Chapter 17

Sulfuric acid is a diprotic acid, strong in the first ionization step and weak in the second \(\left(K_{\mathrm{a}_{2}}=1.1 \times 10^{-2}\right)\) By using appropriate calculations, determine whether it is feasible to titrate \(10.00 \mathrm{mL}\) of \(0.100 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) to two distinct equivalence points with \(0.100 \mathrm{M} \mathrm{NaOH}\)

Carbonic acid is a weak diprotic acid \(\left(\mathrm{H}_{2} \mathrm{CO}_{3}\right)\) with \(K_{a_{1}}=4.43 \times 10^{-7}\) and \(K_{\mathrm{a}_{2}}=4.73 \times 10^{-11} .\) The equiv- alence points for the titration come at approximately pH 4 and 9. Suitable indicators for use in titrating carbonic acid or carbonate solutions are methyl orange and phenolphthalein. (a) Sketch the titration curve that would be obtained in titrating a sample of \(\mathrm{NaHCO}_{3}(\mathrm{aq})\) with \(1.00 \mathrm{M} \mathrm{HCl}\) (b) Sketch the titration curve for \(\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{aq})\) with 1.00 M HCl. (c) What volume of \(0.100 \mathrm{M} \mathrm{HCl}\) is required for the complete neutralization of \(1.00 \mathrm{g} \mathrm{NaHCO}_{3}(\mathrm{s}) ?\) (d) What volume of \(0.100 \mathrm{M} \mathrm{HCl}\) is required for the complete neutralization of \(1.00 \mathrm{g} \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s}) ?\) (e) A sample of NaOH contains a small amount of \(\mathrm{Na}_{2} \mathrm{CO}_{3} .\) For titration to the phenolphthalein end point, \(0.1000 \mathrm{g}\) of this sample requires \(23.98 \mathrm{mL}\) of \(0.1000 \mathrm{M} \mathrm{HCl} .\) An additional \(0.78 \mathrm{mL}\) is required to reach the methyl orange end point. What is the percent \(\mathrm{Na}_{2} \mathrm{CO}_{3},\) by mass, in the sample?

Piperazine is a diprotic weak base used as a corrosion inhibitor and an insecticide. Its ionization is described by the following equations. \(\mathrm{HN}\left(\mathrm{C}_{4} \mathrm{H}_{8}\right) \mathrm{NH}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons\) \(\left[\mathrm{HN}\left(\mathrm{C}_{4} \mathrm{H}_{8}\right) \mathrm{NH}_{2}\right]^{+}+\mathrm{OH}^{-} \quad \mathrm{p} K_{\mathrm{b}_{1}}=4.22\) \(\left[\mathrm{HN}\left(\mathrm{C}_{4} \mathrm{H}_{8}\right) \mathrm{NH}_{2}\right]^{+}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons\) \(\left[\mathrm{H}_{2} \mathrm{N}\left(\mathrm{C}_{4} \mathrm{H}_{8}\right) \mathrm{NH}_{2}\right]^{2+}+\mathrm{OH}^{-} \quad \mathrm{p} K_{\mathrm{b}_{2}}=8.67\) . The piperazine used commercially is a hexahydrate, \(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{N}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O} .\) A \(1.00-\mathrm{g}\) sample of this hexahydrate is dissolved in \(100.0 \mathrm{mL}\) of water and titrated with 0.500 M HCl. Sketch a titration curve for this titration, indicating (a) the initial \(\mathrm{pH} ;\) (b) the pH at the halfneutralization point of the first neutralization; (c) the volume of \(\mathrm{HCl}(\text { aq })\) required to reach the first equivalence point; (d) the pH at the first equivalence point; (e) the \(\mathrm{pH}\) at the point at which the second step of the neutralization is half-completed; (f) the volume of \(0.500 \mathrm{M} \mathrm{HCl}(\) aq) required to reach the second equivalence point of the titration; (g) the pH at the second equivalence point.

A solution is prepared that is \(0.150 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\) and \(0.250 \mathrm{M} \mathrm{NaHCOO}\) (a) Show that this is a buffer solution. (b) Calculate the pH of this buffer solution. (c) What is the final pH if 1.00 L of 0.100 M HCl is added to \(1.00 \mathrm{L}\) of this buffer solution?

