9.1 Conjugate Acid-Base Pairs

This section explores the concept of conjugate acid-base pairs, a fundamental principle in the Brønsted-Lowry theory of acids and bases.

Definitions

A conjugate acid is the species formed when a base accepts a proton ($H^{+}$).

A conjugate base is the species that remains after an acid has donated a proton ($H^{+}$).

In any acid-base reaction, an acid donates a proton to become a conjugate base, and a base accepts that proton to become a conjugate acid. This relationship is represented by the general equilibrium:

$\underset{{\text{(Acid}}_1\text{)}}{\mathrm{HA}}+\underset{{\text{(Base}}_2\text{)}}{B}\rightleftharpoons \underset{{\text{(Conjugate Base}}_1\text{)}}{{\text{A}}^{-}}+\underset{{\text{(Conjugate Acid}}_2\text{)}}{{\text{HB}}^{+}}$

• The pair $HA/A^{-}$ is one conjugate acid-base pair.
• The pair $H{B}^{+}/B$ is the other conjugate acid-base pair.
• A conjugate acid-base pair consists of two species that differ only by a single proton ($H^{+}$).

Strength of Conjugate Pairs

There is an inverse relationship between the strength of an acid or base and its conjugate partner:

• A strong acid readily donates its proton → very weak conjugate base.
• A strong base readily accepts a proton → very weak conjugate acid.
• A weak acid has a relatively strong conjugate base.
• A weak base has a relatively strong conjugate acid.

Examples

1. Ionization of Hydrochloric Acid (HCl) in Water

$\underset{{\text{(Acid}}_1\text{)}}{\mathrm{HCl}}+\underset{{\text{(Base}}_2\text{)}}{{\text{H}}_2\text{O}}\rightleftharpoons \underset{{\text{(Conjugate Base}}_1\text{)}}{{\text{Cl}}^{-}}+\underset{{\text{(Conjugate Acid}}_2\text{)}}{{\text{H}}_3{\text{O}}^{+}}$

• Pair 1: $HCl$ (acid) and $C{l}^{-}$ (conjugate base)
• Pair 2: $H_{2}O$ (base) and $H_3{O}^{+}$ (conjugate acid)

2. Ionization of Ammonia ($N{H}_3$) in Water

$\underset{{\text{(Base}}_1\text{)}}{{\text{NH}}_3}+\underset{{\text{(Acid}}_2\text{)}}{{\text{H}}_2\text{O}}\rightleftharpoons \underset{{\text{(Conjugate Acid}}_1\text{)}}{{\text{NH}}_4^{+}}+\underset{{\text{(Conjugate Base}}_2\text{)}}{{\text{OH}}^{-}}$

• Pair 1: $N{H}_3$ (base) and $N{H}_4^{+}$ (conjugate acid)
• Pair 2: $H_{2}O$ (acid) and $O{H}^{-}$ (conjugate base)

3. Self-ionization of Water ($H_{2}O$)

Water can act as both an acid and a base — a property known as being amphoteric (or amphiprotic).

$\underset{{\text{(Acid}}_1\text{)}}{{\text{H}}_2\text{O}}+\underset{{\text{(Base}}_2\text{)}}{{\text{H}}_2\text{O}}\rightleftharpoons \underset{{\text{(Conjugate Base}}_1\text{)}}{{\text{OH}}^{-}}+\underset{{\text{(Conjugate Acid}}_2\text{)}}{{\text{H}}_3{\text{O}}^{+}}$

• Pair 1: $H_{2}O$ (acid) and $O{H}^{-}$ (conjugate base)
• Pair 2: $H_{2}O$ (base) and $H_3{O}^{+}$ (conjugate acid)

Other amphoteric species include $HC{O}_3^{-}$, $HS{O}_4^{-}$, and $H_{2}P{O}_4^{-}$.

Identifying Conjugate Pairs: Worked Examples

Example 1: What is the conjugate base of $HC{O}_3^{-}$?

Remove one $H^{+}$: $HC{O}_3^{-}\to C{O}_3^{2-}$

∴ Conjugate base = $C{O}_3^{2-}$

Example 2: What is the conjugate acid of $N{H}_3$?

Add one $H^{+}$: $N{H}_3\to N{H}_4^{+}$

∴ Conjugate acid = $N{H}_4^{+}$

Example 3: In $H_{2}S{O}_4+H_{2}O\to HS{O}_4^{-}+H_3{O}^{+}$, identify the two conjugate acid-base pairs.

1. Pair 1: $H_{2}S{O}_4$ (acid) / $HS{O}_4^{-}$ (conjugate base) — differ by one $H^{+}$
2. Pair 2: $H_{2}O$ (base) / $H_3{O}^{+}$ (conjugate acid) — differ by one $H^{+}$

Table of Common Conjugate Acid-Base Pairs