# 8.6 Buffers  (Page 6/9)

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What is [OH ] in a solution of 0.125 M CH 3 NH 2 and 0.130 M CH 3 NH 3 Cl?
${\text{CH}}_{3}{\text{NH}}_{2}\left(aq\right)+{\text{H}}_{2}\text{O}\left(l\right)\phantom{\rule{0.2em}{0ex}}⇌\phantom{\rule{0.2em}{0ex}}{\text{CH}}_{3}{\text{NH}}_{3}{}^{\text{+}}\left(aq\right)+{\text{OH}}^{\text{−}}\left(aq\right)\phantom{\rule{5em}{0ex}}{K}_{\text{b}}=4.4\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}$

[OH ] = 4.2 $×$ 10 −4 M

What is [OH ] in a solution of 1.25 M NH 3 and 0.78 M NH 4 NO 3 ?
${\text{NH}}_{3}\left(aq\right)+{\text{H}}_{2}\text{O}\left(l\right)\phantom{\rule{0.2em}{0ex}}⇌\phantom{\rule{0.2em}{0ex}}{\text{NH}}_{4}{}^{\text{+}}\left(aq\right)+{\text{OH}}^{\text{−}}\left(aq\right)\phantom{\rule{5em}{0ex}}{K}_{\text{b}}=1.8\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-5}$

What concentration of NH 4 NO 3 is required to make [OH ] = 1.0 $×$ 10 −5 in a 0.200- M solution of NH 3 ?

[NH 4 NO 3 ] = 0.36 M

What concentration of NaF is required to make [H 3 O + ] = 2.3 $×$ 10 −4 in a 0.300- M solution of HF?

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:

(a) HCl

(b) KCH 3 CO 2

(c) NaCl

(d) KOH

(e) CH 3 CO 2 H

(a) The added HCl will increase the concentration of H 3 O + slightly, which will react with ${\text{CH}}_{3}{\text{CO}}_{2}{}^{\text{−}}$ and produce CH 3 CO 2 H in the process. Thus, $\left[{\text{CH}}_{3}{\text{CO}}_{2}{}^{\text{−}}\right]$ decreases and [CH 3 CO 2 H] increases.
(b) The added KCH 3 CO 2 will increase the concentration of $\left[{\text{CH}}_{3}{\text{CO}}_{2}{}^{\text{−}}\right]$ which will react with H 3 O + and produce CH 3 CO 2 H in the process. Thus, [H 3 O + ] decreases slightly and [CH 3 CO 2 H] 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 H 3 O + , thus reducing [H 3 O + ]. Some additional CH 3 CO 2 H will dissociate, producing $\left[{\text{CH}}_{3}{\text{CO}}_{2}{}^{\text{−}}\right]$ ions in the process. Thus, [CH 3 CO 2 H] decreases slightly and $\left[{\text{CH}}_{3}{\text{CO}}_{2}{}^{\text{−}}\right]$ increases.
(e) The added CH 3 CO 2 H will increase its concentration, causing more of it to dissociate and producing more $\left[{\text{CH}}_{3}{\text{CO}}_{2}{}^{\text{−}}\right]$ and H 3 O + in the process. Thus, [H 3 O + ] increases slightly and $\left[{\text{CH}}_{3}{\text{CO}}_{2}{}^{\text{−}}\right]$ increases.

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:

(a) KI

(b) NH 3

(c) HI

(d) NaOH

(e) NH 4 Cl

What will be the pH of a buffer solution prepared from 0.20 mol NH 3 , 0.40 mol NH 4 NO 3 , and just enough water to give 1.00 L of solution?

pH = 8.95

Calculate the pH of a buffer solution prepared from 0.155 mol of phosphoric acid, 0.250 mole of KH 2 PO 4 , and enough water to make 0.500 L of solution.

How much solid NaCH 3 CO 2 •3H 2 O 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.)

37 g (0.27 mol)

What mass of NH 4 Cl must be added to 0.750 L of a 0.100- M solution of NH 3 to give a buffer solution with a pH of 9.26? (Hint: Assume a negligible change in volume as the solid is added.)

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 K a for acetic acid.

(a) What is the pH of the solution?

(b) Is the solution acidic or basic?

(c) 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?

(a) pH = 5.222;
(b) The solution is acidic.
(c) pH = 5.221

A 5.36–g sample of NH 4 Cl was added to 25.0 mL of 1.00 M NaOH and the resulting solution

diluted to 0.100 L.

(a) What is the pH of this buffer solution?

(b) Is the solution acidic or basic?

(c) What is the pH of a solution that results when 3.00 mL of 0.034 M HCl is added to the solution?

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

To prepare the best buffer for a weak acid HA and its salt, the ratio $\frac{\left[{\text{H}}_{3}{\text{O}}^{\text{+}}\right]}{{K}_{\text{a}}}$ should be as close to 1 as possible for effective buffer action. The [H 3 O + ] concentration in a buffer of pH 3.1 is [H 3 O + ] = 10 −3.1 = 7.94 $×$ 10 −4 M
We can now solve for K a of the best acid as follows:
$\begin{array}{}\\ \\ \\ \\ \phantom{\rule{0.2em}{0ex}}\frac{\left[{\text{H}}_{3}{\text{O}}^{\text{+}}\right]}{{K}_{\text{a}}}\phantom{\rule{0.2em}{0ex}}=1\\ {K}_{\text{a}}=\phantom{\rule{0.2em}{0ex}}\frac{\left[{\text{H}}_{3}{\text{O}}^{\text{+}}\right]}{1}\phantom{\rule{0.2em}{0ex}}=7.94\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}\end{array}$
In [link] , the acid with the closest K a to 7.94 $×$ 10 −4 is HF, with a K a of 7.2 $×$ 10 −4 .

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

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

For buffers with pHs>7, you should use a weak base and its salt. The most effective buffer will have a ratio $\frac{\left[{\text{OH}}^{\text{−}}\right]}{{K}_{\text{b}}}$ 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 K b of the best base as follows:
$\phantom{\rule{0.2em}{0ex}}\frac{\left[{\text{OH}}^{\text{−}}\right]}{{K}_{\text{b}}}\phantom{\rule{0.2em}{0ex}}=1$
K b = [OH ] = 4.47 $×$ 10 −4
In [link] , the base with the closest K b to 4.47 $×$ 10 −4 is CH 3 NH 2 , with a K b = 4.4 $×$ 10 −4 .

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

What is the pH of 1.000 L of a solution of 100.0 g of glutamic acid (C 5 H 9 NO 4 , a diprotic acid; K 1 = 8.5 $×$ 10 −5 , K 2 = 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?

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