Question 15.12: Codeine (C18H21NO3), a drug used in painkillers and cough me......
Codeine (C_{18}H_{21}NO_{3}), a drug used in painkillers and cough medicines, is a naturally occurring amine that has K_{b} = 1.6\times 10^{-6}. Calculate the pH and the concentrations of all species present in a 0.0012 M solution of codeine.
STRATEGY
Use the procedure outlined in Figure 15.7.
| IDENTIFY | |
| Known | Unknown |
| Concentration of codeine (0.0012 M) | pH |
| K_{b}=1.6\times 10^{-6} | Equilibrium concentrations |
Step 1. Let’s use Cod as an abbreviation for codeine and CodH^{+} for its conjugate acid. The species present initially are Cod (base) and H_{2}O (acid or base).
Step 2. There are two possible proton-transfer reactions:
Cod(aq)+H_{2}O(l)\xrightleftharpoons{} CodH^{+}(aq)+OH^{-}(aq) K_{b} = 1.6\times 10^{-6}\\ H_{2}O(l)+H_{2}O(l)\xrightleftharpoons{} H_{3}O^{+}(aq) + OH^{-}(aq) K_{w} = 1.0\times 10^{-14}Step 3. Since Cod is a much stronger base than H_{2}O (K_{b} >> K_{w}), the principal reaction involves the protonation of codeine.
Step 4.
Table 1
Step 5. The value of x is obtained from the equilibrium equation:
K_{b}=1.6\times 10^{-6}=\frac{[CodH^{+}][OH^{-}]}{[Cod]}=\frac{(x)(x)}{(0.0012 – x)}Assuming that (0.0012 – x) ≈ 0.0012,
x^{2}=(1.6\times 10^{-6})(0.0012)x=4.4\times 10^{-5} Approximation (0.0012 – x) ≈ 0.0012 is justified.
Step 6. The big concentrations are
[CodH^{+}]=[OH^{-}]= x =4.4\times 10^{-5} M[Cod] = 0.0012 – x = 0.0012 – 0.000 044 = 0.0012 M
Step 7. The small concentration is obtained from the subsidiary equilibrium, the dissociation of water:
[H_{3}O^{+}]=\frac{K_{w}}{[OH^{-}]}=\frac{1.0\times 10^{-14}}{4.4\times 10^{-5}}=2.3\times 10^{-10} MStep 8. pH = – log [H_{3}O^{+}] = – log (2.3\times 10^{-10})=9.64
The pH is greater than 7, as expected for a solution of a weak base.
Table 1
| Principal reaction | Cod(aq) | + | H_{2}O(l) | \xrightleftharpoons{} | CodH^{+}(aq) | + | OH^{-}(aq) |
| Initial concentration (M) | 0.0012 | 0 | ∼ 0 | ||||
| Change (M) | -x | +x | +x | ||||
| Equilibrium concentration (M) | 0.0012 – x | x | x |