf{e})$ all of a,
$\mathrm{b},$ and $\mathrm{c} .$

KC
Kevin C.
Numerade Educator

Problem 20

Which of the following solutions is a buffer? (a) A solution made by mixing 100 $\mathrm{mL}$ of 0.100 $\mathrm{MCH}_{3} \mathrm{COOH}$ and 50 mL of $0.100 M \mathrm{NaOH},(\mathbf{b})$ a solution made by mixing 100 $\mathrm{mL}$ of 0.100 $\mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}$ and 500 $\mathrm{mL}$ of 0.100 $\mathrm{M} \mathrm{NaOH}$ , (c) A solution made by mixing 100 $\mathrm{mL}$ of 0.100 $\mathrm{MCH}_{3} \mathrm{COOH}$ and 50 $\mathrm{mL}$ of $0.100 \mathrm{M} \mathrm{HCl},$ $(\mathbf{d} ) $ A solution made by mixing of 0.100 $\mathrm{MCH}_{3} \mathrm{COOK}$ and 50 $\mathrm{mL}$ of 0.100 $\mathrm{M} \mathrm{KCl}$ .

Keenan M.
University of Miami

Problem 21

(a) Calculate the pH of a buffer that is 0.12 $\mathrm{M}$ in lactic acid and 0.11 $\mathrm{M}$ in sodium lactate. (b) Calculate the pH of a buffer formed by mixing 85 mL of 0.13 M lactic acid with 95
mL of 0.15$M$ sodium lactate.

KC
Kevin C.
Numerade Educator

Problem 22

(a) Calculate the $\mathrm{pH}$ of a buffer that is 0.105 $\mathrm{M}$ in $\mathrm{NaHCO}_{3}$ and 0.125 $\mathrm{M}$ in $\mathrm{Na}_{2} \mathrm{CO}_{3}$ . (b) Calculate the pH of a solution
formed by mixing 65 $\mathrm{mL}$ of 0.20 $\mathrm{M} \mathrm{NaHCO}_{3}$ with 75 $\mathrm{mL}$ of 0.15 $\mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3} .$

Keenan M.
University of Miami

Problem 23

A buffer is prepared by adding 20.0 g of sodium acetate $\left(\mathrm{CH}_{3} \mathrm{COONa}\right)$ to 500 $\mathrm{mL}$ of a 0.150 $\mathrm{M}$ acetic acid $\left(\mathrm{CH}_{3} \mathrm{COOH}\right)$ solution. (a) Determine the pH of the buffer. (b) Write the complete ionic equation for the reaction that occurs when a few drops of hydrochloric acid are added to the buffer. (c) Write the complete ionic equation for the reaction that occurs when a few drops of sodium hydroxide solution are added to the buffer.

KC
Kevin C.
Numerade Educator

Problem 24

A buffer is prepared by adding 10.0 $\mathrm{g}$ of ammonium chloride $\left(\mathrm{NH}_{4} \mathrm{Cl}\right)$ to 250 $\mathrm{mL}$ of 1.00 $\mathrm{M} \mathrm{NH}_{3}$ solution. (a) What is the pH of this buffer? (b) Write the complete ionic equation for the reaction that occurs when a few drops of nitric acid are added to the buffer. (c) Write the complete ionic equation for the reaction that occurs when a few drops of potassium hydroxide solution are added to the buffer.

Keenan M.
University of Miami

Problem 25

You are asked to prepare a $\mathrm{pH}=3.00$ buffer solution starting from 1.25 $\mathrm{L}$ of a 1.00 $\mathrm{M}$ solution of hydrofluoric acid $(\mathrm{HF})$ and any amount you need of sodium fluoride $(\mathrm{NaF})$. (a) What is the $\mathrm{pH}$ of the hydrofluoric acid solution prior to adding sodium fluoride? (b) How many grams of sodium fluoride should be added to prepare the buffer solution? Neglect the small volume change that occurs when the sodium fluoride is added.

KC
Kevin C.
Numerade Educator

Problem 26

You are asked to prepare a pH $=4.00$ buffer starting from 1.50 . of 0.0200$M$ solution of benzoic acid $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)$ and any amount you need of sodium benzoate $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COONa}\right) .(\mathbf{a})$ What is the pH of the benzoic acid solution prior to adding sodium benzoate? (b) How many grams of sodium benzoate should be added to prepare the buffer? Neglect the small volume change that occurs when
the sodium benzoate is added.

Keenan M.
University of Miami

Problem 27

A buffer contains 0.10 mol of acetic acid and 0.13 mol of sodium acetate in 1.00 $\mathrm{L}$ (a) What is the pH of this buffer? (b) What is the pH of the buffer after the addition of 0.02 mol of $\mathrm{KOH}$ ? (c) What is the $\mathrm{pH}$ of the buffer after the addition of 0.02 $\mathrm{mol}$ of $\mathrm{HNO}_{3} ?$

KC
Kevin C.
Numerade Educator

Problem 28

A buffer contains 0.15 mol of propionic acid $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOH}\right)$ and 0.10 mol of sodium propionate $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COONa}\right)$ in 1.20 $\mathrm{L}$ . (a) What is the pH of this buffer? (b) What is the pH of the buffer after the addition of 0.01 $\mathrm{mol}$ of $\mathrm{NaOH}$ ? (c) What is the pH of the buffer after the addition of 0.01 $\mathrm{mol}$ of $\mathrm{HI} ?$

Keenan M.
University of Miami

Problem 29

(a) What is the ratio of $\mathrm{HCO}_{3}^{-}$ to $\mathrm{H}_{2} \mathrm{CO}_{3}$ in blood of pH 7.4 ? (b) What is the ratio of $\mathrm{HCO}_{3}^{-}$ to $\mathrm{H}_{2} \mathrm{CO}_{3}$ in an exhausted marathon runner whose blood pH is 7.1$?$

KC
Kevin C.
Numerade Educator

Problem 30

A buffer, consisting of $\mathrm{H}_{2} \mathrm{PO}_{4}^{-}$ and $\mathrm{HPO}_{4}^{2-}$ , helps control the pH of physiological fluids. Many carbonated soft drinks also use this buffer system. What is the pH of a soft drink in which the major syster ingredients are 6.5 $\mathrm{g}$ of $\mathrm{NaH}_{2} \mathrm{PO}_{4}$ and 8.0 $\mathrm{g}$ of $\mathrm{Na}_{2} \mathrm{HPO}_{4}$ per 355 $\mathrm{mL}$ of solution?

Keenan M.
University of Miami

Problem 31

You have to prepare a pH $=3.50$ buffer, and you have the following 0.10$M$ solutions available: $\mathrm{HCOOH}, \mathrm{CH}_{3} \mathrm{COOH}$ , $\mathrm{H}_{3} \mathrm{PO}_{4}, \mathrm{HCOONa}, \mathrm{CH}_{3} \mathrm{COONa}$ , and $\mathrm{NaH}_{2} \mathrm{PO}_{4} .$ Which solutions would you use? How many milliliters of each solution would you use to make approximately 1 L of the buffer?

