Chapter 17

A buffer contains a weak acid, \(\mathrm{HX}\), and its conjugate base. The weak acid has a \(\mathrm{pK}_{a}\) of \(4.5\), and the buffer solution has a pH of 4.3. Without doing a calculation, predict whether \([\mathrm{HX}]=\left[\mathrm{X}^{-}\right],[\mathrm{HX}]>\left[\mathrm{X}^{-}\right]\), or \([\mathrm{HX}]<\left[\mathrm{X}^{-}\right]\) Explain. [Section 17.2]

(a) What is the common-ion effect? (b) Give an example of a salt that can decrease the ionization of \(\mathrm{HNO}_{2}\) in solution.

Use information from Appendix D to calculate the \(\mathrm{pH}\) of (a) a solution that is \(0.060 \mathrm{M}\) in potassium propionate \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOK}\right.\) or \(\left.\mathrm{KC}_{3} \mathrm{H}_{5} \mathrm{O}_{2}\right)\) and \(0.085 \mathrm{Min}\) propionic acid \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOH}\right.\) or \(\left.\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{2}\right) ;\) (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, \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{NHCl} ;\) (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.

Use information from Appendix \(\mathrm{D}\) to calculate the \(\mathrm{pH}\) of (a) a solution that is \(0.150 \mathrm{M}\) in sodium formate \((\mathrm{HCOONa})\) and \(0.200 \mathrm{M}\) in formic acid \((\mathrm{HCOOH})\) (b) a solution that is \(0.210 \mathrm{M}\) in pyridine \(\left(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N}\right)\) and \(0.350 \mathrm{M}\) in pyridinium chloride \(\left(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{NHCl}\right) ;\) (c) a solution that is made by combining \(125 \mathrm{~mL}\) of \(0.050 \mathrm{M}\) hydrofluoric acid with \(50.0 \mathrm{~mL}\) of \(0.10 \mathrm{M}\) sodium fluoride.

(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 \(0.0075 \mathrm{M}\) butanoic acid in a solution containing \(0.085 \mathrm{M}\) sodium butanoate.

(a) Calculate the percentionization of \(0.085 \mathrm{M}\) lactic acid \(\left(K_{a}=1.4 \times 10^{-4}\right) .\) (b) Calculate the percent ionization of \(0.095 M\) lactic acid in a solution containing \(0.0075 M\) sodium lactate.

Explain why a mixture of \(\mathrm{CH}_{3} \mathrm{COOH}\) and \(\mathrm{CH}_{3} \mathrm{COONa}\) can act as a buffer while a mixture of \(\mathrm{HCl}\) and \(\mathrm{NaCl}\) cannot.

Explain why a mixture formed by mixing \(100 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\) and \(50 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{NaOH}\) will act as a buffer.

(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 \(\mathrm{pH}\) 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 \(20.0 \mathrm{~g}\) of acetic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) and \(20.0 \mathrm{~g}\) of sodium acetate \(\left(\mathrm{CH}_{3} \mathrm{COONa}\right)\) to enough water to form \(2.00 \mathrm{~L}\) of solution. (a) Determine the \(\mathrm{pH}\) 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 \(7.00 \mathrm{~g}\) of ammonia \(\left(\mathrm{NH}_{3}\right)\) and \(20.0 \mathrm{~g}\) of ammonium chloride \(\left(\mathrm{NH}_{4} \mathrm{Cl}\right)\) to enough water to form \(2.50 \mathrm{~L}\) of 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.

How many grams of sodium lactate \(\left[\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{COONa}\right.\) or \(\left.\mathrm{NaC}_{3} \mathrm{H}_{5} \mathrm{O}_{3}\right]\) should be added to \(1.00 \mathrm{~L}\) of \(0.150 \mathrm{M}\) lactic acid \(\left[\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{COOH}\right.\) or \(\left.\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{3}\right]\) to form a buffer solution with \(\mathrm{pH} 4.00\) ? Assume that no volume change occurs when the sodium lactate is added.

A buffer solution contains \(0.10 \mathrm{~mol}\) of acetic acid and $0.13 \mathrm{~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 \(0.02\) mol of KOH? (c) What is the 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 \(\mathrm{pH}\) is \(7.1 ?\)

A buffer, consisting of \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) and \(\mathrm{HPO}_{4}^{2-}\), helps control the \(\mathrm{pH}\) of physiological fluids. Many carbonated soft drinks also use this buffer system. What is the \(\mathrm{pH}\) of a soft drink in which the major buffer 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?