Hydrogen peroxide, \(\mathrm{H}_{2} \mathrm{O}_{2},\) is a somewhat stronger acid than water. Its ionization is represented by the equation \(\mathrm{H}_{2} \mathrm{O}_{2}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{HO}_{2}^{-}\) In \(1912,\) the following experiments were performed to obtain an approximate value of \(\mathrm{p} K_{\mathrm{a}}\) for this ionization at \(0^{\circ} \mathrm{C} .\) A sample of \(\mathrm{H}_{2} \mathrm{O}_{2}\) was shaken together with a mixture of water and 1 -pentanol. The mixture settled into two layers. At equilibrium, the hydrogen peroxide had distributed itself between the two layers such that the water layer contained 6.78 times as much \(\mathrm{H}_{2} \mathrm{O}_{2}\) as the 1 -pentanol layer. In a second experiment, a sample of \(\mathrm{H}_{2} \mathrm{O}_{2}\) was shaken together with 0.250 M NaOH(aq) and 1-pentanol. At equilibrium, the concentration of \(\mathrm{H}_{2} \mathrm{O}_{2}\) was \(0.00357 \mathrm{M}\) in the 1-pentanol layer and 0.259 M in the aqueous layer. In a third experiment, a sample of \(\mathrm{H}_{2} \mathrm{O}_{2}\) was brought to equilibrium with a mixture of 1 -pentanol and \(0.125 \mathrm{M}\) \(\mathrm{NaOH}(\mathrm{aq}) ;\) the concentrations of the hydrogen peroxide were \(0.00198 \mathrm{M}\) in the 1 -pentanol and \(0.123 \mathrm{M}\) in the aqueous layer. For water at \(0^{\circ} \mathrm{C}, \mathrm{p} K_{\mathrm{w}}=14.94\) Find an approximate value of \(\mathrm{pK}_{\mathrm{a}}\) for \(\mathrm{H}_{2} \mathrm{O}_{2}\) at \(0^{\circ} \mathrm{C}\) [Hint: The hydrogen peroxide concentration in the aqueous layers is the total concentration of \(\mathrm{H}_{2} \mathrm{O}_{2}\) and \(\mathrm{HO}_{2}^{-}\). Assume that the 1 -pentanol solutions contain no ionic species.

Sodium ammonium hydrogen phosphate, \(\mathrm{NaNH}_{4}\) \(\mathrm{HPO}_{4},\) is a salt in which one of the ionizable \(\mathrm{H}\) atoms of \(\mathrm{H}_{3} \mathrm{PO}_{4}\) is replaced by \(\mathrm{Na}^{+},\) another is replaced by \(\mathrm{NH}_{4}^{+},\) and the third remains in the anion \(\mathrm{HPO}_{4}^{2-}\) Calculate the \(\mathrm{pH}\) of \(0.100 \mathrm{M} \mathrm{NaNH}_{4} \mathrm{HPO}_{4}(\mathrm{aq})\) [Hint: You can use the general method introduced on page \(720 .\) First, identify all the species that could be present and the equilibria involving these species. Then identify the two equilibrium expressions that will predominate and eliminate all the species whose concentrations are likely to be negligible. At that point, only a few algebraic manipulations are required.]

Consider a solution containing two weak monoprotic acids with dissociation constants \(K_{\mathrm{HA}}\) and \(K_{\mathrm{HB}}\). Find the charge balance equation for this system, and use it to derive an expression that gives the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) as a function of the concentrations of \(\mathrm{HA}\) and HB and the various constants.

