Chapter 17

The following boxes represent aqueous solutions containing a weak acid, HA and its conjugate base, \(A^{-}\). Water molecules, hydronium ions, and cations are not shown. Which solution has the highest pH? Explain. [Section 17.1]

A buffer contains a weak acid, HA, and its conjugate base. The weak acid has a \(\mathrm{pK}_{a}\) of 4.5 , and the buffer has a pH of 4.7 . Without doing a calculation, state which of these possibilities are correct at pH 4.7 . (a) \([\mathrm{HA}]>\left[\mathrm{A}^{-}\right]\) (b) \([\mathrm{HA}]=\left[\mathrm{A}^{-}\right],\) or \((\mathbf{c})[\mathrm{HA}]<\left[\mathrm{A}^{-}\right]\).

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 \(\mathrm{A}^{-}\). (b) Common ions alter the equilibrium constant for the reaction of an ionic solid with water. \((\mathbf{c})\) 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 $$ \mathrm{B}(a q)+\mathrm{H}_{2} \mathrm{O}(I) \rightleftharpoons \mathrm{HB}^{+}(a q)+\mathrm{OH}^{-}(a q) . $$ 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 pH of the solution increase, decrease, or stay the same?

(a) Calculate the percent lonization of \(0.0085 \mathrm{M}\) butanoic acid \(\left(K_{a}=1.5 \times 10^{-5}\right),(\mathbf{b})\) Calculate the percent ionization of \(0.0085 \mathrm{M}\) butanoic acid in a solution containing \(0.075 \mathrm{M}\) sodium butanoate.

(a) Calculate the percent ionization of \(0.250 \mathrm{M}\) lactic acid \(\left(K_{a}=1.4 \times 10^{-4}\right) .(\mathbf{b})\) Calculate the percent ionization of \(0.250 \mathrm{M}\) lactic acid in a solution containing \(0.050 \mathrm{M}\) sodium lactate.

Which of the following solutions is a buffer? (a) \(0.20 \mathrm{M}\) formic acid (HCOOH), (b) \(0.20 \mathrm{M}\) formic acid \((\mathrm{HCOOH})\) and \(0.20 \mathrm{M}\) sodium formate (HCOONa), (c) \(0.20 \mathrm{M}\) nitric acid \(\left(\mathrm{HNO}_{3}\right)\) and \(0.20 \mathrm{M}\) sodium nitrate \(\left(\mathrm{NaNO}_{3}\right),\) (d) both b and \(\mathrm{c},(\mathbf{e})\) all of \(\mathrm{a}, \mathrm{b},\) and \(\mathrm{c}\)

Which of the following solutions is a buffer? (a) A solution made by mixing \(50 \mathrm{~mL}\), of \(0.200 \mathrm{M}\) formic acid \((\mathrm{HCOOH})\) and \(250 \mathrm{~mL}\) of \(0.200 \mathrm{M} \mathrm{KOH},(\mathbf{b})\) A solution made by \(\mathrm{mix}\) ing \(50 \mathrm{~mL}\) of \(0.200 \mathrm{M}\) formic acid \((\mathrm{HCOOH})\) and \(25 \mathrm{~mL}\) of \(0.200 \mathrm{M}\) nitric acid \(\left(\mathrm{HNO}_{3}\right),(\mathbf{c})\) A solution made by mixing \(50 \mathrm{~mL}\) of \(0.200 \mathrm{M}\) potassium formate \((\mathrm{HCOOK})\) and \(25 \mathrm{~mL}\) of \(0.200 \mathrm{M} \mathrm{KNO}_{3},\) (d) A solution made by mixing \(50 \mathrm{~mL}\) of \(0.200 \mathrm{M}\) formic acid \((\mathrm{HCOOH})\), and \(25 \mathrm{~mL}\). of \(0.200 \mathrm{MKOH}\).