KC
Kevin C.
Numerade Educator

Problem 32

You have to prepare a $\mathrm{pH}=5.00$ buffer, and you have the following 0.10 $\mathrm{M}$ solutions available: HCOOH, HCOONa, $\mathrm{CH}_{3} \mathrm{COOH}, \mathrm{CH}_{3} \mathrm{COONa}, \mathrm{HCN},$ and $\mathrm{NaCN} .$ Which solutions would you use? How many milliliters of each solution would you use to make approximately 1 $\mathrm{L}$ of the buffer?

Keenan M.
University of Miami

Problem 33

The accompanying graph shows the titration curves for two monoprotic acids. (a) Which curve is that of a strong acid? (b) What is the approximate pH at the equivalence point of each titration? (c) 40.0 $\mathrm{mL}$ of each acid was titrated with $\mathrm{a} 0.100 \mathrm{M}$ base. Which acid is more concentrated? $(\mathbf{d}) $ Estimate the $\mathrm{p} K_{a}$ of the weak acid.

KC
Kevin C.
Numerade Educator

Problem 34

Compare the titration of a strong, monoprotic acid with a strong base to the titration of a weak, monoprotic acid with a strong base. Assume the strong and weak acid solutions initially have the same concentrations. Indicate whether the following statements are true or false. (a) More base is required to reach the equivalence point for the strong acid than the weak acid. (b) The pH at the beginning of the titration is lower for the weak acid than the strong acid. (c) The pH at the equivalence point is 7 no matter which acid is titrated.

Keenan M.
University of Miami

Problem 35

The samples of nitric and acetic acids shown here are both titrated with a 0.100$M$ solution of $\mathrm{NaOH}(a q) .$
Determine whether each of the following statements concerning these titrations is true or false.
(a) A larger volume of $\mathrm{NaOH}(a q)$ is needed to reach the equivalence point in the titration of $\mathrm{HNO}_{3}$ .
(b) The pH at the equivalence point in the HNO $_{3}$ titration will be lower than the $\mathrm{pH}$ at the equivalence point in the $\mathrm{CH}_{3} \mathrm{COOH}$ titration.
(c) Phenolphthalein would be a suitable indicator for both titrations.

KC
Kevin C.
Numerade Educator

Problem 36

Determine whether each of the following statements concerning the titrations in Problem 17.35 is true or false.
(a) The pH at the beginning of the two titrations will be the same.
(b) The titration curves will both be essentially the same after passing the equivalence point.
(c) Methyl red would be a suitable indicator for both titrations.

Keenan M.
University of Miami

Problem 37

Predict whether the equivalence point of each of the following titrations is below, above, or at $\mathrm{pH} 7 :(\mathbf{a}) \mathrm{NaHCO}_{3}$ titrated with $\mathrm{NaOH},(\mathbf{b}) \mathrm{NH}_{3}$ titrated with $\mathrm{HCl},(\mathbf{c}) \mathrm{KOH}$ titrated with HBr.

KC
Kevin C.
Numerade Educator

Problem 38

Predict whether the equivalence point of each of the following titrations is below, above, or at $\mathrm{pH} 7 :$ (a) formic acid titrated with $\mathrm{NaOH},(\mathbf{b})$ calcium hydroxide titrated with perchloric acid, (c) pyridine titrated with nitric acid.

Keenan M.
University of Miami

Problem 39

As shown in Figure $16.8,$ the indicator thymol blue has two color changes. Which color change will generally be more suitable for the titration of a weak acid with a strong base?

KC
Kevin C.
Numerade Educator

Problem 40

Assume that 30.0 $\mathrm{mL}$ of a 0.10 $\mathrm{M}$ solution of a weak base $\mathrm{B}$ that accepts one proton is titrated with a 0.10$M$ solution of the monoprotic strong acid HA. (a) How many moles of HA have been added at the equivalence point? (b) What is the predominant form of B at the equivalence point? (a) Is the pH $7,$ less than $7,$ or more than 7 at the equivalence point?$ (\mathbf{d} )$ Which indicator, phenolphthalein or methyl red, is likely to be the better choice for this titration?

Keenan M.
University of Miami

Problem 41

How many milliliters of 0.0850$M \mathrm{NaOH}$ are required to titrate each of the following solutions to the equivalence point: (a) 40.0 $\mathrm{mL}$ of $0.0900 \mathrm{M} \mathrm{HNO}_{3},$ (\mathbf{b} ) 35.0 $\mathrm{mL}$ of $0.0850 M \mathrm{CH}_{3} \mathrm{COOH},(\mathbf{c}) 50.0 \mathrm{mL}$ of a solution that contains 1.85 $\mathrm{g}$ of $\mathrm{HCl}$ per liter?

KC
Kevin C.
Numerade Educator

Problem 42

How many milliliters of 0.105 $\mathrm{M}$ HCl are needed to titrate each of the following solutions to the equivalence point: (a) 45.0 $\mathrm{mL}$ of $0.0950 \mathrm{MNaOH},(\mathbf{b}) 22.5 \mathrm{mL}$ of $0.118 \mathrm{MNH}_{3},(\mathbf{c}) 125.0$ mL of a solution that contains 1.35 gof NaOH perliter?

Keenan M.
University of Miami

Problem 43

A 20.0 -mL sample of 0.200 $\mathrm{M}$ HBr solution is titrated with 0.200 $\mathrm{M} \mathrm{NaOH}$ solution. Calculate the $\mathrm{pH}$ of the solution after the following volumes of base have been added: (a) 15.0 $\mathrm{mL}$ $(\mathbf{b}) 19.9 \mathrm{mL},(\mathbf{c}) 20.0 \mathrm{mL},(\mathbf{d}) 20.1 \mathrm{mL},(\mathbf{e}) 35.0 \mathrm{mL}$

KC
Kevin C.
Numerade Educator

Problem 44

A 20.0 -mL sample of 0.150 $\mathrm{M} \mathrm{KOH}$ is titrated with 0.125 $\mathrm{M}$ $\mathrm{HClO}_{4}$ solution. Calculate the $\mathrm{pH}$ after the following volumes of acid have been added: (a) $20.0 \mathrm{mL},$ (b) 23.0 $\mathrm{mL}$ $(\mathbf{c}) 24.0 \mathrm{mL},(\mathbf{d}) 25.0 \mathrm{mL},(\mathbf{e}) 30.0 \mathrm{mL}$

Keenan M.
University of Miami

Problem 45

A 35.0-mL sample of 0.150$M$ acetic acid $\left(\mathrm{CH}_{3} \mathrm{COOH}\right)$ is titrated with 0.150 $\mathrm{M} \mathrm{NaOH}$ solution. Calculate the pH after the following volumes of base have been added: (a) 0 $\mathrm{mL}$ (b) $17.5 \mathrm{mL},(\mathrm{c}) 34.5 \mathrm{mL},(\mathbf{d}) 35.0 \mathrm{mL},(\mathbf{e}) 35.5 \mathrm{mL},(\mathbf{f}) 50.0 \mathrm{mL}$

