The pH of 0.005M codeine (C 18H21NO3) solution is 9.95. Calculate its ionization constant and pKb.

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Q. The pH of 0.005M codeine (C 18H21NO3) solution is 9.95. Calculate its ionization constant and pKb.

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Concept understanding — Weak Acid Ionization

Weak Acid Ionization: From Intuition to Precision

Imagine you drop a spoonful of sugar into a glass of water. Some sugar dissolves, but a lot just sits at the bottom. Now imagine you drop a spoonful of salt — it all dissolves completely. Acids behave the same way. Some acids, like hydrochloric acid (HCl), dissolve completely in water — every single molecule breaks apart. Others, like acetic acid (vinegar), only partially break apart. Most of the acid molecules stay intact, and only a few actually ionize.

That's the core idea: weak acids are shy about giving away their hydrogen ion. They don't fully commit.

The Precise Statement

A weak acid ( $HA$ ) in water establishes an equilibrium between the intact acid molecule and its ions:

HA_{(aq)} + H_2O_{(l)} \rightleftharpoons H_3O^+_{(aq)} + A^-_{(aq)}

The double arrow ( $\rightleftharpoons$ ) is the key. It tells you the reaction happens in both directions simultaneously. Some $HA$ molecules break apart to form $H_3O^+$ and $A^-$ , while some $H_3O^+$ and $A^-$ recombine back into $HA$ . At equilibrium, both processes happen at the same rate — so the concentrations stop changing.

Important

For a weak acid, most of the acid remains as $HA$ at equilibrium. Only a tiny fraction exists as ions. This is the opposite of a strong acid, where the forward reaction goes to completion (single arrow: $\rightarrow$ ).

The Quantitative Measure: $K_a$

Every weak acid has a number that tells you exactly how "shy" it is — the acid dissociation constant, $K_a$ :

K_a = \frac{[H_3O^+][A^-]}{[HA]}

K_a = \frac{[H_3O^+][A^-]}{[HA]}

The smaller the $K_a$ , the weaker the acid. For acetic acid (vinegar), $K_a \approx 1.8 \times 10^{-5}$ . That tiny number means the numerator (ions) is very small compared to the denominator (intact acid). For a strong acid like HCl, $K_a$ is effectively infinite — the denominator is essentially zero because all the acid has ionized.

A Concrete Example

Suppose you dissolve 0.10 mol of acetic acid ( $CH_3COOH$ ) in 1 L of water. At equilibrium, you'll find:

$[CH_3COOH] \approx 0.0998$ M (almost all of it is still intact)
$[H_3O^+] \approx 0.0013$ M (only about 1.3% has ionized)
$[CH_3COO^-] \approx 0.0013$ M

Note

|---------|-------------|------------|-----------------|

| $CH_3COOH$ | 0.10 | $-x$ | $0.10 - x$ |

| $H_3O^+$ | 0 | $+x$ | $x$ |

| $CH_3COO^-$ | 0 | $+x$ | $x$ |

Plugging into $K_a = \frac{x^2}{0.10 - x} = 1.8 \times 10^{-5}$ and solving gives $x \approx 0.0013$ M.

Why This Matters …

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A weak base in water establishes equilibrium; from the pH we find $[\text{OH}^-]$ , then use the ionization expression to extract $K_b = 1.62 \times 10^{-6}$ and $\text{pK}_b = 5.79$ .

Codeine is a weak organic base. When dissolved in water it accepts a proton from water molecules, establishing an equilibrium rather than going to completion. The pH tells us the hydrogen-ion concentration at equilibrium, and from that we can work backwards to find how much the base has ionized—which in turn reveals the equilibrium constant $K_b$ .

The strategy is straightforward: convert pH to $[\text{H}^+]$ , use the water equilibrium to find $[\text{OH}^-]$ , recognize that this hydroxide came from the ionization of codeine, then substitute into the $K_b$ expression.

1. Write the ionization equilibrium

Codeine, which we'll call $\text{B}$ for simplicity, accepts a proton from water:

\text{B} + \text{H}_2\text{O} \rightleftharpoons \text{BH}^+ + \text{OH}^-

The ionization constant is

K_b = \frac{[\text{BH}^+][\text{OH}^-]}{[\text{B}]}

2. Find the hydroxide-ion concentration from pH

We are given $\text{pH} = 9.95$ , so

[\text{H}^+] = 10^{-9.95} = 1.122 \times 10^{-10} \, \text{M}

At $25\,^\circ\text{C}$ , water's ion product is $K_w = 1.0 \times 10^{-14}$ , hence

[\text{OH}^-] = \frac{K_w}{[\text{H}^+]} = \frac{1.0 \times 10^{-14}}{1.122 \times 10^{-10}} = 8.913 \times 10^{-5} \, \text{M}

3. Relate equilibrium concentrations to the initial concentration

Start with $c = 0.005 \, \text{M}$ of codeine. Let $x$ be the amount that ionizes. At equilibrium:

Species	Concentration
$\text{B}$	$c - x$
$\text{BH}^+$	$x$
$\text{OH}^-$	$x$

From step 2, $x = [\text{OH}^-] = 8.913 \times 10^{-5} \, \text{M}$ .

The remaining base concentration is

$[\text{B}] = 0.005 - 8.913 \times 10^{-5} = 0.004911 \, \text{M}$ …

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Q.The pH of 0.005M codeine (C 18H21NO3) solution is 9.95. Calculate its ionization constant and pKb.

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