9.6 Strong and Weak Acids

The strength of an acid is determined by the extent to which it ionizes (or dissociates) in water. This extent can be quantified using the acid dissociation constant, $K_a$.

The Acid Dissociation Constant ($K_a$)

For a general weak acid, HX, its ionization in an aqueous solution establishes an equilibrium:

${\mathrm{HX}}_{(aq)}+{\mathrm{H}}_2{\mathrm{O}}_{(l)}\rightleftharpoons {\mathrm{H}}_3{\mathrm{O}}_{(aq)}^{+}+{\mathrm{X}}_{(aq)}^{-}$

The equilibrium constant, $K$, for this reaction is:

$K=\frac{[{\mathrm{H}}_3{\mathrm{O}}^{+}][{\mathrm{X}}^{-}]}{[\mathrm{HX}][{\mathrm{H}}_2\mathrm{O}]}$

Since water acts as the solvent, its concentration $[H_{2}O]$ is very large and remains nearly constant. We can combine the constant $[H_{2}O]$ with the equilibrium constant $K$ to define a new constant, the acid dissociation constant, $K_a$:

$K_a=K[{\mathrm{H}}_2\mathrm{O}]=\frac{[{\mathrm{H}}_3{\mathrm{O}}^{+}][{\mathrm{X}}^{-}]}{[\mathrm{HX}]}$

• $K_a$ is a measure of acid strength: It indicates the extent to which an acid dissociates at equilibrium.
• Temperature Dependence: The value of $K_a$ depends on temperature. For example, the $K_a$ for acetic acid at $25^{\circ }C$ is $1.8\times 10^{-5}$.

The pKa Scale

Since $K_a$ values are often very small and inconvenient to work with, the $p{K}_a$ scale is used for convenience. The relationship is similar to that between $[H^{+}]$ and pH:

$p{K}_a=-\log K_a$

Due to the negative logarithm, there is an inverse relationship between $p{K}_a$ and acid strength:

Comparing Acid Strengths

The table below lists the $K_a$ and $p{K}_a$ values for some common acids at $25^{\circ }C$.

Table 9.2: Ionization Constants and $p{K}_a$ of Acids

Why is HF a Weak Acid?

Despite fluorine being the most electronegative element, HF is a weak acid ($K_a=7.2\times 10^{-4}$) because:

1. The $H-F$ bond has very high bond enthalpy, making it difficult to break.
2. The small $F^{-}$ ion has very high charge density, which restricts its separation from $H_3{O}^{+}$.

In contrast, HCl, HBr, and HI are all strong acids because their $H-X$ bonds are much weaker (longer bonds, lower bond enthalpy).

Worked Example: Calculating $[H^{+}]$ Using an ICE Table

Example 9.5

Calculate the concentration of $H^{+}$ ions in a solution that contains $1.0M$ HF. ($K_a=7.2\times 10^{-4}$)

Solution:

Step 1 — Write the equilibrium reaction: ${\mathrm{HF}}_{(aq)}\rightleftharpoons {\mathrm{H}}_{(aq)}^{+}+{\mathrm{F}}_{(aq)}^{-}$

Step 2 — Set up an ICE table (concentrations in $mold{m}^{-3}$):

Step 3 — Write the $K_a$ expression: $K_a=\frac{[{\mathrm{H}}^{+}][{\mathrm{F}}^{-}]}{[\mathrm{HF}]}=\frac{x^2}{1.0-x}$

Step 4 — Apply the approximation: Since HF is a weak acid, $x\ll 1.0$, so $1.0-x\approx 1.0$: $7.2\times 10^{-4}\approx \frac{x^2}{1.0}$

Step 5 — Solve for x: $x^2=7.2\times 10^{-4}$ $x=\sqrt{7.2\times 10^{-4}}\approx 0.0268M$

Result: $[{\mathrm{H}}^{+}]=0.0268M$