Question 16.18: Determine (a) Kb of the acetate ion (CH3COO^–), (b) Ka of th...
Determine (a) K_b of the acetate ion (\text{CH}_3\text{COO}^–), (b) K_a of the methylammonium ion (\text{CH}_3\text{NH}_3^+), (c) K_b of the fluoride ion (\text{F}^–), and (d) K_a of the ammonium ion (\text{NH}_4^+).
Strategy Each species listed is either a conjugate base or a conjugate acid. Determine the identity of the acid corresponding to each conjugate base and the identity of the base corresponding to each conjugate acid; then, consult Tables 16.7 and 16.8 for their ionization constants. Use the tabulated ionization constants and Equation 16.8 to calculate each indicated K value.
Setup
(a) A K_b value is requested, indicating that the acetate ion is a conjugate base. To identify the corresponding Brønsted acid, add a proton to the formula to get \text{CH}_3\text{COOH} (acetic acid). The K_a of acetic acid (from Table 16.7) is 1.8 × 10^{–5}.
(b) A K_a value is requested, indicating that the methylammonium ion is a conjugate acid. Determine the identity of the corresponding Brønsted base by removing a proton from the formula to get \text{CH}_3\text{NH}_2 (methylamine). The K_b of methylamine (from Table 16.8) is 4.4 × 10^{–4}.
(c) \text{F}^– is the conjugate base of \text{HF; Ka} = 7.1 × 10^{–4}
(d) \text{NH}_4^+ is the conjugate acid of \text{NH}_3; K_b = 1.8 × 10^{–5} . Solving Equation 16.8 separately for K_a and K_b gives, respectively,
K_a = \frac{K_w}{K_b} and K_b = \frac{K_w}{K_a}
| TA B L E 1 6 . 7 Ionization Constants of Some Weak Acids at 25°C | |||
| Name of acid | Formula | Structure | K_a |
| \text{Chloroacetic acid} | \text{CH}_2\text{ClCOOH} |  |
5.6 × 10^{–2} |
| \text{Hydrofluoric acid} | \text{HF} |  |
7.1 × 10^{–4} |
| \text{Nitrous acid} | \text{HNO}_2 |  |
4.5 × 10^{–4} |
| \text{Formic acid} | \text{HCOOH} |  |
1.7 × 10^{–4} |
| \text{Benzoic acid} | \text{C}_6\text{H}_5\text{COOH} |  |
6.5 × 10^{–5} |
| \text{Acetic acid} | \text{CH}_3\text{COOH} |  |
1.8 × 10^{–5} |
| \text{Hydrocyanic acid} | \text{HCN} |  |
4.9 × 10^{–10} |
| \text{Phenol} | \text{C}_6\text{H}_5\text{OH} |  |
1.3 × 10^{–10} |
| TA B L E 1 6 . 8 Ionization Constants of Some Weak Acids at 25°C | |||
| Name of acid | Formula | Structure | K_b |
| \text{Ethylamine} | \text{C}_2\text{H}_5\text{NH}_2 |  |
5.6 × 10^{–4} |
| \text{Methylamine} | \text{CH}_3\text{NH}_2 |  |
4.4 × 10^{–4} |
| \text{Ammonia} | \text{NH}_3 |  |
1.8 × 10^{–5} |
| \text{Pyridine} | \text{C}_5\text{H}_5\text{N} |  |
1.7 × 10^{–9} |
| \text{Aniline} | \text{C}_6\text{H}_5\text{NH}_2 |  |
3.8 × 10^{–10} |
| \text{Urea} | \text{H}_2\text{NCONH}_2 |  |
1.5 × 10^{–14} |
Equation 16.8 K_a × K_b = K_w
(a) Conjugate base \text{CH}_3\text{COO}^–: K_b = \frac{1.0 × 10^{–14}}{1.8 × 10^{–5}} = 5.6 × 10^{–10}
(b) Conjugate acid \text{CH}_3\text{NH}_3^+: K_a = \frac{1.0 × 10^{–14}}{4.4 × 10^{–4}} = 2.3 × 10^{–11}
(c) Conjugate base \text{F}^–: K_b = \frac{1.0 × 10^{–14}}{7.1 × 10^{–4}} = 1.4 × 10^{–11}
(d) Conjugate acid \text{NH}_4^+: K_a = \frac{1.0 × 10^{–14}}{1.8 × 10^{–5}} = 5.6 × 10^{–10}