Chapter 17

A buffer contains a weak acid, HA, and its conjugate base. The weak acid has a \(\mathrm{p} K_{a}\) of \(4.5\), and the buffier has a \(\mathrm{pH}\) of 4.3. Without doing a calculation, state which of these possibilities are correct. (a) \([\mathrm{HA}]=\left[\mathrm{A}^{-}\right]\), (b) \([\mathrm{HA}]>\left[\mathrm{A}^{-}\right]\), or (c) \([\mathrm{HA}]<\left[\mathrm{A}^{-}\right]\). [Section 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 \(\mathrm{M}^{+}\)or \(A^{-}\). (b) Common ions alter the equilibrium constant for the reaction of an ionic

Consider the equilibrium $$ \mathrm{B}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{HB}^{+}(a q)+\mathrm{OH}^{-}(a q) \text {. } $$ Suppose that a salt of \(\mathrm{HB}^{+}\)is added to a solution of \(\mathrm{B}\) 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 \(0.0075 \mathrm{M}\) butanoic acid \(\left(K_{a}=1.5 \times 10^{-5}\right)\). (b) Calculate the percent ionization of \(0.0075 \mathrm{M}\) butanoic acid in a solution containing \(0.085 \mathrm{M}\) sodium butanoate.

(a) Calculate the percent ionization of \(0.125 \mathrm{M}\) lactic acid \(\left(K_{a}=1.4 \times 10^{-4}\right)\). (b) Calculate the percent ionization of \(0.125 \mathrm{M}\) lactic acid in a solution containing \(0.0075 \mathrm{M}\) sodium lactate. Buffers (Section 17.2)

Which of the following solutions is a buffer? (a) \(0.10 \mathrm{M}\) \(\mathrm{CH}_{3} \mathrm{COOH}\) and \(0.10 \mathrm{MCH}_{3} \mathrm{COONa}\), (b) \(0.10 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\), (c) \(0.10 \mathrm{M} \mathrm{HCl}\) and \(0.10 \mathrm{M} \mathrm{NaCl}\), (d) both a and \(c_{1}\) (e) all of a, b, and \(c\).

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

\( A buffer is prepared by adding \)20.0 \mathrm{~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

A buffer is prepared by adding \(10.0 \mathrm{~g}\) of ammonium chloride \(\left(\mathrm{NH}_{4} \mathrm{C}\right.\) ) to \(250 \mathrm{~mL}\) of \(1.00 \mathrm{M} \mathrm{NH}_{3}\) solution. (a) What is the \(\mathrm{pH}\) 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 pH \(=3.00\) buffer solution starting from \(1.25 \mathrm{~L}\) of a \(1.00 \mathrm{M}\) solution of hydrofluoric acid (HF) and any amount you need of sodium fluoride (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.

You are asked to prepare a pH \(=4.00\) buffer starting from \(1.50 \mathrm{~L}\) of \(0.0200 \mathrm{M}\) solution of benzoic acid \(\left(\mathrm{C}_{4} \mathrm{H}_{4} \mathrm{COOH}\right)\) and any amount you need of sodium benzoate \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COONa}\right)\). (a) What is the \(\mathrm{pH}\) 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.

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 \(\mathrm{pH}\) of this buffer? (b) What is the \(\mathrm{pH}\) of the buffer after the addition of \(0.02 \mathrm{~mol}\) 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 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 \(\mathrm{HI} ?\)

(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 \(\mathrm{H}_{3} \mathrm{CO}_{3}\) in an exhausted marathon runner whose blood \(\mathrm{pH}\) is \(7.1\) ?

You have to prepare a \(\mathrm{pH} 3.50\) buffer, and you have the following \(0.10 \mathrm{M}\) 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 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 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 \(\mathrm{pH}\) 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 \(\mathrm{pH} 7\) : (a) \(\mathrm{NaHCO}_{3}\) titrated with \(\mathrm{NaOH}\), (b) \(\mathrm{NH}_{3}\) titrated with \(\mathrm{HCl}\), (c) \(\mathrm{KOH}\) titrated with HBr.

