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6.E: Acid-Base Equilibria (Exercises)

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    364684
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    Polyprotic Acids

    1. Which of the following concentrations would be practically equal in a calculation of the equilibrium concentrations in a 0.134-M solution of H2CO3, a diprotic acid:

    • \(\ce{[H3O+]}\),
    • \([OH^−]\)
    • \([H_2CO_3]\)
    • \(\ce{[HCO3- ]}\)
    • \(\ce{[CO3^2- ]}\)

    No calculations are needed to answer this question.

    Answer
    [H3O+] and \(\ce{[HCO3- ]}\) are equal, H3O+ and \(\ce{HCO3-}\) are practically equal

    2. Calculate the concentration of each species present in a 0.050-M solution of H2S.

    3. Calculate the concentration of each species present in a 0.010-M solution of phthalic acid, C6H4(CO2H)2.

    Answer
    \(\ce{C6H4(CO2H)2}(aq)+\ce{H2O}(l)⇌\ce{H3O+}(aq)+\ce{C6H4(CO2H)(CO2)-}(aq) \hspace{20px} K_\ce{a}=1.1×10^{−3}\)
    \(\ce{C6H4(CO2H)(CO2)}(aq)+\ce{H2O}(l)⇌\ce{H3O+}(aq)+\ce{C6H4(CO2)2^2-}(aq) \hspace{20px} K_\ce{a}=3.9×10^{−6}\)
    [C6H4(CO2H)2] 7.2 × 10−3 M, [C6H4(CO2H)(CO2)] = [H3O+] 2.8 × 10−3 M, \(\ce{[C6H4(CO2)2^2- ]}\)3.9 × 10−6 M, [OH] 3.6 × 10−12 M

    4. Salicylic acid, HOC6H4CO2H, and its derivatives have been used as pain relievers for a long time. Salicylic acid occurs in small amounts in the leaves, bark, and roots of some vegetation (most notably historically in the bark of the willow tree). Extracts of these plants have been used as medications for centuries. The acid was first isolated in the laboratory in 1838.

    a. Both functional groups of salicylic acid ionize in water, with Ka = 1.0 × 10−3 for the—CO2H group and 4.2 × 10−13 for the −OH group. What is the pH of a saturated solution of the acid (solubility = 1.8 g/L)?

    b. Aspirin was discovered as a result of efforts to produce a derivative of salicylic acid that would not be irritating to the stomach lining. Aspirin is acetylsalicylic acid, CH3CO2C6H4CO2H. The −CO2H functional group is still present, but its acidity is reduced, Ka = 3.0 × 10−4. What is the pH of a solution of aspirin with the same concentration as a saturated solution of salicylic acid (See Part a)?

    c. Under some conditions, aspirin reacts with water and forms a solution of salicylic acid and acetic acid:

    \[\ce{CH3CO2C6H4CO2H}(aq)+\ce{H2O}(l)⟶\ce{HOC6H4CO2H}(aq)+\ce{CH3CO2H}(aq)\]

    d. Which of the acids salicylic acid or acetic acid produces more hydronium ions in solution such a solution?

    e. What are the concentrations of molecules and ions in a solution produced by the hydrolysis of 0.50 g of aspirin dissolved in enough water to give 75 mL of solution?

    5. The ion HTe is an amphiprotic species; it can act as either an acid or a base.

    1. Wh at is Ka for the acid reaction of HTe with H2O?
    2. What is Kb for the reaction in which HTe functions as a base in water?
    3. Demonstrate whether or not the second ionization of H2Te can be neglected in the calculation of [HTe] in a 0.10 M solution of H2Te.
    Answer
    a. (K_{\ce a2}=1×10^{−5};\)
    b. \(K_\ce{b}=4.3×10^{−12};\)
    c. \(\ce{\dfrac{[Te^2- ][H3O+]}{[HTe- ]}}=\dfrac{(x)(0.0141+x)}{(0.0141−x)}≈\dfrac{(x)(0.0141)}{0.0141}=1×10^{−5}\). Solving for x gives 1 × 10−5 M. Therefore, compared with 0.014 M, this value is negligible (0.071%).

