Chapter 14

A friend asks the following: "Consider a buffered solution made up of the weak acid HA and its salt NaA. If a strong base like NaOH is added, the HA reacts with the OH - to form A Thus the amount of acid (HA) is decreased, and the amount of base \(\left(\mathrm{A}^{-}\right)\) is increased. Analogously, adding HCl to the buffered solution forms more of the acid (HA) by reacting with the base \(\left(\mathrm{A}^{-}\right)\). Thus how can we claim that a buffered solution resists changes in the pH of the solution?" How would you explain buffering to this friend?

Mixing together solutions of acetic acid and sodium hydroxide can make a buffered solution. Explain. How does the amount of each solution added change the effectiveness of the buffer?

Could a buffered solution be made by mixing aqueous solutions of HCl and NaOH? Explain. Why isn't a mixture of a strong acid and its conjugate base considered a buffered solution?

Sketch two pH curves, one for the titration of a weak acid with a strong base and one for a strong acid with a strong base. How are they similar? How are they different? Account for the similarities and the differences.

Sketch a pH curve for the titration of a weak acid (HA) with a strong base (NaOH). List the major species, and explain how you would go about calculating the pH of the solution at various points, including the halfway point and the equivalence point.

You have a solution of the weak acid HA and add some HCl to it. What are the major species in the solution? What do you need to know to calculate the \(\mathrm{pH}\) of the solution, and how would you use this information? How does the \(\mathrm{pH}\) of the solution of just the HA compare with that of the final mixture? Explain.

You have a solution of the weak acid HA and add some of the salt NaA to it. What are the major species in the solution? What do you need to know to calculate the \(\mathrm{pH}\) of the solution, and how would you use this information? How does the pH of the solution of just the HA compare with that of the final mixture? Explain.

The common ion effect for weak acids is to significantly decrease the dissociation of the acid in water. Explain the common ion effect.

Consider a buffer solution where [weak acid] \(>\) [conjugate base]. How is the pH of the solution related to the \(\mathrm{p} K_{\mathrm{a}}\) value of the weak acid? If [conjugate base] \(>\) [weak acid], how is pH related to \(\mathrm{p} K_{\mathrm{a}} ?\)

A best buffer has about equal quantities of weak acid and conjugate base present as well as having a large concentration of each species present. Explain.

Figure \(14-4\) shows the \(\mathrm{pH}\) curves for the titrations of six different acids by NaOH. Make a similar plot for the titration of three different bases by 0.10 \(M\) HCl. Assume \(50.0 \mathrm{mL}\) of \(0.20 M\) of the bases and assume the three bases are a strong base (KOH), a weak base with \(K_{\mathrm{b}}=1 \times 10^{-5},\) and another weak base with \(K_{\mathrm{b}}=1 \times 10^{-10}\).

Acid-base indicators mark the end point of titrations by "magically" turning a different color. Explain the "magic" behind acid-base indicators.

Which of the following can be classified as buffer solutions? a. \(0.25 M\) HBr \(+0.25 M\) HOBr b. \(0.15 M \mathrm{HClO}_{4}+0.20 \mathrm{M} \mathrm{RbOH}\) c. \(0.50 M\) HOCl \(+0.35 M\) KOCl d. \(0.70 M \mathrm{KOH}+0.70 \mathrm{M} \mathrm{HONH}_{2}\) e. \(0.85 M \mathrm{H}_{2} \mathrm{NNH}_{2}+0.60 \mathrm{M} \mathrm{H}_{2} \mathrm{NNH}_{3} \mathrm{NO}_{3}\)

A certain buffer is made by dissolving \(\mathrm{NaHCO}_{3}\) and \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) in some water. Write equations to show how this buffer neutralizes added \(\mathrm{H}^{+}\) and \(\mathrm{OH}^{-}\).