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?

Assume that \(30.0 \mathrm{~mL}\) of a \(0.10 \mathrm{M}\) solution of a weak base B that accepts one proton is titrated with a \(0.10 \mathrm{M}\) 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? (c) Is the pH 7, less than 7, or more than 7 at the equivalence point? (d) Which indicator, phenolphthalein or methyl red, is likely to be the better choice for this titration?

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

How many milliliters of \(0,105 \mathrm{M} \mathrm{HCl}\) are needed to titrate each of the following solutions to the equivalence point: (a) \(45.0 \mathrm{~mL}\). of \(0.0950 \mathrm{M} \mathrm{NaOH}\), (b) \(22.5 \mathrm{~mL}\), of \(0.118 \mathrm{M} \mathrm{NH}_{3}\), (c) \(125.0 \mathrm{~mL}\). of a solution that contains \(1.35 \mathrm{~g}\) of \(\mathrm{NaOH}\) per liter?

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

\mathrm{~A} 20.0\( - \)\mathrm{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}\(, (c) \)24.0 \mathrm{~mL}\(. (d) \)25.0 \mathrm{~mL}\( (e) \)30.0 \mathrm{~mL}$

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

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

Calculate the \(\mathrm{pH}\) at the equivalence point for titrating \(0.200 \mathrm{M}\) solutions of each of the following bases with \(0.200 \mathrm{M} \mathrm{HBr}\) : (a) sodium hydroxide \((\mathrm{NaOH})\), (b) hydroxylamine \(\left(\mathrm{NH}_{2} \mathrm{OH}\right)\), (c) aniline \(\left(\mathrm{C}_{6} \mathrm{H}_{3} \mathrm{NH}_{2}\right)\).

Calculate the \(\mathrm{pH}\) at the equivalence point in titrating \(0.100 \mathrm{M}\) solutions of each of the following with \(0.080 \mathrm{M} \mathrm{NaOH}\) : (a) hydrobromic acid (HBr), (b) chlorous acid \(\left(\mathrm{HClO}_{2}\right)\), (c) benzoic acid ( \(\left.\mathrm{C}_{4} \mathrm{H}_{3} \mathrm{COOH}\right)\).

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 \(\mathrm{MZ}_{2}\) are 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 \(\mathrm{MA}\) to one saturated in \(\mathrm{MZ}_{2}\), what would be the equilibrium concentration of the cation, \(\mathrm{M}^{2+}\) ?

(a) Why is the concentration of undissolved solid not explicitly included in the expression for the solubility-product constant? (b) Write the expression for the solubility-product constant for cach of the following strong electrolytes: \(\mathrm{AgI}_{1} \mathrm{SrSO}_{4}, \mathrm{Fe}(\mathrm{OH})_{2}\), and \(\mathrm{Hg}_{2} \mathrm{Br}_{1}\). ?

(a) True or false: "solubility" and "solubility-product con. stant" are the same number for a given compound. (b) Write the expression for the solubility- product constant for each of the following ionic compounds: \(\mathrm{MnCO}_{3}, \mathrm{Hg}(\mathrm{OH})_{2}\), 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 \(K_{\text {sp }}\) 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 \(\mathrm{SrF}_{2}\). (c) The \(K_{\text {pp }}\) 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) The molar solubility of \(\mathrm{PbBr}_{2}\) at \(25^{\circ} \mathrm{C}\) is \(1.0 \times 10^{-2} \mathrm{~mol} / \mathrm{L}\) Calculate \(K_{\mathrm{sp}}\). (b) If \(0.0490 \mathrm{~g}\) of \(\mathrm{AgIO}_{3}\) dissolves per liter of solution, calculate the solubility-product constant. (c) Using the appropriate \(K_{1 p}\) value from Appendix D, calculate the \(\mathrm{pH}\) of a saturated solution of \(\mathrm{Ca}(\mathrm{OH})_{2}\) -

A 1.00- \(\mathrm{L}\) 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(II) 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 \(\mathrm{Ca}^{2+}\) lons in solution increase or decrease? (c) Will the concentration of \(F^{-}\)ions in solution increase or decrease?