You have to prepare a pH \(3.50\) buffer, and you have the \(\begin{array}{llll}\text { following } & 0.10 & M & \text { solutions } & \text { available: } & \text { HCOOH, }\end{array}\) \(\mathrm{CH}_{3} \mathrm{COOH}, \mathrm{H}_{3} \mathrm{PO}_{4}, \mathrm{HCOONa}, \mathrm{CH}_{3} \mathrm{COONa}\), and \(\mathrm{NaH}_{2} \mathrm{PO}_{4}\). Which solutions would you use? How many milliliters of each solution would you use to make approximately a liter of the buffer?

You have to prepare a \(\mathrm{pH} 4.80\) buffer, and you have the following \(0.10 \mathrm{M}\) solutions available: formic acid, sodium formate, propionic acid, sodium propionate, phosphoric acid, and sodium dihydrogen phosphate. Which solutions would you use? How many milliliters of each solution would you use to make approximately a liter of the buffer?

How does titration of a strong, monoprotic acid with a strong base differ from titration of a weak, monoprotic acid with a strong base with respect to the following: (a) quantity of base required to reach the equivalence point, (b) \(\mathrm{pH}\) at the beginning of the titration, (c) \(\mathrm{pH}\) at the equivalence point, (d) pH after addition of a slight excess of base, (e) choice of indicator for determining the equivalence point?

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

Predict whether the equivalence point of each of the following titrations is below, above, or at pH 7: (a) formic acid titrated with \(\mathrm{NaOH}\), (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 B that accepts one proton is titrated with a \(0.10 \mathrm{M}\) solution of the monoprotic strong acid \(\mathrm{HX}\). (a) How many moles of \(\mathrm{H} X\) have been added at the equivalence point? (b) What is the predominant form of \(B\) at the equivalence point? (c) What factor determines the \(\mathrm{pH}\) 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 \(0.0900 \mathrm{M} \mathrm{HNO}_{3}\), (b) \(35.0 \mathrm{~mL}\) of \(0.0850 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\), (c) \(50.0 \mathrm{~mL}\) of a solution that con- tains \(1.85 \mathrm{~g}\) 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-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) \(15.0 \mathrm{~mL}\), (b) \(19.9 \mathrm{~mL}\), (c) \(20.0 \mathrm{~mL}\), (d) \(20.1 \mathrm{~mL}\), (e) \(35.0 \mathrm{~mL}\).

A \(30.0-\mathrm{mL}\) 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) \(30.0 \mathrm{~mL}\), (b) \(35.0 \mathrm{~mL}\), (c) \(36.0 \mathrm{~mL}\), (d) \(37.0 \mathrm{~mL}\), (e) \(40.0 \mathrm{~mL}\).

A \(35.0-\mathrm{mL}\) 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: (d) \(35.0 \mathrm{~mL},(\mathrm{e}) \overline{35.5 \mathrm{~mL}}\) (a) \(0 \mathrm{~mL}\), (b) \(17.5 \mathrm{~mL}\), (c) \(34.5 \mathrm{~mL}\), (f) \(50.0 \mathrm{~mL}\).

Consider the titration of \(30.0 \mathrm{~mL}\) of \(0.030 \mathrm{M} \mathrm{NH}_{3}\) 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) \(10.0 \mathrm{~mL}\), (c) \(20.0 \mathrm{~mL}\), (d) \(35.0 \mathrm{~mL}\), (e) \(36.0 \mathrm{~mL}\), (f) \(37.0 \mathrm{~mL}\).

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

Calculate the \(\mathrm{pH}\) at the equivalence point in titrating \(0.100 \mathrm{M}\) solutions of each of the following with \(0.080 \mathrm{M}\) \(\mathrm{NaOH}:\) (a) hydrobromic acid \((\mathrm{HBr})\), (b) lactic acid \(\left[\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{COOH}\right]\), (c) sodium hydrogen chromate \(\left(\mathrm{NaHCrO}_{4}\right)\)

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

(a) Explain the difference between solubility and solubility-product constant. (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 \(K_{s p}\) at this temperature? (b) It is found that \(1.1 \times 10^{-2} \mathrm{~g}\) of \(\mathrm{Sr} \mathrm{F}_{2}\) dissolves per \(100 \mathrm{~mL}\) of aqueous solution at \(25^{\circ} \mathrm{C}\). Calculate the solubility product for \(\mathrm{SrF}_{2}\). (c) The \(K_{s p}\) 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) The molar solubility of \(\mathrm{PbBr}_{2}\) at \(25^{\circ} \mathrm{C}\) is \(1.0 \times 10^{-2} \mathrm{~mol} / \mathrm{L}\). Calculate \(K_{s p^{2}}\) (b) If \(0.0490 \mathrm{~g}\) of \(\mathrm{AgIO}_{3}\) dissolves per liter of solution, calculate the solubilityproduct constant. (c) Using the appropriate \(K_{s p}\) value from Appendix D, calculate the solubility of \(\mathrm{Cu}(\mathrm{OH})_{2}\) in grams per liter of solution.