A buffer is prepared by dissolving \(\mathrm{HONH}_{2}\) and \(\mathrm{HONH}_{3} \mathrm{NO}_{3}\) in some water. Write equations to show how this buffer neutralizes added \(\mathrm{H}^{+}\) and \(\mathrm{OH}^{-}\).

Calculate the pH of each of the following solutions. a. \(0.100 M\) propanoic acid \(\left(\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{2}, K_{\mathrm{a}}=1.3 \times 10^{-5}\right)\) b. \(0.100 M\) sodium propanoate \(\left(\mathrm{NaC}_{3} \mathrm{H}_{5} \mathrm{O}_{2}\right)\) c. pure \(\mathrm{H}_{2} \mathrm{O}\) d. a mixture containing \(0.100 M \mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{2}\) and \(0.100 M\) \(\mathrm{NaC}_{3} \mathrm{H}_{5} \mathrm{O}_{2}\)

Calculate the \(\mathrm{pH}\) of each of the following solutions. a. \(0.100 M\) HONH \(_{2}\left(K_{\mathrm{b}}=1.1 \times 10^{-8}\right)\) b. \(0.100 M\) HONH \(_{3}\) Cl c. pure \(\mathrm{H}_{2} \mathrm{O}\) d. a mixture containing 0.100 \(M \mathrm{HONH}_{2}\) and \(0.100 \mathrm{M}\) \(\mathrm{HONH}_{3} \mathrm{Cl}\)

Calculate the \(\mathrm{pH}\) of each of the following buffered solutions. a. \(0.10 M\) acetic acid/0.25 \(M\) sodium acetate b. \(0.25 M\) acetic acid/0.10 \(M\) sodium acetate c. \(0.080 M\) acetic acid/0.20 \(M\) sodium acetate d. \(0.20 M\) acetic acid/0.080 \(M\) sodium acetate

Calculate the \(\mathrm{pH}\) of each of the following buffered solutions. a. \(0.50 M C_{2} H_{5} N H_{2} / 0.25 M C_{2} H_{5} N H_{3} C l\) b. \(0.25 M C_{2} H_{5} N H_{2} / 0.50 M C_{2} H_{5} N H_{3} C l\) c. \(0.50 M C_{2} H_{5} N H_{2} / 0.50 M C_{2} H_{5} N H_{3} C l\)

A buffered solution is made by adding \(50.0 \mathrm{g} \mathrm{NH}_{4} \mathrm{Cl}\) to 1.00 \(\mathrm{L}\) of a 0.75-M solution of \(\mathrm{NH}_{3}\). Calculate the pH of the final solution. (Assume no volume change.)

Calculate the \(\mathrm{pH}\) after 0.010 mole of gaseous \(\mathrm{HCl}\) is added to \(250.0 \mathrm{mL}\) of each of the following buffered solutions. a. \(0.050 M \mathrm{NH}_{3} / 0.15 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}\) b. \(0.50 M \mathrm{NH}_{3} / 1.50 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}\) Do the two original buffered solutions differ in their pH or their capacity? What advantage is there in having a buffer with a greater capacity?

An aqueous solution contains dissolved \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3} \mathrm{Cl}\) and \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2} .\) The concentration of \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\) is \(0.50 M\) and \(\mathrm{pH}\) is 4.20 a. Calculate the concentration of \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}\) in this buffer solution. b. Calculate the \(\mathrm{pH}\) after \(4.0 \mathrm{g} \mathrm{NaOH}(s)\) is added to \(1.0 \mathrm{L}\) of this solution. (Neglect any volume change.)

