Chapter 17

An unknown solid is entirely soluble in water. On addition of dilute 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 pH is adjusted to 8 and \(\mathrm{H}_{2} \mathrm{~S}\) is again added; no precipitate forms. No precipitate forms upon addition of \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\). (See Figure 7.23.) 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, \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}, \mathrm{HgO}_{3}, \mathrm{ZnSO}_{4}, \mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2}\), 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) \(\mathrm{Cr}(\mathrm{OH})_{2}\) and \(\mathrm{Fe}(\mathrm{OH})_{3}\), (c) \(\mathrm{Mg}^{2+}\) and \(\mathrm{K}^{4}\), (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) Na+ and \(\mathrm{Ca}^{2+}\), (b) \(\mathrm{Cu}^{2+}\) and \(\mathrm{Mg}^{2+}\), (c) \(\mathrm{Pb}^{2+}\) and \(\mathrm{Al}^{3+}\), (d) \(\mathrm{Ag}^{+}\)and \(\mathrm{Hg}^{2+}\).

A 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 indeed present. Why is this possibly an erroneots conclusion?

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

Furoic acid \(\left(\mathrm{HC}_{3} \mathrm{H}_{3} \mathrm{O}_{3}\right)\) 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 \(\left(\mathrm{NaC}_{3} \mathrm{H}_{3} \mathrm{O}_{3}\right)\) to enough water to form \(0.250 \mathrm{~L}\) of solution, (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 \(0.22 \mathrm{M} \mathrm{NaC} \mathrm{C}_{3} \mathrm{H}_{3} \mathrm{O}_{3}\) and diluting the total volume to \(125 \mathrm{~mL}\). (c) a solution prepared by adding \(50.0 \mathrm{~mL}\) of \(1.65 \mathrm{M} \mathrm{NaOH}\) solution to \(0.500 \mathrm{~L}\) of \(0.0850 \mathrm{M} \mathrm{HC} \mathrm{H}_{3} \mathrm{O}_{3}\).

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

Equal quantities of \(0.010 \mathrm{M}\) 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 HA and 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 \(K_{\mathrm{b}}\) for \(\mathrm{B}\) ?

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

\mathrm{~A}\( biochemist needs \)750 \mathrm{~mL}\( of an acetic acid-sodium acetate buffer with pH 4.50. Solid sodium acetate ( \)\left.\mathrm{CH}_{3} \mathrm{COONa}\right)\( and glacial acetic acid \)\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\( are available. Glacial acetic acid is \)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}_{4} \mathrm{COONa}$ and how many milliliters of glacial acetic acid must be used?

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 \(27.4 \mathrm{~mL}\) 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 \(\mathrm{pH}\) was found to be 6.50. What is the \(K_{a}\) for the unknown acid?

A sample of \(0.1687 \mathrm{~g}\) of an unknown monoprotic acid was dissolved in \(25.0 \mathrm{~mL}\). of water and titrated with \(0.1150 \mathrm{M}\) \(\mathrm{NaOH}\). The acid required \(15.5 \mathrm{~mL}\) of base to reach the equivalence point. (a) What is the molecular weight of the acid? (b) After \(7.25 \mathrm{~mL}\) 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?

Mathematically prove that the 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 \(\mathrm{p}_{u}\) for the acid.

A weak monoprotic acid is titrated with \(0.100 \mathrm{M} \mathrm{NaOH}\). It requires \(50.0 \mathrm{~mL}\) of the \(\mathrm{NaOH}\) 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 pKa of the weak acid.

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

A person suffering from anxiety begins breathing rapidly and as a result suffers alkalosis, an increase in blood \(\mathrm{pH}\). (a) Using Equation 17.10, explain how rapid breathing can cause the \(\mathrm{pH}\) of blood to increase. (b) One cure for this problem is breathing in a paper bag. Why does this procedure lower blood \(\mathrm{pH}\) ?

The solubility of \(\mathrm{CaCO}_{3}\) is \(\mathrm{pH}\) dependent. (a) Calculate the molar solubility of \(\mathrm{CaCO}_{3}\left(K_{a p}=4.5 \times 10^{-9}\right)\) 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 (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)? (d) What is the molar solubility of \(\mathrm{CaCO}_{3}\) at the \(\mathrm{pH}\) of the ocean (8.3)? (e) If the pH is buffered at \(7.5\), what is the molar solubility of \(\mathrm{CaCO}_{3}\) ?