    Buffers

    6. Explain why a buffer can be prepared from a mixture of NH4Cl and NaOH but not from NH3 and NaOH.

    7. Explain why the pH does not change significantly when a small amount of an acid or a base is added to a solution that contains equal amounts of the acid H3PO4 and a salt of its conjugate base NaH2PO4.

    Answer
    Excess H3O+ is removed primarily by the reaction:
    \(\ce{H3O+}(aq)+\ce{H2PO4-}(aq)⟶\ce{H3PO4}(aq)+\ce{H2O}(l)\) Excess base is removed by the reaction: \(\ce{OH-}(aq)+\ce{H3PO4}(aq)⟶\ce{H2PO4-}(aq)+\ce{H2O}(l)\)

    8. Explain why the pH does not change significantly when a small amount of an acid or a base is added to a solution that contains equal amounts of the base NH3 and a salt of its conjugate acid NH4Cl.

    9. What is [H3O+] in a solution of 0.25 M CH3CO2H and 0.030 M NaCH3CO2?

    \(\ce{CH3CO2H}(aq)+\ce{H2O}(l)⇌\ce{H3O+}(aq)+\ce{CH3CO2-}(aq) \hspace{20px} K_\ce{a}=1.8×10^{−5}\)

    Answer
    [H3O+] = 1.5 × 10−4 M

    10. What is [H3O+] in a solution of 0.075 M HNO2 and 0.030 M NaNO2?

    Answer
    \(\ce{HNO2}(aq)+\ce{H2O}(l)⇌\ce{H3O+}(aq)+\ce{NO2-}(aq) \hspace{20px} K_\ce{a}=4.5×10^{−5}\)

    11. What is [OH] in a solution of 0.125 M CH3NH2 and 0.130 M CH3NH3Cl?

    Answer
    \(\ce{CH3NH2}(aq)+\ce{H2O}(l)⇌\ce{CH3NH3+}(aq)+\ce{OH-}(aq) \hspace{20px} K_\ce{b}=4.4×10^{−4}\)
    [OH] = 4.2 × 10−4 M

    12. What is [OH] in a solution of 1.25 M NH3 and 0.78 M NH4NO3?

    Answer
    \(\ce{NH3}(aq)+\ce{H2O}(l)⇌\ce{NH4+}(aq)+\ce{OH-}(aq) \hspace{20px} K_\ce{b}=1.8×10^{−5}\)

    13. What concentration of NH4NO3 is required to make [OH] = 1.0 × 10−5 in a 0.200-M solution of NH3?

    Answer
    [NH4NO3] = 0.36 M

    14. What concentration of NaF is required to make [H3O+] = 2.3 × 10−4 in a 0.300-M solution of HF?

    15. What is the effect on the concentration of acetic acid, hydronium ion, and acetate ion when the following are added to an acidic buffer solution of equal concentrations of acetic acid and sodium acetate:

    1. HCl
    2. KCH3CO2
    3. NaCl
    4. KOH
    5. CH3CO2H
    Answer
    a. The added HCl will increase the concentration of H3O+ slightly, which will react with \(\ce{CH3CO2-}\) and produce CH3CO2H in the process. Thus, \(\ce{[CH3CO2- ]}\) decreases and [CH3CO2H] increases.
    b. The added KCH3CO2 will increase the concentration of \(\ce{[CH3CO2- ]}\) which will react with H3O+ and produce CH3CO2 H in the process. Thus, [H3O+] decreases slightly and [CH3CO2H] increases.
    c. The added NaCl will have no effect on the concentration of the ions.
    d. The added KOH will produce OH ions, which will react with the H3O+, thus reducing [H3O+]. Some additional CH3CO2H will dissociate, producing \(\ce{[CH3CO2- ]}\) ions in the process. Thus, [CH3CO2H] decreases slightly and \(\ce{[CH3CO2- ]}\) increases.
    e. The added CH3CO2H will increase its concentration, causing more of it to dissociate and producing more \(\ce{[CH3CO2- ]}\) and H3O+ in the process. Thus, [H3O+] increases slightly and \(\ce{[CH3CO2- ]}\) increases.