KC
Kevin C.
Numerade Educator

Problem 46

Consider the titration of 30.0 $\mathrm{mL}$ of 0.050 $\mathrm{M} \mathrm{NH}_{3}$ with 0.025 $\mathrm{M}$ HCl. Calculate the pH after the following volumes of titrant have been added: (a) $0 \mathrm{mL},$ (b) $20.0 \mathrm{mL},(\mathrm{c}) 59.0$ $\mathrm{mL},(\mathbf{d}) 60.0 \mathrm{mL},(\mathbf{e}) 61.0 \mathrm{mL},(\mathbf{f}) 65.0 \mathrm{mL}$

Keenan M.
University of Miami

Problem 47

Calculate the $\mathrm{pH}$ at the equivalence point for titrating 0.200 $\mathrm{M}$ solutions of each of the following bases with 0.200 $M \mathrm{HBr} :(\mathbf{a})$ sodium hydroxide $(\mathrm{NaOH}),(\mathbf{b})$ hydroxylamine $\left(\mathrm{NH}_{2} \mathrm{OH}\right),(\mathbf{c})$ aniline $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\right)$

KC
Kevin C.
Numerade Educator

Problem 48

Calculate the $\mathrm{pH}$ at the equivalence point in titrating 0.100 M solutions of each of the following with 0.080 $\mathrm{M}$ NaOH: (a) hydrobromic acid (HBr), (b) chlorous acid (HClO_{2} ) , (c) benzoic acid $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)$

Keenan M.
University of Miami

Problem 49

For each statement, indicate whether it is true or false.
(a) The solubility of a slightly soluble salt can be expressed in units of moles per liter.
(b) The solubility product of a slightly soluble salt is simply the square of the solubility.
(c) The solubility of a slightly soluble salt is independent of the presence of a common ion.
(d) The solubility product of a slightly soluble salt is independent of the presence of a common ion.

KC
Kevin C.
Numerade Educator

Problem 50

The solubility of two slightly soluble salts of $\mathrm{M}^{2+}, \mathrm{MA}$ and $\mathrm{MZ}_{2},$ is the same, $4 \times 10^{-4} \mathrm{mol} / \mathrm{L}$ . (a) Which has the larger numerical value for the solubility product constant? (b) In a saturated solution of each salt in water, which has the higher concentration of $\mathrm{M}^{2+} ?$ (c) If you added an equal volume of a solution saturated in MA to one saturated in $\mathrm{MZ}_{2},$ what would be the equilibrium concentration of the
cation, $\mathrm{M}^{2+}$ ?

Keenan M.
University of Miami

Problem 51

Write the expression for the solubility-product constant for each of the following ionic compounds: AgI,
SrSO $_{4}, \mathrm{Fe}(\mathrm{OH})_{2},$ and $\mathrm{Hg}_{2} \mathrm{Br}_{2}$ .

KC
Kevin C.
Numerade Educator

Problem 52

(a) True or false: “solubility” and “solubility-product constant” are the same number for a given compound. (b) Write the expression for the solubility-product constant for each of the following ionic compounds: MnCO $_{3}, \mathrm{Hg}(\mathrm{OH})_{2},$ and $\mathrm{Cu}_{3}\left(\mathrm{PO}_{4}\right)_{2} .$

Keenan M.
University of Miami

Problem 53

(a) If the molar solubility of $\mathrm{CaF}_{2}$ at $35^{\circ} \mathrm{C}$ is $1.24 \times 10^{-3} \mathrm{mol} / \mathrm{L},$ what is $K_{s p}$ at this temperature? (b) It is found that $1.1 \times 10^{-2} \mathrm{g} \mathrm{SrF}_{2}$ dissolves per 100 $\mathrm{mL}$ of aqueous solution at $25^{\circ} \mathrm{C}$ Calculate the solubility product for $\mathrm{SrF}_{2 .}(\mathbf{c})$ The $K_{s p}$ of $\mathrm{Ba}\left(\mathrm{IO}_{3}\right)_{2}$ at $25^{\circ} \mathrm{C}$ is $6.0 \times 10^{-10} .$ What is the molar solubility of $\mathrm{Ba}\left(\mathrm{IO}_{3}\right)_{2} ?$

KC
Kevin C.
Numerade Educator

Problem 54

(a) The molar solubility of $\mathrm{PbBr}_{2}$ at $25^{\circ} \mathrm{C}$ is $1.0 \times 10^{-2} \mathrm{mol} / \mathrm{L}$ Calculate $K_{s p-}(\mathbf{b})$ If 0.0490 $\mathrm{g}$ of $\mathrm{AgIO}_{3}$ dissolves per liter of solution, calculate the solubility-product constant. (c) Using the appropriate $K_{s p}$ value from Appendix $D$ , calculate the $\mathrm{pH}$ of a saturated solution of $\mathrm{Ca}(\mathrm{OH})_{2}$ .

Keenan M.
University of Miami

Problem 55

A 1.00 -L solution saturated at $25^{\circ} \mathrm{C}$ with calcium oxalate $\left(\mathrm{CaC}_{2} \mathrm{O}_{4}\right)$ contains 0.0061 $\mathrm{g}$ of $\mathrm{CaC}_{2} \mathrm{O}_{4} .$ Calculate the solubility-product constant for this salt at $25^{\circ} \mathrm{C}$ .

KC
Kevin C.
Numerade Educator

Problem 56

A 1.00 -L. solution saturated at $25^{\circ} \mathrm{C}$ with lead(lI) iodide contains 0.54 $\mathrm{g}$ of $\mathrm{Pbl}_{2}$ . Calculate the solubility-product constant for this salt at $25^{\circ} \mathrm{C}$ .

Keenan M.
University of Miami

Problem 57

Using Appendix D, calculate the molar solubility of AgBr in (a) pure water, ( b) $3.0 \times 10^{-2}$ MAgNO $_{3}$ solution, $(\mathbf{c}) 0.10 M$ NaBr solution.

Check back soon!

Problem 58

Calculate the solubility of $\mathrm{LaF}_{3}$ in grams per liter in (a) pure water, $(\mathbf{b}) 0.010 M$ KF solution, $(\mathbf{c}) 0.050 M \mathrm{LaCl}_{3}$ solution.

Keenan M.
University of Miami

Problem 59

Consider a beaker containing a saturated solution of $\mathrm{CaF}_{2}$ in equilibrium with undissolved $\mathrm{CaF}_{2}(s)$. Solid $\mathrm{CaCl}_{2}$ is then added to the solution. (a) Will the amount of solid $\mathrm{CaF}_{2}$ at the bottom of the beaker increase, decrease, or remain the same? (b) Will the concentration of $\mathrm{Ca}^{2+}$ ions in solution increase or decrease? (c) Will the concentration of $\mathbf{F}^{-}$ ions in solution increase or decrease?