Carbonate buffers are important in regulating the pH of blood at \(7.40 .\) If the carbonic acid concentration in a sample of blood is 0.0012 \(M,\) determine the bicarbonate ion concentration required to buffer the \(\mathrm{pH}\) of blood at \(\mathrm{pH}=7.40\). \(\mathrm{H}_{2} \mathrm{CQ}_{3}(a g) \rightleftharpoons \mathrm{HCQ}_{3}^{-}(a g)+\mathrm{H}^{+}(a g) \quad \) \(K_{\mathrm{a}}=4.3 \times 10^{-7}\)

When a person exercises, muscle contractions produce lactic acid. Moderate increases in lactic acid can be handled by the blood buffers without decreasing the pH of blood. However, excessive amounts of lactic acid can overload the blood buffer system, resulting in a lowering of the blood pH. A condition called acidosis is diagnosed if the blood pH falls to 7.35 or lower. Assume the primary blood buffer system is the carbonate buffer system described in Exercise \(45 .\) Calculate what happens to the \(\left[\mathrm{H}_{2} \mathrm{CO}_{3}\right] /\left[\mathrm{HCO}_{3}^{-}\right]\) ratio in blood when the \(\mathrm{pH}\) decreases from 7.40 to 7.35.

Calculate the \(\mathrm{pH}\) of a solution that is \(0.40 \mathrm{M} \mathrm{H}_{2} \mathrm{NNH}_{2}\) and \(0.80 M \mathrm{H}_{2} \mathrm{NNH}_{3} \mathrm{NO}_{3} .\) In order for this buffer to have \(\mathrm{pH}=\) \(\mathrm{p} K_{\mathrm{a}},\) would you add HCl or NaOH? What quantity (moles) of which reagent would you add to \(1.0 \mathrm{L}\) of the original buffer so that the resulting solution has \(\mathrm{pH}=\mathrm{p} K_{\mathrm{a}} ?\)

Which of the following mixtures would result in buffered solutions when 1.0 L of each of the two solutions are mixed? a. \(0.1 M\) KOH and \(0.1 M \mathrm{CH}_{3} \mathrm{NH}_{3} \mathrm{Cl}\) b. \(0.1 M\) KOH and \(0.2 M \mathrm{CH}_{3} \mathrm{NH}_{2}\) c. \(0.2 M\) KOH and \(0.1 M \mathrm{CH}_{3} \mathrm{NH}_{3} \mathrm{Cl}\) d. \(0.1 M \mathrm{KOH}\) and \(0.2 M \mathrm{CH}_{3} \mathrm{NH}_{3} \mathrm{Cl}\)

Which of the following mixtures would result in a buffered solution when 1.0 L of each of the two solutions are mixed? a. \(0.2 M\) HNO and \(0.4 M \mathrm{NaNO}_{3}\) b. \(0.2 M \mathrm{HNO}_{3}\) and \(0.4 \mathrm{M} \mathrm{HF}\) c. \(0.2 \mathrm{M} \mathrm{HNO}_{3}\) and \(0.4 \mathrm{M} \mathrm{NaF}\) d. \(0.2 M\) HNO \(_{3}\) and \(0.4 M\) NaOH

Sketch the titration curve for the titration of a generic weak base B with a strong acid. The titration reaction is $$\mathbf{B}+\mathbf{H}^{+} \rightleftharpoons \mathbf{B H}^{+}$$ On this curve, indicate the points that correspond to the following: a. the stoichiometric (equivalence) point b. the region with maximum buffering c. \(\mathrm{pH}=\mathrm{p} K_{\mathrm{a}}\) d. \(\mathrm{pH}\) depends only on \([\mathrm{B}]\) e. \(\mathrm{pH}\) depends only on \(\left[\mathrm{BH}^{+}\right]\) f. \(\mathrm{pH}\) depends only on the amount of excess strong acid added

Consider the titration of \(40.0 \mathrm{mL}\) of \(0.200 \mathrm{M} \mathrm{HClO}_{4}\) by \(0.100 M\) KOH. Calculate the \(p\) H of the resulting solution after the following volumes of KOH have been added. a. \(0.0 \mathrm{mL}\) b. \(10.0 \mathrm{mL}\) c. \(40.0 \mathrm{mL}\) d. \(80.0 \mathrm{mL}\) e. \(100.0 \mathrm{mL}\)