A very common buffer agent used in the study of biochemical processes is the weak base TRIS, \(\left(\mathrm{HOCH}_{2}\right)_{3} \mathrm{CNH}_{2},\) which has a \(\mathrm{pK}_{\mathrm{b}}\) of 5.91 at \(25^{\circ} \mathrm{C} . \mathrm{A}\) student is given a sample of the hydrochloride of TRIS together with standard solutions of \(10 \mathrm{M}\) NaOH and HCl. (a) Using TRIS, how might the student prepare 1 L of a buffer of \(\mathrm{pH}=7.79 ?\) (b) In one experiment, 30 mmol of protons are released into \(500 \mathrm{mL}\) of the buffer prepared in part (a). Is the capacity of the buffer sufficient? What is the resulting pH? (c) Another student accidentally adds \(20 \mathrm{mL}\) of \(10 \mathrm{M}\) HCl to 500 mL of the buffer solution prepared in part (a). Is the buffer ruined? If so, how could the buffer be regenerated?

The Henderson-Hasselbalch equation can be written as \(\mathrm{pH}=\mathrm{p} K_{\mathrm{a}}-\log \left(\frac{1}{\alpha}-1\right)\) where \(\alpha=\frac{\left[\mathrm{A}^{-}\right]}{\left[\mathrm{A}^{-}\right]+[\mathrm{HA}]}\) Thus, the degree of ionization \((\alpha)\) of an acid can be determined if both the \(\mathrm{pH}\) of the solution and the \(\mathrm{p} K_{\mathrm{a}}\) of the acid are known. (a) Use this equation to plot the pH versus the degree of ionization for the second ionization constant of phosphoric acid \(\left(K_{\mathrm{a}}=6.3 \times 10^{-8}\right)\) (b) If \(\mathrm{pH}=\mathrm{p} K_{\mathrm{a}}\) what is the degree of ionization? (c) If the solution had a pH of 6.0 what would the value of \(\alpha\) be?

The \(\mathrm{pH}\) of ocean water depends on the amount of atmospheric carbon dioxide. The dissolution of carbon dioxide in ocean water can be approximated by the following chemical reactions (Henry's Law constant for \(\left.\mathrm{CO}_{2} \text { is } K_{\mathrm{H}}=\left[\mathrm{CO}_{2}(\mathrm{aq})\right] /\left[\mathrm{CO}_{2}(\mathrm{g})\right]=0.8317 .\right)\) \(\mathrm{CO}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{aq})\) \(\mathrm{CaCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{Ca}^{2+}(\mathrm{aq})+\mathrm{CO}_{3}^{-}(\mathrm{aq})\) \(\mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{CO}_{3}^{-}(\mathrm{aq}) \rightleftharpoons \mathrm{HCO}_{3}^{-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) \(\mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{HCO}_{3}^{-}(\mathrm{aq}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(1)\) (a) Use the equations above to determine the hydronium ion concentration as a function of \(\left[\mathrm{CO}_{2}(\mathrm{g})\right]\) and \(\left[\mathrm{Ca}^{2+}\right]\) (b) During preindustrial conditions, we will assume that the equilibrium concentration of \(\left[\mathrm{CO}_{2}(\mathrm{g})\right]=280\) ppm and \(\left[\mathrm{Ca}^{2+}\right]=10.24 \mathrm{mM} .\) Calculate the \(\mathrm{pH}\) of a sample of ocean water.

In 1922 Donald D. van Slyke ( J. Biol. Chem., 52, 525) defined a quantity known as the buffer index: \(\beta=\mathrm{d} C_{\mathrm{b}} / \mathrm{d}(\mathrm{pH}),\) where \(\mathrm{d} C_{\mathrm{b}}\) represents the increment of moles of strong base to one liter of the buffer. For the addition of a strong acid, he wrote \(\beta=-\mathrm{d} C_{\mathrm{a}} / \mathrm{d}(\mathrm{pH})\) By applying this idea to a monoprotic acid and its conjugate base, we can derive the following expression: \(\beta=2.303\left(\frac{K_{w}}{\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]}+\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]+\frac{\mathrm{CK}_{\mathrm{a}}\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]}{\left(\mathrm{K}_{\mathrm{a}}+\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\right)^{2}}\right)\) where \(C\) is the total concentration of monoprotic acid and conjugate base. (a) Use the above expression to calculate the buffer index for the acetic acid buffer with a total acetic acid and acetate ion concentration of \(2.0 \times 10^{-2}\) and a \(\mathrm{pH}=5.0\) (b) Use the buffer index from part (a) and calculate the \(\mathrm{pH}\) of the buffer after the addition of of a strong acid. (Hint: Let \(\left.\mathrm{d} C_{\mathrm{a}} / \mathrm{d}(\mathrm{pH}) \approx \Delta C_{\mathrm{a}} / \Delta \mathrm{pH} .\right)\) (c) Make a plot of \(\beta\) versus \(\mathrm{pH}\) for a \(0.1 \mathrm{M}\) acetic acid buffer system. Locate the maximum buffer index as well as the minimum buffer indices.