A buffer, consisting of \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) and \(\mathrm{HPO}_{4}^{2-}\), helps control the 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 \(10.0 \mathrm{~g}\) of \(\mathrm{KH}_{2} \mathrm{PO}_{4}\) and \(10.0 \mathrm{~g}\) of \(\mathrm{K}_{2} \mathrm{HPO}_{4}\) per \(0.500 \mathrm{~L}\) of solution?

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 \(\mathrm{pH}\) at the beginning of the titration is lower for the weak acid than the strong acid. \((\mathbf{c})\) The pH at the equivalence point is 7 no matter which acid is titrated.

The samples of nitric and acetic acids shown here are both titrated with a \(0.100 \mathrm{M}\) solution of \(\mathrm{NaOH}(a q)\). \(25.0 \mathrm{~mL}\) of \(1.0 \mathrm{MHNO}_{3}(a q) \quad 25.0 \mathrm{~mL}\) of \(1.0 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}(a q)\) Determine whether each of the following statements concerning these titrations is true or false. (a) A larger volume of \(\mathrm{NaOH}(a q)\) is needed to reach the equivalence point in the titration of \(\mathrm{HNO}_{3}\) (b) The \(\mathrm{pH}\) at the equivalence point in the \(\mathrm{HNO}_{3}\) titration will be lower than the \(\mathrm{pH}\) at the equivalence point in the \(\mathrm{CH}_{3} \mathrm{COOH}\) titration. (c) Phenolphthalein would be a suitable indicator for both titrations.

Predict whether the equivalence point of each of the following titrations is below, above, or at pH 7: (a) \(\mathrm{NaHCO}_{3}\) titrated with \(\mathrm{NaOH},(\mathbf{b}) \mathrm{NH}_{3}\) titrated with \(\mathrm{HCl},(\mathbf{c}) \mathrm{KOH}\) titrated with \(\mathrm{HBr}\).

Predict whether the equivalence point of each of the following titrations is below, above, or at pH 7: (a) benzoic acid titrated with \(\mathrm{KOH},(\mathbf{b})\) ammonia titrated with iodic acid, (c) hydroxylamine with hydrochloric 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 \(0.10 \mathrm{M}\) 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? (a) Is the \(\mathrm{pH} 7\), 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 \(0.0750 \mathrm{M} \mathrm{KOH}\) are required to titrate each of the following solutions to the equivalence point: (a) \(30.0 \mathrm{~mL}\) of \(0.0900 \mathrm{M} \mathrm{HCOOH}\), (b) \(45.0 \mathrm{~mL}\) of \(0.0750 \mathrm{M} \mathrm{HNO}_{3},(\mathbf{c}) 50.0 \mathrm{~mL}\) of a solution that contains \(3.00 \mathrm{~g}\) of HBr per liter?

How many milliliters of \(0.105 \mathrm{MHCl}\) are needed to titrate each of the following solutions to the equivalence point: (a) 45.0 \(\mathrm{mL}\), of \(0.0950 \mathrm{MNaOH}\) (b) \(22.5 \mathrm{~mL}\) of \(0.118 \mathrm{MNH}_{3}\), (c) 125.0 \(\mathrm{mL}\). of a solution that contains \(1.35 \mathrm{~g}\) of \(\mathrm{NaOH}\) per liter?

A \(10.0-\mathrm{mL}\) sample of \(0.250 \mathrm{MHNO}_{3}\) solution is titrated with \(0.100 \mathrm{MKOH}\) solution. Calculate the \(\mathrm{pH}\) of the solution after the following volumes of base have been added: (a) \(20.0 \mathrm{~mL}\), (b) \(24.9 \mathrm{~mL}\), (c) \(25.0 \mathrm{~mL}\), (d) \(25.1 \mathrm{~mL}\), , (e) \(30.0 \mathrm{~mL}\)

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 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 \(10.0-\mathrm{ml}\). sample of \(0.250 \mathrm{M}\) acetic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) is titrated with \(0.100 \mathrm{M} \mathrm{KOH}\) solution. Calculate the \(\mathrm{pH}\) after the following volumes of base have been added: (a) \(0 \mathrm{~mL}\), (b) \(12.5 \mathrm{~mL}\), (c) \(24.5 \mathrm{~mL}\) (d) \(25.0 \mathrm{~mL}\), (e) \(25.5 \mathrm{~mL}\) (f) \(30.0 \mathrm{~mL}\).