KC
Kevin C.
Numerade Educator

Problem 60

Consider a beaker containing a saturated solution of $\mathrm{PbI}_{2}$ in equilibrium with undissolved $\mathrm{PbI}_{2}(s)$. Now solid $\mathrm{K} \mathrm{I}$ is added to this solution. (a) Will the amount of solid $\mathrm{PbI}_{2}$ at the bottom of the beaker increase, decrease, or remain the same? (b) Will the concentration of $\mathrm{Pb}^{2+}$ ions in solution increase or decrease? (c) Will the concentration of $I$ ions in solution increase or decrease?

Keenan M.
University of Miami

Problem 61

Calculate the solubility of $\mathrm{Mn}(\mathrm{OH})_{2}$ in grams per liter when buffered at $\mathrm{pH}(\mathbf{a}) 7.0,(\mathbf{b}) 9.5,(\mathbf{c}) 11.8 .$

KC
Kevin C.
Numerade Educator

Problem 62

Calculate the molar solubility of $\mathrm{Ni}(\mathrm{OH})_{2}$ when buffered at $\mathrm{pH}(\mathbf{a}) 8.0,(\mathbf{b}) 10.0,(\mathbf{c}) 12.0 .$

Keenan M.
University of Miami

Problem 63

Which of the following salts will be substantially more soluble in acidic solution than in pure water: (a) ZnCO $_{3}$ $\mathbf{b} ) \mathrm{ZnS},(\mathbf{c}) \mathrm{BiI}_{3},(\mathbf{d}) \mathrm{AgCN},(\mathbf{e}) \mathrm{Ba}_{3}\left(\mathrm{PO}_{4}\right)_{2} ?$

KC
Kevin C.
Numerade Educator

Problem 64

For each of the following slightly soluble salts, write the net ionic equation, if any, for reaction with a strong acid:
(a) MnS, $(\mathbf{b}) \mathrm{Pbl}_{2,}(\mathbf{c}) \mathrm{AuCl}_{3},(\mathbf{d}) \mathrm{Hg}_{2} \mathrm{C}_{2} \mathrm{O}_{4},$ (e) CuBr.

Keenan M.
University of Miami

Problem 65

From the value of $K_{f}$ listed in Table $17.1,$ calculate the concentration of $\mathrm{Ni}^{2}(a q)$ and $\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}^{2+}$ that are present at equilibrium after dissolving 1.25 $\mathrm{g} \mathrm{NiCl}_{2}$ in 100.0 $\mathrm{mL}$ of 0.20 $\mathrm{MN} \mathrm{H}_{3}(a q) .$

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Problem 66

From the value of $K_{f}$ listed in Table $17.1,$ calculate the concentration of $\mathrm{NH}_{3}$ required to just dissolve 0.020 $\mathrm{mol}$ of $\mathrm{NiC}_{2} \mathrm{O}_{4}\left(K_{s p}=4 \times 10^{-10}\right)$ in 1.00 $\mathrm{L}$ of solution? (Hint: You can neglect the hydrolysis of $\mathrm{C}_{2} \mathrm{O}_{4}^{2-}$ because the solution will be quite basic.)

Keenan M.
University of Miami

Problem 67

Use values of $K_{s p}$ for AgI and $K_{f}$ for $A g(C N)_{2}^{-}$ to (a) calculate the molar solubility of Agl in pure water, (b) calculate the equilibrium constant for the reaction $\operatorname{AgI}(s)+2 \mathrm{CN}^{-}(a q) \rightleftharpoons \mathrm{Ag}(\mathrm{CN})_{2}^{-}(a q)+\mathrm{I}^{-}(a q), \quad(\mathbf{c})$ determine the molar solubility of AgI in a 0.100 $\mathrm{MNaCN}$ solution.

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Problem 68

Using the value of $K_{s p}$ for $\mathrm{Ag}_{2} \mathrm{S}, K_{a 1}$ and $K_{a 2}$ for $\mathrm{H}_{2} \mathrm{S},$ and $K_{f}=1.1 \times 10^{5}$ for $\mathrm{AgCl}_{2}^{-}$ , calculate the equilibrium constant for the following reaction:
$\mathrm{Ag}_{2} \mathrm{S}(s)+4 \mathrm{Cl}^{-}(a q)+2 \mathrm{H}^{+}(a q) \rightleftharpoons 2 \mathrm{AgCl}_{2}^{-}(a q)+\mathrm{H}_{2} \mathrm{S}(a q)$

Keenan M.
University of Miami

Problem 69

(a) Will $\mathrm{Ca}(\mathrm{OH})_{2}$ precipitate from solution if the $\mathrm{p} \mathrm{H}$ of a 0.050 M solution of $\mathrm{CaCl}_{2}$ is adjusted to 8.0? (b) Will $\mathrm{Ag}_{2} \mathrm{SO}_{4}$ precipitate when 100 mL of 0.050 M $\mathrm{AgNO}_{3}$ is mixed with 10 mL of $5.0 \times 10^{-2} \mathrm{MNa}_{2} \mathrm{SO}_{4}$ solution?

KC
Kevin C.
Numerade Educator

Problem 70

(a) Will $\mathrm{Co}(\mathrm{OH})_{2}$ precipitate from solution if the $\mathbf{p H}$ of a 0.020 M solution of $\mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2}$ is adjusted to 8.5? (b) Will $\mathrm{AgIO}_{3}$ precipitate when 20 mL of 0.010 M $\mathrm{AglO}_{3}$ is mixed with 10 mL of 0.015 $M \mathrm{NaIO}_{3}$? ( $K_{s p}$ of $\mathrm{AgIO}_{3}$ is $3.1 \times 10^{8}$)?

Keenan M.
University of Miami

Problem 71

Calculate the minimum $p H$ needed to precipitate $\mathrm{Mn}(\mathrm{OH})_{2}$ so completely that the concentration of $\mathrm{Mn}^{2+}(a q)$ is less than 1$\mu \mathrm{g}$ per liter $[1$ part per billion $(\mathrm{ppb})]$

KC
Kevin C.
Numerade Educator

Problem 72

Suppose that a 10 -mL sample of a solution is to be tested for $\mathrm{I}^{-}$ ion by addition of 1 $\mathrm{drop}(0.2 \mathrm{mL})$ of 0.10 $\mathrm{MPb}\left(\mathrm{NO}_{3}\right)_{2}$ . What is the minimum number of grams of I $\mathrm{I}^{-}$ that must be present for $\mathrm{PbI}_{2}(s)$ to form?

Keenan M.
University of Miami

Problem 73

A solution contains $2.0 \times 10^{-4} M \mathrm{Ag}^{+}(a q)$ a n d $1.5 \times 10^{-3} M \mathrm{Pb}^{2+}(a q)$. I f N a I i s a d d e d , w i l l A g I ($K_{s p}=8.3 \times 10^{-17}$) or $\mathrm{PbI}_{2}\left(K_{s p}=7.9 \times 10^{-9}\right)$ precipitate first? Specify the concentration of
$\mathrm{I}^{-}(a q)$ needed to begin precipitation.