Consider a beaker containing a saturated solution of \(\mathrm{Pbl}_{2}\) in equilibrium with undissolved \(\mathrm{Pbl}_{2}(s)\). Now solid KI is added to this solution. (a) Will the amount of solid \(\mathrm{Pbl}_{2}\) 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 \(1^{-}\)ions in solution increase or decrease?

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

Which of the following salts will be substantially more soluble in acidic solution than in pure water: (a) \(\mathrm{ZnCO}_{3^{*}}\) (b) \(\mathrm{ZnS}\), (c) \(\mathrm{Bil}_{3}\) (d) \(\mathrm{AgCN}_{4}\), (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, (b) \(\mathrm{PbF}_{2}\), (c) \(\mathrm{AuCl}_{3}\) (d) \(\mathrm{Hg}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) (e) \(\mathrm{CuBr}\).

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 \(\mathrm{MN} \mathrm{H}_{3}(a q) .\)

To what final concentration of \(\mathrm{NH}_{3}\) must a solution be adjusted to just dissolve \(0.020 \mathrm{~mol}\) of \(\mathrm{NiC}_{2} \mathrm{O}_{4}\left(K_{u p}=4 \times 10^{-10}\right)\) in 1.0 L of solution? (Hint: You can neglect the hydrolysis of \(\mathrm{C}_{2} \mathrm{O}_{4}{\underline{\phantom{xx}}}^{2-}\) because the solution will be quite basic.)

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

(a) Will \(\mathrm{Co}(\mathrm{OH})_{2}\) precipitate from solution if the pH of a \(0.020 \mathrm{M}\) solution of \(\mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2}\) is adjusted to \(8.5\) ? (b) Will \(\mathrm{AgIO}_{3}\) precipitate when \(20 \mathrm{~mL}\) of \(0.010 \mathrm{M} \mathrm{AgIO}\) is mixed with \(10 \mathrm{~mL}\) of \(0.015 \mathrm{M} \mathrm{NalO}_{3}\) ? \(\left(K_{4}\right.\) of \(\mathrm{AglO}_{3}\) is \(\left.3.1 \times 10^{-t}\right)\).

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

A solution contains \(2.0 \times 10^{-4} \mathrm{MAg}^{+}\)and \(1.5 \times 10^{-3} \mathrm{M} \mathrm{Pb}^{2+}\). If \(\mathrm{NaI}\) is added, will \(\mathrm{AgI}^{\mathrm{I}}\left(K_{4 p}=8.3 \times 10^{-17}\right)\) or \(\mathrm{PbI}_{2}\) \(\left(K_{\text {sp }}=7.9 \times 10^{-9}\right)\) precipitate first? Specify the concentration of \(I^{-}\)needed to begin precipitation.

\mathrm{~A}\( solution of \)\mathrm{Na}_{2} \mathrm{SO}_{4}\( is added dropwise to a solution that is \)0.010 \mathrm{M}_{\text {in } \mathrm{Ba}^{2+}}\( and \)0.010 \mathrm{M}\( in \)\mathrm{Sr}^{2+}\(. (a) What concentration of \)\mathrm{SO}_{4}^{2-}\( is necessary to begin precipitation? (Neglect volume changes, \)\mathrm{BaSO}_{4} ; K_{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-}$ when the second cation begins to precipitate?

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

A \(1.0 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}\) solution is slowly added to \(10.0 \mathrm{~mL}\) of a solution that is \(0.20 \mathrm{M}^{\text {in } \mathrm{Ca}^{++}}\)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 \(\mathrm{Ag}_{3} \mathrm{SO}_{4}\left(K_{p}=1.5 \times 10^{-5}\right)\) ? (b) How much \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) solution must be added to initiate the precipitation