Consider the titration of \(30.0 \mathrm{~mL}\) of \(0.050 \mathrm{M} \mathrm{NH}_{3}\) with \(0.025 \mathrm{MHCl}\). 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 M HBr: (a) sodium hydroxide (NaOH), (b) hydroxylamine \(\left(\mathrm{NH}_{2} \mathrm{OH}\right),(\mathbf{c})\) aniline \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\right)\)

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 \(\mathrm{M}^{2+} ?(\mathbf{c})\) 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: \(\mathrm{BaCrO}_{4}, \mathrm{CuS}, \mathrm{PbCl}_{2}\) and \(\mathrm{LaF}_{3}\).

(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: \(\mathrm{MnCO}_{3}, \mathrm{Hg}(\mathrm{OH})_{2},\) 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 \(1.1 \times 10^{-2} \mathrm{~g} \mathrm{SrF}_{2}\) 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 1.50-L solution saturated at \(25^{\circ} \mathrm{C}\) with cobalt carbonate \(\left(\mathrm{CoCO}_{3}\right)\) contains \(2.71 \mathrm{mg}\) of \(\mathrm{CoCO}_{3} .\) 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 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 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 \(\mathrm{KI}\) 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?

Calculate the solubility of \(\mathrm{Mn}(\mathrm{OH})_{2}\) in grams per liter when buffered at \(\mathrm{pH}\) (a) \(7.0,(\mathbf{b}) 9.5,(\mathbf{c}) 11.8\).

Which of the following salts will be substantially more soluble in an \(\mathrm{HNO}_{3}\) solution than in pure water: (a) \(\mathrm{BaSO}_{4}\) (b) CuS (c) \(\mathrm{Cd}(\mathrm{OH})_{2}\) (d) \(\mathrm{PbF}_{2}\) (e) \(\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2} ?\)

For each of the following slightly soluble salts, write the net ionic equation, if any, for reaction with a strong acid: (a) MnS, (b) \(P \mathrm{bF}_{2}\) (c) \(\mathrm{AuCl}_{3}\) (d) \(\mathrm{Hg}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) (e) CuBr.

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

A solution of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is added dropwise to a solution that is \(0.010 \mathrm{M}\) in \(\mathrm{Ba}^{2+}(a q)\) and \(0.010 \mathrm{M}\) in \(\mathrm{Sr}^{2+}(a q)\). (a) What concentration of \(\mathrm{SO}_{4}^{2-}\) is necessary to begin precipitation? (Neglect volume changes. BaSO \(_{4}: K_{i p}=1.1 \times 10^{-10} ; \mathrm{SrSO}_{4}\) \(\left.K_{s p}=3.2 \times 10^{-7} .\right)(\mathbf{b})\) 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: \(0.20 \mathrm{MCrO}_{4}^{2-}, 0.10 \mathrm{MCO}_{3}^{2-},\) and \(0.010 \mathrm{MCl}^{-}\). If a dilute \(\mathrm{AgNO}_{3}\) solution is slowly added to the solution, what is the first compound to precipitate: \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}\left(K_{4 p}=1.2 \times 10^{-12}\right), \mathrm{Ag}_{2} \mathrm{CO}_{3}\left(K_{4 p}=8.1 \times 10^{-12}\right)\) or \(\mathrm{AgCl}\left(K_{\mathrm{sp}}=1.8 \times 10^{-10}\right) ?\)

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 \(0.20 \mathrm{M}\) in \(\mathrm{Ca}^{2+}\) and \(0.30 \mathrm{M}\) in \(\mathrm{Ag}^{+}\). (a) Which compound will precipitate first: \(\operatorname{CaSO}_{4}\left(K_{s p}=2.4 \times 10^{-5}\right)\) or \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\left(K_{\mathrm{sp}}=1.5 \times 10^{-5}\right) ?(\mathbf{b})\) How \(\mathrm{much} \mathrm{Na}_{2} \mathrm{SO}_{4}\) solu- tion must be added to initiate the precipitation?

