# 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 $[H_2O]$ is very large and remains nearly constant. We can combine the constant $[H_2O]$ 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 $K_a$ is dependent on temperature. For example, the $K_a$ for acetic acid at $25^{\circ}C$ is $1.8 \times 10^{-5}$. > **The greater the value of $K_a$, the stronger the acid.** ## The pKa Scale Since $K_a$ values are often very small and inconvenient to work with, the **$pK_a$** scale is used for convenience. The relationship is similar to that between $[H^+]$ and pH. $$ pK_a = -\log K_a $$ * Due to the negative logarithm, there is an *inverse relationship* between $pK_a$ and acid strength. > **The smaller the value of $pK_a$, the stronger the acid.** ## Comparing Acid Strengths The table below lists the $K_a$ and $pK_a$ values for some common acids at $25^{\circ}C$. For more details on the properties of elements like halogens in these acids, see . **Table 9.2: Ionization Constants and $pK_a$ of Acids** | Name of Acid | Formula | $K_a$ | $pK_a$ | | :--- | :--- | :--- | :--- | | Perchloric acid | $HClO_4$ | $1.0 \times 10^{10}$ | -10.0 | | Hydroiodic acid | HI | $1.0 \times 10^{10}$ | -10.0 | | Hydrobromic acid | HBr | $1.0 \times 10^{9}$ | -9.0 | | Hydrochloric acid | HCl | $1.0 \times 10^{6}$ | -6.0 | | Sulphuric acid | $H_2SO_4$ | $1.0 \times 10^{3}$ | -3.0 | | Hydrofluoric acid | HF | $7.2 \times 10^{-4}$ | +3.1 | | Formic acid | HCOOH | $1.8 \times 10^{-4}$ | +3.75 | | Benzoic acid | $C_6H_5COOH$ | $6.3 \times 10^{-5}$ | +4.2 | | Acetic acid | $CH_3COOH$ | $1.8 \times 10^{-5}$ | +4.7 | | Phenol | $C_6H_5OH$ | $1.3 \times 10^{-10}$ | +9.89 | | Water | $H_2O$ | $1.8 \times 10^{-16}$ | +15.7 | ## Worked Examples ### Example 9.5 Calculate the concentration of $H^+$ ions in a solution that contains $1.0 \, M$ HF. ($K_a = 7.2 \times 10^{-4}$). **Solution:** 1. **Write the equilibrium reaction:** $$ \mathrm{HF}_{(aq)} \rightleftharpoons \mathrm{H}^{+}_{(aq)} + \mathrm{F}^{-}_{(aq)} $$ 2. **Set up an ICE table** (Initial, Change, Equilibrium) to track concentrations in $mol\,dm^{-3}$: | Concentration | HF | $H^+$ | $F^-$ | | :--- | :--- | :--- | :--- | | **Initial (I)** | 1.0 M | 0 | 0 | | **Change (C)** | -x | +x | +x | | **Equilibrium (E)**| 1.0 - x | x | x | 3. **Write the $K_a$ expression and substitute equilibrium values:** $$ K_a = \frac{[\mathrm{H}^{+}][\mathrm{F}^{-}]}{[\mathrm{HF}]} $$ $$ 7.2 \times 10^{-4} = \frac{(x)(x)}{1.0 - x} = \frac{x^2}{1.0 - x} $$ 4. **Apply the approximation:** Since HF is a weak acid, the extent of dissociation (x) is very small compared to the initial concentration (1.0 M). We can approximate $1.0 - x \approx 1.0$. $$ 7.2 \times 10^{-4} \approx \frac{x^2}{1.0} $$ 5. **Solve for x:** $$ x^2 = 7.2 \times 10^{-4} $$ $$ x = \sqrt{7.2 \times 10^{-4}} $$ $$ x \approx 0.0268 \, M $$ 6. **State the final answer:** The concentration of $H^+$ ions at equilibrium is equal to x. $$ [\mathrm{H}^{+}] = 0.0268 \, M $$ ## Possible Questions and Answers **Q:** From the table, which is the strongest acid? **A:** Perchloric acid ($HClO_4$) and Hydroiodic acid (HI) are the strongest, with the highest $K_a$ value ($1.0 \times 10^{10}$) and lowest $pK_a$ value (-10.0). **Q:** From the table, which is the weakest acid? **A:** Water ($H_2O$) is the weakest acid, with the smallest $K_a$ value ($1.8 \times 10^{-16}$) and highest $pK_a$ value (+15.7). **Q:** Which is a stronger acid, HCl or HF? **A:** HCl is a much stronger acid. Its $K_a$ ($1.0 \times 10^6$) is about 10 billion times larger than the $K_a$ of HF ($7.2 \times 10^{-4}$). This is also reflected in their $pK_a$ values (-6.0 for HCl vs. +3.1 for HF).