Chapter 17

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]

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.

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?

(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.

(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.

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 \(\mathrm{c} .\)

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 \(\mathrm{M} \mathrm{KCl}\) .

(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 \(\mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3} .\)

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.

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.

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.

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 \(\mathrm{HNO}_{3} ?\)

(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\(?\)

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?

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?

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.

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.

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.

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?

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?

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?

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 \(\mathrm{mL}\) \((\mathbf{b}) 19.9 \mathrm{mL},(\mathbf{c}) 20.0 \mathrm{mL},(\mathbf{d}) 20.1 \mathrm{mL},(\mathbf{e}) 35.0 \mathrm{mL}\)

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 \(\mathrm{mL}\) \((\mathbf{c}) 24.0 \mathrm{mL},(\mathbf{d}) 25.0 \mathrm{mL},(\mathbf{e}) 30.0 \mathrm{mL}\)

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) \(17.5 \mathrm{mL},(\mathrm{c}) 34.5 \mathrm{mL},(\mathbf{d}) 35.0 \mathrm{mL},(\mathbf{e}) 35.5 \mathrm{mL},(\mathbf{f}) 50.0 \mathrm{mL}\)

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 \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\right)\)

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 \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)\)

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.

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, \(\mathrm{M}^{2+}\) ?

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

(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 \(\mathrm{Cu}_{3}\left(\mathrm{PO}_{4}\right)_{2} .\)

(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 \(\mathrm{Ba}\left(\mathrm{IO}_{3}\right)_{2} ?\)

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 \(25^{\circ} \mathrm{C}\) .

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 \(25^{\circ} \mathrm{C}\) .

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?

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?

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

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.

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.

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: \(\mathrm{Ag}_{2} \mathrm{S}(s)+4 \mathrm{Cl}^{-}(a q)+2 \mathrm{H}^{+}(a q) \rightleftharpoons 2 \mathrm{AgCl}_{2}^{-}(a q)+\mathrm{H}_{2} \mathrm{S}(a q)\)

(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?

(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 \(3.1 \times 10^{8}\))?

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.

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?

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 \(\mathrm{AgCl}\left(K_{s p}=1.8 \times 10^{-10}\right) ?\)

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: \(\mathrm{Al}^{3+}, \mathrm{Na}^{+}, \mathrm{Ag}^{+}, \mathrm{Mg}^{2+} ?\)

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 \(\mathrm{Hg}^{2+}\) .

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.

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 \(1.0 \times 10^{-5} M .\)

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?

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 \(\mathrm{B}\) ?