KC
Kevin C.
Numerade Educator

Problem 74

A solution of $\mathrm{Na}_{2} \mathrm{SO}_{4}$ is added dropwise to a solution that is 0.010$M$ in $\mathrm{Ba}^{2+}(a q)$ and 0.010$M$ in $\mathrm{Sr}^{2+}(a q) .$ (a) What concentration of $\mathrm{SO}_{4}^{2-}$ is necessary to begin precipitation? (Neglect volume changes. $\mathrm{BaSO}_{4} : K_{s p}=1.1 \times 10^{-10} ; \mathrm{SrSO}_{4}$: $K_{s p}=3.2 \times 10^{-7} . )$ (b) Which cation precipitates first? (c) What is the concentration of $\mathrm{SO}_{4}^{2-}(a q)$ when the second cation begins to precipitate?

Keenan M.
University of Miami

Problem 75

A solution contains three anions with the following concentrations: $0.20 M \mathrm{CrO}_{4}^{2-}, 0.10 M \mathrm{CO}_{3}^{2-}$ , a n d 0.010$M \mathrm{Cl}^{-} .$ If a dilute AgNO $_{3}$ solution is slowly added to the solution, what is the first compound to precipitate: $\mathrm{Ag}_{2} \mathrm{CrO}_{4}\left(K_{s p}=1.2 \times 10^{-12}\right), \mathrm{Ag}_{2} \mathrm{CO}_{3}\left(K_{s p}=8.1 \times 10^{-12}\right)$ or $\mathrm{AgCl}\left(K_{s p}=1.8 \times 10^{-10}\right) ?$

KC
Kevin C.
Numerade Educator

Problem 76

A 1.0 $\mathrm{MN} \mathrm{a}_{2} \mathrm{SO}_{4}$ solution is slowly added to 10.0 $\mathrm{mL}$ of a solution that is 0.20 $\mathrm{M}$ in $\mathrm{Ca}^{2+}$ and 0.30 $\mathrm{M}$ in $\mathrm{Ag}^{+} .$ (a) Which compound will precipitate first: $\mathrm{CaSO}_{4}\left(K_{\mathrm{sp}}=2.4 \times 10^{-5}\right)$ or $\mathrm{Ag}_{2} \mathrm{SO}_{4}\left(K_{s p}=1.5 \times 10^{-5}\right) ?(\mathbf{b})$ How much $\mathrm{Na}_{2}
mathrm{SO}_{4}$ solution must be added to initiate the precipitation?

Keenan M.
University of Miami

Problem 77

A solution containing several metal ions is treated with dilute HCl; no precipitate forms. The $\mathrm{pH}$ is adjusted to about $1,$ and $\mathrm{H}_{2} \mathrm{S}$ is bubbled through. Again, no precipitate forms. The $\mathrm{pH}$ of the solution is then adjusted to about $8 .$ Again,
$\mathrm{H}_{2} \mathrm{S}$ is bubbled through. This time a precipitate forms. The filtrate from this solution is treated with $\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4} .$ No precipitate forms. Which of these metal cations are either possibly present or definitely absent: $\mathrm{Al}^{3+}, \mathrm{Na}^{+}, \mathrm{Ag}^{+}, \mathrm{Mg}^{2+} ?$

KC
Kevin C.
Numerade Educator

Problem 78

An unknown solid is entirely soluble in water. On addition of dilute $\mathrm{HCl}$ , a precipitate forms. After the precipitate is filtered off, the pH is adjusted to about 1 and $\mathrm{H}_{2} \mathrm{S}$ is bubbled in; a precipitate again forms. After filtering off this precipitate, the pH is adjusted to 8 and $\mathrm{H}_{2} \mathrm{S}$ is again added; no precipitate forms. No precipitate forms upon addition of $\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}$ . The remaining solution shows a yellow color in a flame test (see Figure 7.22 ). Based on these observations, which of the following compounds might be present, which are definitely present, and which are definitely absent: CdS, Pb $\left(\mathrm{NO}_{3}\right)_{2}, \mathrm{HgO}, \mathrm{ZnSO}_{4}, \mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2},$ and $\mathrm{Na}_{2} \mathrm{SO}_{4} ?$

Keenan M.
University of Miami

Problem 79

In the course of various qualitative analysis procedures, the following mixtures are encountered: (a) $Z n^{2+}$ and $C d^{2}+$ (b) $C r(O H)_{3}$ and $F e(O H)_{3},(\mathbf{c}) M g^{2+}$ and $K^{+},(\mathbf{d}) A g^{+}$ and $M n^{2+} .$ Suggest how each mixture might be separated.

KC
Kevin C.
Numerade Educator

Problem 80

Suggest how the cations in each of the following solution mixtures can be separated: (a) $\mathrm{Na}^{+}$ and $\mathrm{Cd}^{2+},(\mathbf{b}) \mathrm{Cu}^{2+}$ and $\mathrm{Mg}^{2+},(\mathbf{c}) \mathrm{Pb}^{2+}$ and $\mathrm{Al}^{3+},(\mathbf{d}) \mathrm{Ag}^{+}$ and $\mathrm{Hg}^{2+}$ .

Keenan M.
University of Miami

Problem 81

(a) Precipitation of the group 4 cations of Figure 17.23 requires a basic medium. Why is this so? (b) What is the most significant difference between the sulfides precipitated in group 2 and those precipitated in group 3? (c) Suggest a procedure that would serve to redissolve the group 3 cations following their precipitation.

KC
Kevin C.
Numerade Educator

Problem 82

A student who is in a great hurry to finish his laboratory work decides that his qualitative analysis unknown contains a metal ion from group 4 of Figure 17.23. He therefore tests his sample directly with $\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}$, skipping earlier tests for the metal ions in groups 1, 2, and 3. He observes a precipitate and concludes that a metal ion from group 4 is indeedpresent. Why is this possibly an erroneous conclusion?

Keenan M.
University of Miami

Problem 83

Derive an equation similar to the Henderson-Hasselbalch equation relating the pOH of a buffer to the $\mathrm{p} K_{b}$ of its base component.

KC
Kevin C.
Numerade Educator

Problem 84

Rainwater is acidic because $\mathrm{CO}_{2}(\mathrm{g})$ dissolves in the water, creating carbonic acid, $\mathrm{H}_{2} \mathrm{CO}_{3}$ . If the rainwater is too acidic, it will react with limestone and seashells (which are principally made of calcium carbonate, CaCO_ $_{3} ) .$ Calculate the concentrations of carbonic acid, bicarbonate ion $\left(\mathrm{HCO}_{3}^{-}\right)$ and carbonate ion $\left(\mathrm{CO}_{3}^{2-}\right)$ that are in a raindrop that has a pH of 5.60 , assuming that the sum of all three species in the raindrop is $1.0 \times 10^{-5} M .$