    16. What is the effect on the concentration of ammonia, hydroxide ion, and ammonium ion when the following are added to a basic buffer solution of equal concentrations of ammonia and ammonium nitrate:

    1. KI
    2. NH3
    3. HI
    4. NaOH
    5. NH4Cl

    17. What will be the pH of a buffer solution prepared from 0.20 mol NH3, 0.40 mol NH4NO3, and just enough water to give 1.00 L of solution?

    Answer
    pH = 8.95

    18. Calculate the pH of a buffer solution prepared from 0.155 mol of phosphoric acid, 0.250 mole of KH2PO4, and enough water to make 0.500 L of solution.

    19. How much solid NaCH3CO2•3H2O must be added to 0.300 L of a 0.50-M acetic acid solution to give a buffer with a pH of 5.00? (Hint: Assume a negligible change in volume as the solid is added.)

    Answer
    37 g (0.27 mol)

    20. What mass of NH4Cl must be added to 0.750 L of a 0.100-M solution of NH3 to give a buffer solution with a pH of 9.26? (Hint: Assume a negligible change in volume as the solid is added.)

    21. A buffer solution is prepared from equal volumes of 0.200 M acetic acid and 0.600 M sodium acetate. Use 1.80 × 10−5 as Ka for acetic acid.

    a. What is the pH of the solution?

    b. Is the solution acidic or basic?

    22. What is the pH of a solution that results when 3.00 mL of 0.034 M HCl is added to 0.200 L of the original buffer?

    1. pH = 5.222;
    2. The solution is acidic. (c) pH = 5.221

    23. A 5.36–g sample of NH4Cl was added to 25.0 mL of 1.00 M NaOH and the resulting solution diluted to 0.100 L.

    1. What is the pH of this buffer solution?
    2. Is the solution acidic or basic?
    3. What is the pH of a solution that results when 3.00 mL of 0.034 M HCl is added to the solution?

    24. Which acid in [link] is most appropriate for preparation of a buffer solution with a pH of 3.1? Explain your choice.

    Answer
    To prepare the best buffer for a weak acid HA and its salt, the ratio \(\dfrac{\ce{[H3O+]}}{K_\ce{a}}\) should be as close to 1 as possible for effective buffer action. The [H3O+] concentration in a buffer of pH 3.1 is [H3O+] = 10−3.1 = 7.94 × 10−4 M
    We can now solve for Ka of the best acid as follows:
    \(\dfrac{\ce{[H3O+]}}{K_\ce{a}}=1\)
    \(K_\ce{a}=\dfrac{\ce{[H3O+]}}{1}=7.94×10^{−4}\)
    In [link], the acid with the closest Ka to 7.94 × 10−4 is HF, with a Ka of 7.2 × 10−4.

    25. Which acid in [link] is most appropriate for preparation of a buffer solution with a pH of 3.7? Explain your choice.

    26. Which base in [link] is most appropriate for preparation of a buffer solution with a pH of 10.65? Explain your choice.

    Answer
    For buffers with pHs > 7, you should use a weak base and its salt. The most effective buffer will have a ratio \(\dfrac{\ce{[OH- ]}}{K_\ce{b}}\) that is as close to 1 as possible. The pOH of the buffer is 14.00 − 10.65 = 3.35. Therefore, [OH] is [OH] = 10−pOH = 10−3.35 = 4.467 × 10−4 M.
    We can now solve for Kb of the best base as follows: \(\dfrac{\ce{[OH- ]}}{K_\ce{b}}=1\) Kb = [OH] = 4.47 × 10−4 In [link], the base with the closest Kb to 4.47 × 10−4 is CH3NH2, with a Kb = 4.4 × 10−4.

    27. Which base in [link] is most appropriate for preparation of a buffer solution with a pH of 9.20? Explain your choice.

    28. Saccharin, C7H4NSO3H, is a weak acid (Ka = 2.1 × 10−2). If 0.250 L of diet cola with a buffered pH of 5.48 was prepared from 2.00 × 10−3 g of sodium saccharide, Na(C7H4NSO3), what are the final concentrations of saccharine and sodium saccharide in the solution?

