Chapter 17

Derive an equation similar to the HendersonHasselbalch equation relating the pOH of a buffer to the \(\mathrm{p} K_{b}\) of its base component.

Benzenesulfonic acid is a monoprotic acid with \(\mathrm{p} K_{a}=2.25 .\) Calculate the \(\mathrm{pH}\) of a buffer composed of \(0.150 \mathrm{M}\) benzenesulfonic acid and \(0.125 \mathrm{M}\) sodium benzensulfonate.

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 \((\mathrm{a})\) 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; (b) a solution formed by mixing \(30.0 \mathrm{~mL}\) of \(0.250 \mathrm{MHC}_{5} \mathrm{H}_{3} \mathrm{O}_{3}\) 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 \(125 \mathrm{~mL} ;\) (c) a solution prepared by adding \(50.0 \mathrm{~mL}\) of \(1.65 \mathrm{M} \mathrm{NaOH}\) solution to \(0.500 \mathrm{Lof} 0.0850 \mathrm{M} \mathrm{HC}_{5} \mathrm{H}_{3} \mathrm{O}_{3}\)

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

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

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

A biochemist needs \(750 \mathrm{~mL}\) of an acetic acid-sodium ?cetate buffer with pH 4.50. Solid sodium acetatè \(\left(\mathrm{CH}_{3} \mathrm{COONa}\right)\) 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 \(\mathrm{CH}_{3} \mathrm{COONa}\) and how many milliliters of glacial acetic acid must be used?

A sample of \(0.2140 \mathrm{~g}\) of an unkown 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?

Show 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 \(\mathrm{pK}_{a}\) for the acid.

If \(40.00 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3}\) is titrated with \(0.100 \mathrm{M}\) \(\mathrm{HCl}\), calculate (a) the \(\mathrm{pH}\) at the start of the titration; (b) the volume of \(\mathrm{HCl}\) required to reach the first equivalence point and the predominant species present at this point; (c) the volume of \(\mathrm{HCl}\) required to reach the second equivalence point and the predominant species present at this point; (d) the \(\mathrm{pH}\) at the second equivalence point.

A hypothetical weak acid, HA, was combined with \(\mathrm{NaOH}\) in the following proportions: \(0.20 \mathrm{~mol}\) of \(\mathrm{HA}\), \(0.080 \mathrm{~mol}\) of \(\mathrm{NaOH}\). The mixture was diluted to a total volume of \(1.0 \mathrm{~L}\), and the \(\mathrm{pH}\) measured. \((\mathrm{a})\) If \(\mathrm{pH}=4.80\), what is the \(\mathrm{pK}_{a}\) of the acid? (b) How many additional moles of \(\mathrm{NaOH}\) should be added to the solution to increase the \(\mathrm{pH}\) to \(5.00 ?\)

Suppose you want to do a physiological experiment that calls for a \(\mathrm{pH} 6.5\) buffer. You find that the organism with which you are working is not sensitive to the weak acid \(\mathrm{H}_{2} \mathrm{X}\left(K_{a 1}=2 \times 10^{-2} ; K_{a 2}=5.0 \times 10^{-7}\right)\) or its sodium salts. You have available a \(1.0 \mathrm{M}\) solution of this acid and a \(1.0 M\) solution of \(\mathrm{NaOH}\). How much of the \(\mathrm{NaOH}\) solution should be added to \(1.0 \mathrm{~L}\) of the acid to give a buffer at \(\mathrm{pH} 6.50 ?\) (lgnore any volume change.)

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 \(\mathrm{a}\) buffer with \(\mathrm{pH}=3.75 ?\)

Describe the solubility of \(\mathrm{CaCO}_{3}\) in each of the following solutions compared to its solubility in water: (a) in \(0.10 \mathrm{M} \mathrm{NaCl}\) solution; \((\mathrm{b})\) in \(0.10 \mathrm{M} \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) solution; (c) \(0.10 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3}\); (d) \(0.10 \mathrm{M}\) HCl solution. (Answer same, less soluble, or more soluble.)

Toothenamel is composed of hydroxyapatite, whose simplest formula is \(\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right){ }_{3} \mathrm{OH}\), and whose corresponding \(K_{s p}=6.8 \times 10^{-27}\). As discussed in the "Chemistry and Life" box in Section \(17.5\), 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.

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

Seawater contains \(0.13 \%\) magnesium by mass, and has a density of \(1.025 \mathrm{~g} / \mathrm{mL}\). What fraction of the magnesium can be removed by adding a stoichiometric quantity of \(\mathrm{CaO}\) (that is, one mole of \(\mathrm{CaO}\) for each mole of \(\mathrm{Mg}^{2+}\) )?

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 \(2.0 \times 10^{-8} M\) for the \(\mathrm{Ba}^{2+}\) ion in solution?

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.

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

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

(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 \(\left(\mathrm{NaCHO}_{2}\right)\). (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 \(0.15 \mathrm{M} \mathrm{HCl}\) is mixed with \(50.0 \mathrm{~m}\) L of \(0.15 \mathrm{M} \mathrm{NaCHO}_{2}\).

(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 \(\mathrm{pH}\) 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. Do both the molecular weight and \(K_{a}\) value agree with your choice?

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 \(0.40 \mathrm{M} \mathrm{HCl}\). 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.

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?

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 \(3.1 \times 10^{-2} \mathrm{~mol} / \mathrm{L}-\mathrm{atm}\). The \(\mathrm{CO}_{2}\) is an acidic oxide, reacting with \(\mathrm{H}_{2} \mathrm{O}\) to form \(\mathrm{H}_{2} \mathrm{CO}_{3}\).

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 \(0.0983 \mathrm{M}\) \(\mathrm{HCl}\) to reach the end point. Calculate \(K_{s p}\) for \(\mathrm{Ca}(\mathrm{OH})_{2}\) Compare your result with that in Appendix D. Do you think the solution was kept at \(25^{\circ} \mathrm{C}\) ?

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 \(\mathrm{Ag}^{+}\) 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 main-tain an appropriate concentration of \(\mathrm{Ag}^{+}\) is to add a slightly soluble salt to the pool. Using \(K_{s p}\) values from Appendix \(\mathrm{D}\), calculate the equilibrium concentration of \(\mathrm{Ag}^{+}\) in parts per billion that would exist in equilibrium with (a) \(\mathrm{AgCl}\), (b) \(\mathrm{AgBr}\), (c) AgI.

Fluoridation of drinking water is employed in many places to aid in the prevention of dental caries. Typically the \(\mathrm{F}^{-}\) ion concentration is adjusted to about 1 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 ppb. Could a precipitate of \(\mathrm{CaF}_{2}\) form under these conditions? (Make any necessary approximations.)