Keenan M.
University of Miami

Problem 85

Furoic acid $\left(\mathrm{HC}_{5} \mathrm{H}_{3} \mathrm{O}_{3}\right)$ has a $K_{a}$ value of $6.76 \times 10^{-4}$ at $25^{\circ} \mathrm{C}$ . Calculate the $\mathrm{pH}$ at $25^{\circ} \mathrm{C}$ of (a) a solution formed by adding 25.0 $\mathrm{g}$ of furoic acid and 30.0 $\mathrm{g}$ of sodium furoate $\left(\mathrm{NaC}_{5} \mathrm{H}_{3} \mathrm{O}_{3}\right)$ to enough water to form 0.250 $\mathrm{L}$ of solution, $(\mathbf{b})$ a solution formed by mixing 30.0 $\mathrm{mL}$ of 0.250 $\mathrm{M}$$\mathrm{HC}_{5} \mathrm{H}_{3} \mathrm{O}_{3}$ and 20.0 $\mathrm{mL}$ of 0.22 $\mathrm{M} \mathrm{NaC}_{5} \mathrm{H}_{3} \mathrm{O}_{3}$ and diluting the total volume to $125 \mathrm{mL},(\mathbf{c})$ a solution prepared by adding 50.0 $\mathrm{mL}$ of 1.65 $\mathrm{MNaOH}$ solution to 0.500 $\mathrm{L}$ of 0.0850 $\mathrm{M}$
$\mathrm{HC}_{5} \mathrm{H}_{3} \mathrm{O}_{3} .$

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Problem 86

The acid-base indicator bromcresol green is a weak acid. The yellow acid and blue base forms of the indicator are present in equal concentrations in a solution when the pH is $4.68 .$ What is the p $K_{a}$ for bromcresol green?

Keenan M.
University of Miami

Problem 87

Equal quantities of 0.010$M$ solutions of an acid $\mathrm{HA}$ and a base $\mathrm{B}$ are mixed. The $\mathrm{pH}$ of the resulting solution is $9.2 .$ (a) Write the chemical equation and equilibrium-constant expression for the reaction between $\mathrm{HA}$ and $\mathrm{B}$ . (b) If $K_{a}$ for $\mathrm{HA}$ is $8.0 \times 10^{-5}$ , what is the value of the equilibrium constant for the reaction between $\mathrm{HA}$ and $\mathrm{B} ?$ (c) What is the value of $K_{b}$ for $\mathrm{B}$ ?

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Problem 88

Two buffers are prepared by adding an equal number of moles of formic acid (HCOOH) and sodium formate (HCOONa) to enough water to make 1.00 L of solution. Buffer A is prepared using 1.00 mol each of formic acid and sodium formate. Buffer B is prepared by using 0.010 mol of each. (a) Calculate the pH of each buffer. (b) Which buffer will have the greater buffer capacity? (c) Calculate the change in pH for each buffer upon the addition of 1.0 $\mathrm{mL}$ of 1.00$M$ HCl. (d) Calculate the change in pH for each buffer upon the addition of 10 $\mathrm{mL}$ of 1.00 $\mathrm{M} \mathrm{HCl}$

Keenan M.
University of Miami

Problem 89

A biochemist needs 750 $\mathrm{mL}$ of an acetic acid-sodium acetate buffer with $\mathrm{pH} 4.50 .$ Solid sodium acetate $(\mathrm{CH}_{3}$$ \mathrm{COONa}$ and glacial acetic acid $\left(\mathrm{CH}_{3} \mathrm{COOH}\right)$ are \right. available. Glacial acetic acid is 99$\% \mathrm{CH}_{3} \mathrm{COOH}$ by mass and has a density of 1.05 $\mathrm{g} / \mathrm{mL}$ . If the buffer is to be 0.15 $\mathrm{M}$ in $\mathrm{CH}_{3} \mathrm{COOH}$ , how many grams of $\mathrm{CH}_{3} \mathrm{COONa}$ and how many milliliters of glacial acetic acid must be used?

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Problem 90

A sample of 0.2140 $\mathrm{g}$ of an unknown monoprotic acid was dissolved in 25.0 $\mathrm{mL}$ of water and titrated with 0.0950 $\mathrm{M}$$ \mathrm{NaOH}$. The acid required 30.0 $\mathrm{mL}$ of base to reach the equivalence point. (a) What is the molar mass of the acid? (b) After 15.0 $\mathrm{mL}$ of base had been added in the titration, the pH was found to be $6.50 .$ What is the $K_{a}$ for the unknown acid?

Keenan M.
University of Miami

Problem 91

A sample of 0.1687 gof an unknown monoprotic acid was dissolved in 25.0 mL. of water and titrated with 0.1150 $\mathrm{M}$ NaOH. The acid required 15.5 $\mathrm{mL}$ of base to reach the equivalence point. (a) What is the molar mass of the acid? (b) After 7.25 mL of base had been added in the titration, the pH was found to be $2.85 .$ What is the $K_{a}$ for the unknown acid?

KC
Kevin C.
Numerade Educator

Problem 92

Mathematically prove that the $\mathrm{pH}$ at the halfway point of a titration of a weak acid with a strong base (where the volume of added base is half of that needed to reach the equivalence point) is equal to p $K_{a}$ for the acid.

Keenan M.
University of Miami

Problem 93

A weak monoprotic acid is titrated with 0.100 $\mathrm{M}$ NaOH. It requires 50.0 $\mathrm{mL}$ of the NaOH solution to reach the equivalence point. After 25.0 $\mathrm{mL}$ of base is added, the pH of the solution is $3.62 .$ Estimate the $\mathrm{p} K_{a}$ of the weak acid.

KC
Kevin C.
Numerade Educator

Problem 94

What is the pH of a solution made by mixing 0.30 mol NaOH, 0.25 mol $\mathrm{Na}_{2} \mathrm{HPO}_{4},$ and 0.20 $\mathrm{mol} \mathrm{H}_{3} \mathrm{PO}_{4}$ with water and diluting to 1.00 $\mathrm{L}$ ?

Keenan M.
University of Miami

Problem 95

Suppose you want to do a physiological experiment that calls for a pH 6.50 buffer. You find that the organism with which you are working is not sensitive to the weak acid $\mathrm{H}_{2} \mathrm{A}\left(K_{a 1}=2 \times 10^{-2} ; K_{a 2}=5.0 \times 10^{-7}\right)$ or its sodium salts. You have available a 1.0 $\mathrm{M}$ solution of this acid and a 1.0 $\mathrm{M}$ solution of $\mathrm{NaOH} .$ How much of the NaOH solution should be added to 1.0 $\mathrm{L}$ of the acid to give a buffer at pH 6.50$?$ (Ignore any volume change.)

KC
Kevin C.
Numerade Educator

Problem 96

How many microliters of 1.000$M$ NaOH solution must be added to 25.00 $\mathrm{mL}$ of a 0.1000 $\mathrm{M}$ solution of lactic acid $\left[\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{COOH}$ or $\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{3}\right]$ to produce a buffer with
$\mathrm{pH}=3.75 ?$

Keenan M.
University of Miami

Problem 97

Lead(II) carbonate, PbCO $_{3},$ is one of the components of the passivating layer that forms inside lead pipes.(a) If the $K_{s p}$ for $\mathrm{PbCO}_{3}$ is $7.4 \times 10^{-14}$ what is the molarity of $\mathrm{Pb}^{2+}$ in a saturated solution of lead(II) carbonate? (b) What is the concentration in ppb of $\mathrm{Pb}^{2+}$ ions in a saturated solution? (c) Will the solubility of $\mathrm{PbCO}_{3}$ increase or decrease as the $\mathrm{pH}$ is lowered? $(\boldsymbol{d} )$The EPA threshold for acceptable levels of lead ions in water is 15 ppb. Does a saturated solution of lead(II) carbonate produce a solution that exceeds the EPA limit?