    Answer
    The molar mass of sodium saccharide is 205.169 g/mol. Using the abbreviations HA for saccharin and NaA for sodium saccharide the number of moles of NaA in the solution is:
    9.75 × 10−6 mol. This ionizes initially to form saccharin ions, A, with: [A] = 3.9 × 10−5 M

    29. What is the pH of 1.000 L of a solution of 100.0 g of glutamic acid (C5H9NO4, a diprotic acid; K1 = 8.5 × 10−5, K2 = 3.39 × 10−10) to which has been added 20.0 g of NaOH during the preparation of monosodium glutamate, the flavoring agent? What is the pH when exactly 1 mol of NaOH per mole of acid has been added?

    Acid-Base Titrations

    30. Explain how to choose the appropriate acid-base indicator for the titration of a weak base with a strong acid.

    Answer
    At the equivalence point in the titration of a weak base with a strong acid, the resulting solution is slightly acidic due to the presence of the conjugate acid. Thus, pick an indicator that changes color in the acidic range and brackets the pH at the equivalence point. Methyl orange is a good example.

    31. Explain why an acid-base indicator changes color over a range of pH values rather than at a specific pH.

    32. Why can we ignore the contribution of water to the concentrations of H3O+ in the solutions of following acids:

    • 0.0092 M HClO, a weak acid
    • 0.0810 M HCN, a weak acid
    • 0.120 M \(\ce{Fe(H2O)6^2+}\) a weak acid, Ka = 1.6 × 10−7

    but not the contribution of water to the concentration of OH?

    Answer
    In an acid solution, the only source of OH ions is water. We use Kw to calculate the concentration. If the contribution from water was neglected, the concentration of OH would be zero.

    33. Why can we ignore the contribution of water to the concentration of OH in a solution of the following bases:

    0.0784 M C6H5NH2, a weak base

    0.11 M (CH3)3N, a weak base

    but not the contribution of water to the concentration of H3O+?

    34. Draw a curve for a series of solutions of HF. Plot [H3O+]total on the vertical axis and the total concentration of HF (the sum of the concentrations of both the ionized and nonionized HF molecules) on the horizontal axis. Let the total concentration of HF vary from 1 × 10−10 M to 1 × 10−2 M.

    Answer
    A graph is shown that is titled “Plot of [ H subscript 3 O superscript + ] Against [ H F ].” The horizontal axis is labeled “[ H F ], M.” The axis begins at 10 superscript negative 10 and includes markings every 10 superscript 2 units up to 1.0. The vertical axis is labeled “[ H subscript 3 O superscript plus ], M” and begins at 10 superscript negative 10 and increases by 10 superscript 2 up to 1.0. A black curve starts at the left side of the graph at (10 superscript negative 10, 10 superscript negative 7). The line extends horizontally to a horizontal axis value of 10 superscript negative 8. After this, the line gradually increases at a steady rate to a value just over 10 superscript negative 3 at a horizontal axis value of 10 superscript negative 2.

    35. Draw a curve similar to that shown in Figure for a series of solutions of NH3. Plot [OH] on the vertical axis and the total concentration of NH3 (both ionized and nonionized NH3 molecules) on the horizontal axis. Let the total concentration of NH3 vary from 1 × 10−10 M to 1 × 10−2 M.

    36. Calculate the pH at the following points in a titration of 40 mL (0.040 L) of 0.100 M barbituric acid (Ka = 9.8 × 10−5) with 0.100 M KOH.

    a. no KOH added

    b. 20 mL of KOH solution added

    c. 39 mL of KOH solution added

    d. 40 mL of KOH solution added

    e. 41 mL of KOH solution added

    Answer
    a. pH = 2.50; b. pH = 4.01; c. pH = 5.60; d. pH = 8.35; e. pH = 11.08

    37. The indicator dinitrophenol is an acid with a Ka of 1.1 × 10−4. In a 1.0 × 10−4-M solution, it is colorless in acid and yellow in base. Calculate the pH range over which it goes from 10% ionized (colorless) to 90% ionized (yellow).


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