Consider the titration of \(80.0 \mathrm{mL}\) of \(0.100 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\) by \(0.400 M\) HCl. Calculate the \(p H\) of the resulting solution after the following volumes of HCl have been added. a. \(0.0 \mathrm{mL}\) b. \(20.0 \mathrm{mL}\) c. \(30.0 \mathrm{mL}\) d. \(40.0 \mathrm{mL}\) e. \(80.0 \mathrm{mL}\)

Consider the titration of \(100.0 \mathrm{mL}\) of \(0.200 M\) acetic acid \(\left(K_{\mathrm{a}}=1.8 \times 10^{-5}\right)\) by \(0.100 M\) KOH. Calculate the \(\mathrm{pH}\) of the resulting solution after the following volumes of KOH have been added. a. \(0.0 \mathrm{mL}\) b. \(50.0 \mathrm{mL}\) c. \(100.0 \mathrm{mL}\) d. \(40.0 \mathrm{mL}\) e. \(50.0 \mathrm{mL}\) f. \(100.0 \mathrm{mL}\)

Consider the titration of \(100.0 \mathrm{mL}\) of \(0.100 \mathrm{M} \mathrm{H}_{2} \mathrm{NNH}_{2}\) \(\left(K_{\mathrm{b}}=3.0 \times 10^{-6}\right)\) by \(0.200 M\) HNO \(_{3}\). Calculate the pH of the resulting solution after the following volumes of \(\mathrm{HNO}_{3}\) have been added. a. \(0.0 \mathrm{mL}\) b. \(20.0 \mathrm{mL}\) c. \(25.0 \mathrm{mL}\) d. \(40.0 \mathrm{mL}\) e. \(50.0 \mathrm{mL}\) f. \(100.0 \mathrm{mL}\)

Lactic acid is a common by-product of cellular respiration and is often said to cause the "burn" associated with strenuous activity. A 25.0 -mL sample of 0.100 \(M\) lactic acid (HC \(_{3} \mathrm{H}_{5} \mathrm{O}_{3}\), \(\mathrm{p} K_{\mathrm{a}}=3.86\) is titrated with \(0.100 \mathrm{M}\) NaOH solution. Calculate the \(\mathrm{pH}\) after the addition of \(0.0 \mathrm{mL}, 4.0 \mathrm{mL}, 8.0 \mathrm{mL}, 12.5 \mathrm{mL}\) \(20.0 \mathrm{mL}, 24.0 \mathrm{mL}, 24.5 \mathrm{mL}, 24.9 \mathrm{mL}, 25.0 \mathrm{mL}, 25.1 \mathrm{mL}\) \(26.0 \mathrm{mL}, 28.0 \mathrm{mL},\) and \(30.0 \mathrm{mL}\) of the NaOH. Plot the results of your calculations as pH versus milliliters of NaOH added.

Calculate the \(\mathrm{pH}\) at the halfway point and at the equivalence point for each of the following titrations. a. \(100.0 \mathrm{mL}\) of \(0.10 \mathrm{M} \mathrm{HC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}\left(K_{\mathrm{a}}=6.4 \times 10^{-5}\right)\) titrated by 0.10 \(M \mathrm{NaOH}\) b. \(100.0 \mathrm{mL}\) of \(0.10 \mathrm{M} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\left(K_{\mathrm{b}}=5.6 \times 10^{-4}\right)\) titrated by 0.20 \(M \mathrm{HNO}_{3}\) c. \(100.0 \mathrm{mL}\) of \(0.50 \mathrm{M}\) HCl titrated by \(0.25 \mathrm{M} \mathrm{NaOH}\)

In the titration of \(50.0 \mathrm{mL}\) of \(1.0 \mathrm{M}\) methylamine, \(\mathrm{CH}_{3} \mathrm{NH}_{2}\) \(\left(K_{\mathrm{b}}=4.4 \times 10^{-4}\right),\) with \(0.50 M\) HCl, calculate the pH under the following conditions. a. after \(50.0 \mathrm{mL}\) of \(0.50 \mathrm{M}\) HCl has been added b. at the stoichiometric point