Tooth enamel is composed of hydroxyapatite, whose simplest formula is \(\mathrm{Ca}_{\mathrm{s}}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH}\), and whose corresponding \(K_{s p}=6.8 \times 10^{-27}\). As discussed in the "Chemistry and Life" box on page 755, fluoride in fluorinated water or in toothpaste reacts with hydroxyapatite to form fluoroapatite, \(\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{~F}_{\text {k }}\) whose \(K_{p}=1.0 \times 10^{-40}\), (a) Write the expression for the solubility-constant for hydroxyapatite and for fluoroapatite. (b) Calculate the molar solubility of each of these compounds.

Calculate the solubility of \(\mathrm{Mg}_{\mathrm{g}}(\mathrm{OH})_{2}\) in \(0.50 \mathrm{M} \mathrm{NH} \mathrm{NCl}_{4}\).

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 \(2.0 \times 10^{-4} \mathrm{M}\) for the \(\mathrm{Ba}^{+}\)ion in solution?

The value of \(K_{a p}\) for \(\mathrm{Mg}_{3}\left(\mathrm{AsO}_{4}\right)_{2}\) is \(2.1 \times 10^{-20}\). The \(\mathrm{AsO}_{4}{\underline{\phantom{xx}}}^{3-}\) ion is derived from the weak acid \(\mathrm{H}_{3} \mathrm{AsO}_{4}\left(\mathrm{pK}_{\mathrm{a} 1}=\right.\) \(\left.2.22 ; \mathrm{pK}_{u 2}=6.98 ; \mathrm{p} K_{u 3}=11.50\right)\). When asked to calculate the molar solubility of \(\mathrm{Mg}_{3}\left(\mathrm{AsO}_{4}\right)_{2}\) in water, a student used the \(K_{p p}\) expression and assumed that \(\left[\mathrm{Mg}^{2+}\right]=1.5\left[\mathrm{AsO}_{4}{\underline{\phantom{xx}}}^{3-}\right]\). Why was this a mistake?

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

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

(a) A 0.1044-g sample of an unknown monoprotic acid requires \(22.10 \mathrm{~mL}\) of \(0.0500 \mathrm{M} \mathrm{NaOH}\) to reach the end point. What is the molecular weight 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.

Aspirin has the structural formula CC(=O)Oc1ccccc1C(=O)O At body temperature \(\left(37^{\circ} \mathrm{C}\right), K_{d}\) 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 pH is 2 , what percent of the aspirin is in the form of neutral molecules?

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

Excess \(\mathrm{Ca}(\mathrm{OH})_{2}\) is shaken with water to produce a saturated solution. The solution is filtered, and a \(50.00-\mathrm{mL}\) sample titrated with \(\mathrm{HCl}\) requires \(11.23 \mathrm{~mL}\) of \(0.0983 \mathrm{M} \mathrm{HQ}\) to reach the end point. Calculate \(K_{\mathrm{wp}}\) for \(\mathrm{Ca}(\mathrm{OH})_{2}\). Compare your result with that in Appendix D. \(25^{\circ} \mathrm{C}\). Suggest a reason for any differences you find between your value and the one in Appendix D.

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

A concentration of 10-100 parts per billion (by mass) of \(\mathrm{Ag}^{4}\) is an effective disinfectant in swimming pools. However, if the concentration exceeds this range, the \(\mathrm{Ag}^{+}\)can cause adverse health effects. One way to maintain an appropriate concentration of \(\mathrm{Ag}^{+}\)is to add a slightly soluble salt to the pool. Using \(K_{s p}\) values from Appendix D, calculate the equilibrium concentration of \(\mathrm{Ag}^{+}\)in parts per billion that would exist in equilibrium with (a) AgCl, (b) AgBr, (c) AgI.

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 \(1 \mathrm{ppb}\). 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 \(8 \mathrm{ppb}\). Could a precipitate of \(\mathrm{CaF}_{2}\) form under these conditions? (Make any necessary approximations.)

Baking soda (sodium bicarbonate, \(\mathrm{NaHCO}_{3}\) ) reacts with acids in foods to form carbonic acid \(\left(\mathrm{H}_{2} \mathrm{CO}_{3}\right)\), which in turn decomposes to water and carbon dioxide gas. In a cake batter, the \(\mathrm{CO}_{2}(\mathrm{~g})\) 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 \(\mathrm{mol} / \mathrm{L}\). (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 \(350^{\circ} \mathrm{F}\).

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 HF.