Amino acids contain both an acidic carboxylic acid group \((-\mathrm{COOH})\) and a basic amino group \(\left(-\mathrm{NH}_{2}\right)\) The amino group can be protonated (that is, it has an extra proton attached) in a strongly acidic solution. This produces a diprotic acid of the form \(\mathrm{H}_{2} \mathrm{A}^{+}\), as exemplified by the protonated amino acid alanine. The protonated amino acid has two ionizable protons that can be titrated with \(\mathrm{OH}^{-}\) For the \(-\mathrm{COOH}\) group, \(\mathrm{pK}_{\mathrm{a}_{1}}=2.34 ;\) for the \(-\mathrm{NH}_{3}^{+}\) group, \(\mathrm{p} K_{\mathrm{a}_{2}}=9.69 .\) Consider the titration of a 0.500 M solution of alanine hydrochloride with \(0.500 \mathrm{M} \mathrm{NaOH}\) solution. What is the \(\mathrm{pH}\) of \((\mathrm{a})\) the \(0.500 \mathrm{M}\) alanine hydrochloride; (b) the solution at the first half- neutralization point; (c) the solution at the first equivalence point? The dominant form of alanine present at the first equivalence point is electrically neutral despite the positive charge and negative charge it possesses. The point at which the neutral form is produced is called the isoelectric point. Confirm that the \(\mathrm{pH}\) at the isoelectric point is \(\mathrm{pH}=\frac{1}{2}\left(\mathrm{pK}_{\mathrm{a}_{1}}+\mathrm{p} \mathrm{K}_{\mathrm{a}_{2}}\right)\) What is the \(\mathrm{pH}\) of the solution (d) halfway between the first and second equivalence points? (e) at the second equivalence point? (f) Calculate the pH values of the solutions when the following volumes of the \(0.500 \mathrm{M} \mathrm{NaOH}\) have been added to \(50 \mathrm{mL}\) of the \(0.500 \mathrm{M}\) alanine hydrochloride solution: \(10.0 \mathrm{mL}, 20.0 \mathrm{mL}, 30.0 \mathrm{mL}, 40.0 \mathrm{mL}, 50.0 \mathrm{mL}\) \(60.0 \mathrm{mL}, 70.0 \mathrm{mL}, 80.0 \mathrm{mL}, 90.0 \mathrm{mL}, 100.0 \mathrm{mL},\) and \(110.0 \mathrm{mL}\) (g) Sketch the titration curve for the 0.500 M solution of alanine hydrochloride, and label significant points on the curve.

In your own words, define or explain the following terms or symbols: (a) mmol; (b) HIn; (c) equivalence point of a titration; (d) titration curve.

Briefly describe each of the following ideas, phenomena, or methods: (a) the common-ion effect; (b) the use of a buffer solution to maintain a constant \(\mathrm{pH}\) (c) the determination of \(\mathrm{p} K_{\mathrm{a}}\) of a weak acid from a titration curve; (d) the measurement of \(\mathrm{pH}\) with an acid-base indicator.

Explain the important distinctions between each pair of terms: (a) buffer capacity and buffer range; (b) hydrolysis and neutralization; (c) first and second equivalence points in the titration of a weak diprotic acid; (d) equivalence point of a titration and end point of an indicator.