You have \(75.0 \mathrm{mL}\) of \(0.10 \mathrm{M}\) HA. After adding \(30.0 \mathrm{mL}\) of \(0.10 M \mathrm{NaOH},\) the \(\mathrm{pH}\) is \(5.50 .\) What is the \(K_{\mathrm{a}}\) value of \(\mathrm{HA} ?\)

A student dissolves 0.0100 mole of an unknown weak base in \(100.0 \mathrm{mL}\) water and titrates the solution with \(0.100 \mathrm{M} \mathrm{HNO}_{3}\) After \(40.0 \mathrm{mL}\) of \(0.100 \mathrm{M} \mathrm{HNO}_{3}\) was added, the \(\mathrm{pH}\) of the resulting solution was \(8.00 .\) Calculate the \(K_{\mathrm{b}}\) value for the weak base.

Two drops of indicator HIn \(\left(K_{\mathrm{a}}=1.0 \times 10^{-9}\right),\) where HIn is yellow and \(\operatorname{In}^{-}\) is blue, are placed in \(100.0 \mathrm{mL}\) of \(0.10 \mathrm{M}\) HCl. a. What color is the solution initially? b. The solution is titrated with 0.10 \(M\) NaOH. At what pH will the color change (yellow to greenish yellow) occur? c. What color will the solution be after \(200.0 \mathrm{mL}\) NaOH has been added?

A certain indicator HIn has a \(\mathrm{p} K_{\mathrm{a}}\) of 3.00 and a color change becomes visible when \(7.00 \%\) of the indicator has been converted to \(\operatorname{In}^{-} .\) At what \(\mathrm{pH}\) is this color change visible?

Derive an equation analogous to the Henderson-Hasselbalch equation but relating \(\mathrm{pOH}\) and \(\mathrm{p} K_{\mathrm{b}}\) of a buffered solution composed of a weak base and its conjugate acid, such as \(\mathrm{NH}_{3}\) and \(\mathrm{NH}_{4}^{+}\).

a. Calculate the pH of a buffered solution that is 0.100 \(M\) in \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H}\) (benzoic acid, \(K_{\mathrm{a}}=6.4 \times 10^{-5}\) ) and \(0.100 M\) in \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{Na}\) b. Calculate the \(\mathrm{pH}\) after \(20.0 \%\) (by moles) of the benzoic acid is converted to benzoate anion by addition of a strong base. Use the dissociation equilibrium $$ \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H}(a q) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2}^{-}(a q)+\mathrm{H}^{+}(a q)$$ to calculate the pH. c. Do the same as in part b, but use the following equilibrium to calculate the pH: \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H}(a q)+\mathrm{OH}^{-}(a q)\) d. Do your answers in parts \(b\) and c agree? Explain.

Tris(hydroxymethyl)aminomethane, commonly called TRIS or Trizma, is often used as a buffer in biochemical studies. Its buffering range is \(\mathrm{pH} 7\) to \(9,\) and \(K_{\mathrm{b}}\) is \(1.19 \times 10^{-6}\) for the aqueous reaction $$\left(\mathrm{HOCH}_{2}\right)_{3} \mathrm{CNH}_{2}+\mathrm{H}_{2}\mathrm{O}\rightleftharpoons\left(\mathrm{HOCH}_{2}\right)_{3} \mathrm{CNH}_{3}^{+}+\mathrm{OH}^{-}$$ a. What is the optimal pH for TRIS buffers? b. Calculate the ratio [TRIS]/[TTRISH \(\left.^{+}\right]\) at \(\mathrm{pH}=7.00\) and at \(\mathrm{pH}=9.00\) c. A buffer is prepared by diluting \(50.0 \mathrm{g}\) TRIS base and \(65.0 \mathrm{g}\) TRIS hydrochloride (written as TRISHCl) to a total volume of 2.0 L. What is the pH of this buffer? What is the \(\mathrm{pH}\) after \(0.50 \mathrm{mL}\) of \(12 \mathrm{M}\) HCl is added to a 200.0-mL portion of the buffer?