KC
Kevin C.
Numerade Educator

Problem 98

For each pair of compounds, use $K_{s p}$ values to determine which has the greater molar solubility: (a) Cds or Cus, (b) $\mathrm{PbCO}_{3}$ or $\mathrm{BaCrO}_{4}$ (c) $\mathrm{Ni}(\mathrm{OH})_{2}$ or $\mathrm{NiCO}_{3}$ $(\boldsymbol{d} ) AgI or $\mathrm{Ag}_{2} \mathrm{SO}_{4}$

Keenan M.
University of Miami

Problem 99

The solubility of $\mathrm{CaCO}_{3}$ is pH dependent. (a) Calculate the molar solubility of $\mathrm{CaCO}_{3}\left(K_{s p}=4.5 \times 10^{-9}\right)$ neglecting the acid-base character of the carbonate ion. (b) Use the $K_{b}$ expression for the $\mathrm{CO}_{3}^{2-}$ ion to determine the equilibrium constant for the reaction
$$\mathrm{CaCO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons_{\mathrm{Ca}^{2+}(a q)+\mathrm{HCO}_{3}^{-}(a q)+\mathrm{OH}^{-}(a q)}$$
(c) If we assume that the only sources of $\mathrm{Ca}^{2+}, \mathrm{HCO}_{3}^{-}$ and $\mathrm{OH}^{-}$ ions are from the dissolution of $\mathrm{CaCO}_{3},$ what is the molar solubility of $\mathrm{CaCO}_{3}$ using the equilibrium expression from part (b)? $(\boldsymbol{d} )$What is the molar solubility of $\mathrm{CaCO}_{3}$ at the pH of the ocean $(8.3) ?(\mathbf{e})$ If the $\mathrm{pH}$ is buffered at $7.5,$ what is the molar solubility of $\mathrm{CaCO}_{3} ?$

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Problem 100

Tooth enamel is composed of hydroxyapatite, whose simplest formula is $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH}$ , and whose corresponding $K_{\mathrm{sp}}=6.8 \times 10^{-27}$ . As discussed in the Chemistry and Life box on page $746,$ fluoride in fluorinated water or in toothpaste reacts with hydroxyapatite to form fluoroapatite, $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{F},$ whose $K_{s p}=1.0 \times 10^{-60}$ (a) Write the expression for the solubility-constant for hydroxyapatite and for fluoroapatite. (b) Calculate the molar solubility of each of these compounds.

Keenan M.
University of Miami

Problem 101

Salts containing the phosphate ion are added to municipal water supplies to prevent the corrosion oflead pipes. (a) Based on the $\mathrm{pK}_{a}$ values for phosphoric acid $\left(\mathrm{pK}_{a 1}=7.5 \times 10^{-3} , \right.$ $\mathrm{p} K_{a 2}=6.2 \times 10^{-8}, \mathrm{p} K_{a 3}=4.2 \times 10^{-13} )$ what is the $\mathrm{K}_{b}$ value for the $\mathrm{PO}_{4}^{3-}$ ion? (b) What is the pH of a $1 \times 10^{-3}$ $M$ solution of $\mathrm{Na}_{3} \mathrm{PO}_{4}$ (you can ignore the formation of $\mathrm{H}_{2} \mathrm{PO}_{4}^{-}$ and $\mathrm{H}_{3} \mathrm{PO}_{4} ) ?$

KC
Kevin C.
Numerade Educator

Problem 102

Calculate the solubility of $\mathrm{Mg}(\mathrm{OH})_{2}$ in 0.50 $\mathrm{MNH}_{4} \mathrm{Cl}$

Keenan M.
University of Miami

Problem 103

The solubility-product constant for barium permanganate, $\mathrm{Ba}\left(\mathrm{MnO}_{4}\right)_{2},$ is $2.5 \times 10^{-10}$ . Assume that solid $\mathrm{Ba}\left(\mathrm{MnO}_{4}\right)_{2}$ is in equilibrium with a solution of $\mathrm{KMnO}_{4} .$ What concentration of $\mathrm{KMnO}_{4}$ is required to establish a concentration of $2.0 \times 10^{-8} \mathrm{M}$ for the $\mathrm{Ba}^{2+}$ ion in solution?

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Problem 104

Calculate the ratio of $\left[\mathrm{Ca}^{2+}\right]$ to $\left[\mathrm{Fe}^{2+}\right]$ in a lake in which
the water is in equilibrium with deposits of both $\mathrm{CaCO}_{3}$ and $\mathrm{FeCO}_{3}$ . Assume that the water is slightly basic and that the hydrolysis of the carbonate ion can therefore be ignored.

Keenan M.
University of Miami

Problem 105

The solubility product constants of $\mathrm{PbSO}_{4}$ and $\mathrm{SrSO}_{4}$ are $6.3 \times 10^{-7}$ and $3.2 \times 10^{-7}$ , respectively. What are the values of $\left[\mathrm{SO}_{4}^{2-}\right],\left[\mathrm{Pb}^{2+}\right],$ and $\left[\mathrm{Sr}^{2+}\right]$ in a solution at equilibrium with both substances?

KC
Kevin C.
Numerade Educator

Problem 106

A buffer of what $\mathrm{pH}$ is needed to give a Mg $^{2+}$ concentration of $3.0 \times 10^{-2} \mathrm{M}$ in equilibrium with solid magnesium oxalate?

Keenan M.
University of Miami

Problem 107

The value of $K_{s p}$ for $\mathrm{Mg}_{3}\left(\mathrm{AsO}_{4}\right)_{2}$ is $2.1 \times 10^{-20}$ . The $\mathrm{AsO}_{4}^{3-}$ ion is derived from the weak acid $\mathrm{H}_{3} \mathrm{AsO}_{4}\left(\mathrm{pK}_{a 1}=\right.$ $2.22 ; \mathrm{p} K_{a 2}=6.98 ; \mathrm{p} K_{a 3}=11.50 )$ . (a) Calculate the molar solubility of $\mathrm{Mg}_{3}\left(\mathrm{AsO}_{4}\right)_{2}$ in water. (b) Calculate the pH of a saturated solution of $\mathrm{Mg}_{3}\left(\mathrm{AsO}_{4}\right)_{2}$ in water.

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Problem 108

The solubility product for Zn (OH) $_{2}$ is $3.0 \times 10^{-16} .$ The formation constant for the hydroxo complex, Zn (OH) $_{4}^{2-}$ , is 4.6 $\times 10^{17} .$ What concentration of $\mathrm{OH}^{-}$ is required to dissolve 0.015 mol of $\mathrm{Zn}(\mathrm{OH})_{2}$ in a liter of solution?