A solution containing several metal ions is treated with dilute HCl; no precipitate forms. The 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. 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 \(\mathrm{Hg}^{2+} .\)

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 erroneous 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.

Furoic acid \(\left(\mathrm{HC}_{5} \mathrm{H}_{3} \mathrm{O}_{3}\right)\) has a \(K_{a}\) value of \(6.76 \times 10^{-4} \mathrm{at}\) \(25^{\circ} \mathrm{C}\). Calculate the \(\mathrm{pH}\) at \(25^{\circ} \mathrm{C}\) of \((\mathbf{a})\) a solution formed by adding \(30.0 \mathrm{~g}\) of furoic acid and \(25.0 \mathrm{~g}\) of sodium furoate \(\left(\mathrm{NaC}_{5} \mathrm{H}_{3} \mathrm{O}_{3}\right)\) to enough water to form \(0.300 \mathrm{~L}\) of solution, \((\mathbf{b})\) a solution formed by mixing \(20.0 \mathrm{~mL}\). of \(0.200 \mathrm{M}\) \(\mathrm{HC}_{\mathrm{s}} \mathrm{H}_{3} \mathrm{O}_{3}\) and \(30.0 \mathrm{~mL}\) of \(0.250 \mathrm{M} \mathrm{NaC}_{5} \mathrm{H}_{3} \mathrm{O}_{3}\) and diluting the total volume to \(125 \mathrm{~mL},(\mathbf{c})\) a solution prepared by adding \(25.0 \mathrm{~mL}\) of \(1.00 \mathrm{M} \mathrm{NaOH}\) solution to \(100.0 \mathrm{~mL}\) of \(0.100 \mathrm{MHC}_{3} \mathrm{H}_{3} \mathrm{O}_{3}\)

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 pH is \(4.68 .\) What is the \(p K_{a}\) for bromcresol green?

Equal quantities of \(0.010 \mathrm{M}\) solutions of an acid HA and a base B are mixed. The 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 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 \(K_{h}\) for B?

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 \(30.0 \mathrm{~mL}\). 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 \(500 \mathrm{mg}\) of an unknown monoprotic acid was dissolved in \(50.0 \mathrm{~mL}\) of water and titrated with \(0.200 \mathrm{M}\) KOH. The acid required \(20.60 \mathrm{~mL}\) of base to reach the equivalence point. (a) What is the molar mass of the acid? (b) After \(10.30 \mathrm{~mL}\) of base had been added in the titration, the pH was found to be \(4.20 .\) What is the \(p K_{a}\) for the unknown acid

Mathematically prove 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 \(\mathrm{p} K_{a}\) for the acid.

A weak monoprotic acid is titrated with \(0.100 \mathrm{M} \mathrm{NaOH}\). It requires \(25.0 \mathrm{~mL}\) of the \(\mathrm{NaOH}\) solution to reach the equivalence point. After \(12.5 \mathrm{~mL}\). of base is added, the pH of the solution is 4.16 . Estimate the \(\mathrm{p} K_{a}\) of the weak acid.

Suppose you want to do a physiological experiment that calls for a pH 6.50 buffer. You find that the organism with which you are working is not sensitive to the weak acid \(\mathrm{H}_{2} \mathrm{~A}\left(K_{a 1}=2 \times 10^{-2} ; K_{a 2}=5.0 \times 10^{-7}\right)\) or its sodium salts. You have available a \(1.0 \mathrm{M}\) solution of this acid and \(\mathrm{a}\) \(1.0 \mathrm{M}\) 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 \(\mathrm{pH}\) \(6.50 ?\) (Ignore 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 a buffer with \(\mathrm{pH}=3.75 ?\)