You make 1.00 L of a buffered solution \((p H=4.00)\) by mixing acetic acid and sodium acetate. You have \(1.00 M\) solutions of each component of the buffered solution. What volume of each solution do you mix to make such a buffered solution?

Amino acids are the building blocks for all proteins in our bodies. A structure for the amino acid alanine is All amino acids have at least two functional groups with acidic or basic properties. In alanine, the carboxylic acid group has \(K_{\mathrm{a}}=4.5 \times 10^{-3}\) and the amino group has \(K_{\mathrm{b}}=\) \(7.4 \times 10^{-5} .\) Because of the two groups with acidic or basic properties, three different charged ions of alanine are possible when alanine is dissolved in water. Which of these ions would predominate in a solution with \(\left[\mathrm{H}^{+}\right]=1.0\) \(\mathrm{M} ?\) In a solution with \(\left[\mathrm{OH}^{-}\right]=1.0\) \(\mathrm {M} ?\)

Phosphate buffers are important in regulating the \(\mathrm{pH}\) of intracellular fluids at \(\mathrm{pH}\) values generally between 7.1 and 7.2 a. What is the concentration ratio of \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) to \(\mathrm{HPO}_{4}^{2-}\) in intracellular fluid at \(\mathrm{pH}=7.15 ?\) \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}(a q) \rightleftharpoons \mathrm{HPO}_{4}^{2-}(a q)+\mathrm{H}^{+}(a q) \quad K_{\mathrm{a}}=6.2 \times 10^{-8}\) b. Why is a buffer composed of \(\mathrm{H}_{3} \mathrm{PO}_{4}\) and \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) ineffective in buffering the \(\mathrm{pH}\) of intracellular fluid? \(\mathrm{H}_{3} \mathrm{PO}_{4}(a q) \rightleftharpoons \mathrm{H}_{2} \mathrm{PO}_{4}^{-}(a q)+\mathrm{H}^{+}(a q) \quad K_{\mathrm{a}}=7.5 \times 10^{-3}\)

What quantity (moles) of HCl(g) must be added to \(1.0 \mathrm{L}\) of \(2.0 \mathrm{M}\) NaOH to achieve a pH of 0.00? (Neglect any volume changes.)

Calculate the volume of \(1.50 \times 10^{-2} \mathrm{M}\) NaOH that must be added to \(500.0 \mathrm{mL}\) of \(0.200 \mathrm{M}\) HCl to give a solution that has \(\mathrm{pH}=2.15\).

Repeat the procedure in Exercise \(61,\) but for the titration of \(25.0 \mathrm{mL}\) of 0.100 \(\mathrm{M}\) \(\mathrm{HNO}_{3}\) with 0.100 \(\mathrm{M}\) \(\mathrm{NaOH}\).

A 0.210 -g sample of an acid (molar mass \(=192 \mathrm{g} / \mathrm{mol}\) ) is titrated with \(30.5 \mathrm{mL}\) of \(0.108 \mathrm{M} \mathrm{NaOH}\) to a phenolphthalein end point. Is the acid monoprotic, diprotic, or triprotic?

The active ingredient in aspirin is acetylsalicylic acid. A \(2.51-\mathrm{g}\) sample of acetylsalicylic acid required \(27.36 \mathrm{mL}\) of \(0.5106 M\) NaOH for complete reaction. Addition of \(13.68 \mathrm{mL}\) of \(0.5106 \mathrm{M}\) HCl to the flask containing the aspirin and the sodium hydroxide produced a mixture with \(\mathrm{pH}=3.48 .\) Determine the molar mass of acetylsalicylic acid and its \(K_{\mathrm{a}}\) value. State any assumptions you must make to reach your answer.