Keenan M.
University of Miami

Problem 109

The value of $K_{s p}$ for $\mathrm{Cd}(\mathrm{OH})_{2}$ is $2.5 \times 10^{-14} .$ (a) What is the molar solubility of $\mathrm{Cd}(\mathrm{OH})_{2} ?$ $(\mathbf{b} ) $The solubility of $\mathrm{Cd}(\mathrm{OH})_{2}$ can be increased through formation of the complex ion $\mathrm{CdBr}_{4}^{2-}\left(K_{f}=5 \times 10^{3}\right) .$ If solid $\mathrm{Cd}(\mathrm{OH})_{2}$ is added to a NaBr solution, what is the initial concentration of NaBr needed to increase the molar solubility of $\mathrm{Cd}(\mathrm{OH})_{2}$ to $1.0 \times 10^{-3} \mathrm{mol} / \mathrm{L} ?$

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Problem 110

(a) Write the net ionic equation for the reaction that occurs when a solution of hydrochloric acid (HCl) is mixed with a solution of sodium formate (NaCHO $_{2} )$ . (b) Calculate the equilibrium constant for this reaction. (c) Calculate the equilibrium concentrations of $\mathrm{Na}^{+}, \mathrm{Cl}^{-}, \mathrm{H}^{+}, \mathrm{CHO}_{2}^{-}$ and $\mathrm{HCHO}_{2}$ when 50.0 $\mathrm{mL}$ of 0.15 $\mathrm{MCl}$ is mixed with 50.0 $\mathrm{mL}$ of 0.15 $\mathrm{MNaCHO}_{2} .$

Keenan M.
University of Miami

Problem 111

(a) $\mathrm{A} .0 .1044$ -g sample of an unknown monoprotic acid requires 22.10 $\mathrm{mL}$ of 0.0500 $\mathrm{MNaOH}$ to reach the end point. What is the molar mass of the unknown? (b) As the acid is titrated, the pH of the solution after the addition of 11.05 $\mathrm{mL}$ of the base is $4.89 .$ What is the $K_{a}$ for the acid? (c) Using Appendix D, suggest the identity of the acid.

KC
Kevin C.
Numerade Educator

Problem 112

A sample of 7.5 $\mathrm{L}$ of $\mathrm{NH}_{3}$ gas at $22^{\circ} \mathrm{C}$ and 735 torr is bubbled into a 0.50 -L solution of 0.40 $\mathrm{M}$ HCl. Assuming that all the $\mathrm{NH}_{3}$ dissolves and that the volume of the solution remains $0.50 \mathrm{L},$ calculate the $\mathrm{pH}$ of the resulting solution.

Keenan M.
University of Miami

Problem 113

Aspirin has the structural formula
At body temperature $\left(37^{\circ} \mathrm{C}\right), K_{a}$ for aspirin equals $3 \times 10^{-5} .$ If two aspirin tablets, each having a mass of $325 \mathrm{mg},$ are dissolved in a full stomach whose volume is 1 $\mathrm{L}$ and whose $\mathrm{pH}$ is $2,$ what percent of the aspirin is in the
form of neutral molecules?

KC
Kevin C.
Numerade Educator

Problem 114

What is the $\mathrm{pH}$ at $25^{\circ} \mathrm{C}$ of water saturated with $\mathrm{CO}_{2}$ at a
partial pressure of 1.10 atm? The Henry's law constant for $\mathrm{CO}_{2}$ at $25^{\circ} \mathrm{C}$ is $3.1 \times 10^{-2} \mathrm{mol} / \mathrm{L}$ -atm.

Keenan M.
University of Miami

Problem 115

Excess $\mathrm{Ca}(\mathrm{OH})_{2}$ is shaken with water to produce a saturated solution. The solution is filtered, and a 50.00 -mL sample titrated with HCl requires 11.23 $\mathrm{mL}$ of 0.0983$M \mathrm{HCl}$ to reach the end point. Calculate $K_{s p}$ for $\mathrm{Ca}(\mathrm{OH})_{2}$ . Compare your result with that in Appendix D. Suggest a reason for any differences you find between your value and the one in Appendix D.

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Problem 116

The osmotic pressure of a saturated solution of strontium sulfate at $25^{\circ} \mathrm{C}$ is 21 torr. What is the solubility product of this salt at $25^{\circ} \mathrm{C} ?$

Keenan M.
University of Miami

Problem 117

A concentration of 10–100 parts per billion (by mass) of Ag+ is an effective disinfectant in swimming pools. However, if the concentration exceeds this range, the Ag+ can cause adverse health effects. One way to maintain an appropriate concentration of Ag+ is to add a slightly soluble salt to the pool. Using $K_{s p}$ values from Appendix $\mathrm{D},$ calculate the the equilibrium concentration of Ag+ in parts per billion that would exist in equilibrium with (a) $\mathrm{AgCl},(\mathbf{b}) \mathrm{AgBr},(\mathbf{c}) \mathrm{AgI}$

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Problem 118

Fluoridation of drinking water is employed in many places to aid in the prevention of tooth decay. Typically. the F- ion concentration is adjusted to about 1 ppm. Some water supplies are also "hard"; that is, they contain certain cations such as $\mathrm{Ca}^{2+}$ that interfere with the action of soap. Consider a case where the concentration of $\mathrm{Ca}^{2+}$ is 8 ppm. Could a precipitate of $\mathrm{CaF}_{2}$ form under these conditions? (Make any necessary approximations.)

Keenan M.
University of Miami

Problem 119

Baking soda (sodium bicarbonate, $\mathrm{NaHCO}_{3}$) reacts with acids in foods to form carbonic acid ($\mathrm{H}_{2} \mathrm{CO}_{3}$), which in turn decomposes to water and carbon dioxide gas. In a cake batter, the $\mathrm{CO}_{2}(g)$ forms bubbles and causes the cake to rise. (a) A rule of thumb in baking is that 1$/ 2$ teaspoon of baking soda is neutralized by one cup of sour milk. The acid component in sour milk is lactic acid, $\mathrm{CH}_{3} \mathrm{CH (\mathrm{OH}) $\mathrm{COOH}$ .Write the chemical equation for this neutralization reaction. (b) The density of baking soda is 2.16 $\mathrm{g} / \mathrm{cm}^{3} .$ Calculate the concentration of lactic acid in one cup of sour milk(assuming the rule of thumb applies), in units of mol/L. (One cup $=236.6 \mathrm{mL}=48$ teaspoons). (c) If 1/2 teaspoon of baking soda is indeed completely neutralized by the lactic acid in sour milk, calculate the volume of carbon dioxide gas that would be produced at 1 atm pressure, in an oven set to $350^{\circ} \mathrm{F}$ .

KC
Kevin C.
Numerade Educator

Problem 120

In nonaqueous solvents, it is possible to react HF to create $\mathrm{H}_{2} \mathrm{F}^{+} .$ Which of these statements follows from this observation? (a) HF can act like a strong acid in nonaqueous solvents, (b) HF can act like a base in nonaqueous solvents,(c) HF is thermodynamically unstable, (d) There is an acid in the nonaqueous medium that is a stronger acid than HE:

Keenan M.
University of Miami