## 9.7 Strong and Weak Bases ### Defining Base Strength The strength of a base is defined by its ability to accept a proton ($H^+$) from a solvent, typically water. The more readily a base accepts a proton, the stronger it is. #### Strong Bases Strong bases are substances that ionize completely in an aqueous solution to produce hydroxide ions ($OH^-$). They are typically hydroxides of alkali metals (Group 1) and alkaline earth metals (Group 2). Examples of strong bases include: - **Sodium Hydroxide ($NaOH$)**: $$NaOH_{(aq)} \rightarrow Na^+_{(aq)} + OH^-_{(aq)}$$ - **Potassium Hydroxide ($KOH$)**: $$KOH_{(aq)} \rightarrow K^+_{(aq)} + OH^-_{(aq)}$$ The hydroxide ion ($OH^-$) produced is a strong Brønsted-Lowry base because it readily accepts a proton to form water: $$OH^-_{(aq)} + H^+_{(aq)} \rightarrow H_2O_{(l)}$$ #### Weak Bases and Equilibrium Weak bases do not ionize completely in water. Instead, they establish an equilibrium where only a fraction of the base molecules accept a proton from water. For a generic weak base, B, the equilibrium reaction in water is: $$B_{(aq)} + H_2O_{(l)} \rightleftharpoons BH^+_{(aq)} + OH^-_{(aq)}$$ ### The Base Ionization Constant ($K_b$) The extent of ionization for a weak base is quantified by the **base ionization constant ($K_b$)**. It is the equilibrium constant for the reaction of the base with water. The expression for $K_b$ is: $$K_b = \frac{[BH^+][OH^-]}{[B]}$$ - A **large $K_b$ value** indicates a high degree of ionization, meaning the base is relatively **strong**. - A **small $K_b$ value** indicates a low degree of ionization, meaning the base is **weak**. ### The $pK_b$ Value For convenience, the strength of a base is often expressed using the **$pK_b$**, which is the negative logarithm of the base ionization constant. $$pK_b = -\log K_b$$ - A **small $pK_b$ value** corresponds to a large $K_b$, indicating a **stronger base**. - A **large $pK_b$ value** corresponds to a small $K_b$, indicating a **weaker base**. ### $K_b$ and $pK_b$ Values of Some Common Bases The table below shows the $K_b$ and $pK_b$ values for several common bases at standard conditions. | Name of Base | Formula | $K_b$ | $pK_b$ | | :------------ | :------------------------- | :-------------------- | :----- | | Diethylamine | $(\mathrm{C}_2\mathrm{H}_5)_2\mathrm{NH}$ | $9.6 \times 10^{-4}$ | 3.02 | | Ethylamine | $\mathrm{C}_2\mathrm{H}_5\mathrm{NH}_2$ | $5.6 \times 10^{-4}$ | 3.25 | | Methylamine | $\mathrm{CH}_3\mathrm{NH}_2$ | $4.5 \times 10^{-4}$ | 3.34 | | Ammonia | $\mathrm{NH}_3$ | $1.7 \times 10^{-5}$ | 4.76 | | Pyridine | $\mathrm{C}_5\mathrm{H}_5\mathrm{N}$ | $5.6 \times 10^{-9}$ | 8.25 | | Aniline | $\mathrm{C}_6\mathrm{H}_5\mathrm{NH}_2$ | $4.3 \times 10^{-10}$ | 9.37 | **Analysis:** - Based on the $pK_b$ values, the order of base strength from strongest to weakest is: Diethylamine > Ethylamine > Methylamine > Ammonia > Pyridine > Aniline. - **Diethylamine** is the strongest base listed in the table (smallest $pK_b$). - **Aniline** is the weakest base listed (largest $pK_b$).