Write equations to show how each of the following buffer solutions reacts with a small added amount of a strong acid or a strong base: (a) HCOOH-KHCOO; (b) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}-\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}^{+} \mathrm{Cl}^{-}\) (c) \(\mathrm{KH}_{2} \mathrm{PO}_{4}-\mathrm{Na}_{2} \mathrm{HPO}_{4}\)

A 25.00 -mL sample of \(0.0100 \mathrm{M} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\left(\mathrm{K}_{\mathrm{a}}=\right.\) \(\left.6.3 \times 10^{-5}\right)\) is titrated with \(0.0100 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\) Calculate the \(\mathrm{pH}\) (a) of the initial acid solution; (b) after the addition of 6.25 mL of \(0.0100 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\) (c) at the equivalence point; (d) after the addition of a total of \(15.00 \mathrm{mL}\) of \(0.0100 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\)

To repress the ionization of formic acid, HCOOH(aq), which of the following should be added to the solution? (a) \(\mathrm{NaCl} ;\) (b) \(\mathrm{NaOH}\); (c) \(\mathrm{NaHCOO}\); (d) \(\mathrm{NaNO}_{3}\)

To increase the ionization of formic acid, \(\mathrm{HCOOH}(\mathrm{aq})\) which of the following should be added to the solution? (a) \(\mathrm{NaCl} ;\) (b) \(\mathrm{NaHCOO} ;(\mathrm{c}) \mathrm{H}_{2} \mathrm{SO}_{4} ;\) (d) \(\mathrm{NaHCO}_{3}\)

To convert \(\mathrm{NH}_{4}^{+}(\text {aq })\) to \(\mathrm{NH}_{3}(\mathrm{aq}),\) (a) add \(\mathrm{H}_{3} \mathrm{O}^{+}\) (b) raise the \(\mathrm{pH} ;\) (c) add \(\mathrm{KNO}_{3}(\mathrm{aq}) ;\) (d) add \(\mathrm{NaCl}\).

During the titration of equal concentrations of a weak base and a strong acid, at what point would the \(\mathrm{pH}=\mathrm{p} K_{\mathrm{a}} ?(\mathrm{a})\) the initial \(\mathrm{pH} ;\) (b) halfway to the equivalence point; (c) at the equivalence point; (d) past the equivalence point.

Calculate the pH of the buffer formed by mixing equal volumes \(\left[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\right]=1.49 \mathrm{M} \quad\) with \(\quad\left[\mathrm{HClO}_{4}\right]=\) 1.001 M. \(K_{\mathrm{b}}=4.3 \times 10^{-4}\)

Calculate the \(\mathrm{pH}\) of a \(0.5 \mathrm{M}\) solution of \(\mathrm{Ca}(\mathrm{HSe})_{2}\), given that \(\mathrm{H}_{2}\) Se has \(K_{\mathrm{a}_{1}}=1.3 \times 10^{-4}\) and \(K_{\mathrm{a}_{2}}=1 \times 10^{-11}\)

The effect of adding \(0.001 \mathrm{mol} \mathrm{KOH}\) to 1.00 Lof a solution that is \(0.10 \mathrm{M} \mathrm{NH}_{3}-0.10 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}\) is to (a) raise the pH very slightly; (b) lower the pH very slightly; (c) raise the pH by several units; (d) lower the pH by several units.

The most acidic of the following \(0.10 \mathrm{M}\) salt solutions is (a) \(\mathrm{Na}_{2} \mathrm{S} ;\) (b) \(\mathrm{NaHSO}_{4} ;\) (c) \(\mathrm{NaHCO}_{3} ;\) (d) \(\mathrm{Na}_{2} \mathrm{HPO}_{4}\)

If an indicator is to be used in an acid-base titration having an equivalence point in the pH range 8 to 10 , the indicator must (a) be a weak base; (b) have \(K_{\mathrm{a}}=1 \times 10^{-9} ;(\mathrm{c})\) ionize in two steps; (d) be added to the solution only after the solution has become alkaline.

Indicate whether you would expect the equivalence point of each of the following titrations to be below, above, or at \(\mathrm{pH}\) 7. Explain your reasoning. (a) \(\mathrm{NaHCO}_{3}(\mathrm{aq})\) is titrated with \(\mathrm{NaOH}(\mathrm{aq})\) (a) (b) \(\mathrm{HCl}(\mathrm{aq})\) is titrated with \(\mathrm{NH}_{3}(\mathrm{aq}) ;\) (c) \(\mathrm{KOH}(\mathrm{aq})\) is titrated with HI(aq).