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(II) iodide contains \(0.54 \mathrm{~g}\) of \(\mathrm{PbI}_{2}\). Calculate the solubility- product constant for this salt at \(25^{\circ} \mathrm{C}\).

Calculate the molar solubility of \(\mathrm{Fe}(\mathrm{OH})_{2}\) 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) \(\mathrm{ZnS},(\mathrm{c}) \mathrm{BiI}_{3}\) (d) \(\mathrm{AgCN}\), (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 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 Curt in \(1.0 \mathrm{~L}\) of a solution that contains a total of \(1 \times 10^{-3} \mathrm{~mol}\) of copper(II) ion and that is \(0.10 \mathrm{M}\) in \(\mathrm{NH}_{3}\).

To what final concentration of \(\mathrm{NH}_{3}\) must a solution be adjusted to just dissolve \(0.020 \mathrm{~mol}\) of \(\mathrm{NiC}_{2} \mathrm{O}_{4}\) \(\left(K_{s p}=4 \times 10^{-10}\right)\) in \(1.0 \mathrm{~L}\) 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.)

By using the values of \(K_{s p}\) for \(\mathrm{AgI}\) and \(K_{f}\) for \(\mathrm{Ag}(\mathrm{CN})_{2}^{-}\), calculate the equilibrium constant for the reaction $$ \mathrm{AgI}(\mathrm{s})+2 \mathrm{CN}^{-}(a q) \rightleftharpoons \mathrm{Ag}(\mathrm{CN})_{2}^{-}(a q)+\mathrm{I}^{-}(a q) $$

(a) Will \(\mathrm{Ca}(\mathrm{OH})_{2}\) precipitate from solution if the \(\mathrm{pH}\) 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 \(0.050 \mathrm{M} \mathrm{AgNO}_{3}\) 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 \(\mathrm{pH}\) 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 \(0.010 \mathrm{M} \mathrm{AgNO}_{3}\) is mixed with \(10 \mathrm{~mL}\) of \(0.015 \mathrm{M} \mathrm{NaIO}_{3} ?\left(K_{s p}\right.\) of \(\mathrm{AgIO}_{3}\) is \(3.1 \times 10^{-8}\).)

A solution contains \(20 \times 10^{-4} \mathrm{M} \mathrm{Ag}^{+}\) and \(1.5 \times 10^{-3} \mathrm{M} \mathrm{Pb}^{2+}\). If NaI is added, will AgI \(\left(K_{s p}=8.3 \times 10^{-17}\right)\) or \(\mathrm{PbI}_{2}\left(K_{s p}=7.9 \times 10^{-9}\right)\) precipi- tate first? Specify the concentration of \(\mathrm{I}^{-}\) needed to begin precipitation.

A solution of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is added dropwise to a solution that is \(0.010 \mathrm{M}\) in \(\mathrm{Ba}^{2+}\) and \(0.010 \mathrm{M}\) in \(\mathrm{Sr}^{2+}\). (a) What concentration of \(\mathrm{SO}_{4}{\underline{\phantom{xx}}}^{2-}\) is necessary to begin precipita- tion? (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 precipi- tates first? (c) What is the concentration of \(\mathrm{SO}_{4}^{2-}\) when the second cation begins to precipitate?

A solution containing an unknown number of metal ions is treated with dilute \(\mathrm{HCl} ;\) 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 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.

An unknown solid is entirely soluble in water. On addition of dilute \(\mathrm{HCl}\), a precipitate forms. After the precipitate is filtered off, the \(\mathrm{pH}\) is adjusted to about 1 and \(\mathrm{H}_{2} \mathrm{~S}\) is bubbled in; a precipitate again forms. After filtering off this precipitate, the \(\mathrm{pH}\) 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. Based on these observations, which of the following compounds might be present, which are definitely present, and which are definitely absent: \(\mathrm{CdS}, \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}, \mathrm{HgO}, \mathrm{ZnSO}_{4}, \mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2}\) and \(\mathrm{Na}_{2} \mathrm{SO}_{4} ?\)

In the course of various qualitative analysis procedures, the following mixtures are encountered: (a) \(\mathrm{Zn}^{2+}\) and \(\mathrm{Cd}^{2+}\), (b) \(\mathrm{Cr}(\mathrm{OH})_{3}\) and \(\mathrm{Fe}(\mathrm{OH})_{3}\) (c) \(\mathrm{Mg}^{2+}\) and \(\mathrm{K}^{+}\), (d) \(\mathrm{Ag}^{+}\) and \(\mathrm{Mn}^{2+}\). Suggest how each mixture might be separated.

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

(a) Precipitation of the group 4 cations (Figure 17.22) 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.