R3.1.17 The pH of a buffer solution (Higher Level Only)

Factors Affecting Buffer pH

The Henderson-Hasselbalch Equation: A Tool for Predicting Buffer pH

1. As discussed earlier, buffers consist of a weak acid and its conjugate base (or a weak base and its conjugate acid), which work together to resist pH changes.
2. The precise pH of a buffer solution can be calculated using the Henderson-Hasselbalch equation:

$$\text{pH}=\text{pKa}+\log \frac{[{\text{A}}^{-}]}{[\text{HA}]}$$

Where:

• $[A^{-}]$: Concentration of the conjugate base.
• $[HA]$: Concentration of the weak acid.
• $\text{pKa}$: The negative logarithm of the acid dissociation constant $K_a$ of the weak acid.

1. The Role of $\text{pKa}$

• The $\text{pKa}$ of a weak acid is a measure of its tendency to donate protons ${\text{H}}^{+}$.
• A lower $\text{pKa}$ corresponds to a stronger weak acid, while a higher $\text{pKa}$ indicates a weaker acid.

Buffers are most effective when their pH is close to the $\text{pKa}$ of the weak acid, which occurs when $[A^{-}]=[HA]$.

2. The Concentration Ratio $[A^{-}]/[HA]$

The logarithmic term in the Henderson-Hasselbalch equation allows for precise adjustment of the buffer’s pH by altering the ratio of $[A^{-}]$ to $[HA]$.

• If $[A^{-}]=[HA]$, then ($\log \frac{[A^{-}]}{[HA]}=0$, and $\text{pH}=\text{pKa}$.
• If $[A^{-}]>[HA]$, the $\text{pH}>\text{pKa}$.
• If $[A^{-}]<[HA]$, the $\text{pH}<\text{pKa}$.

Effect of Dilution on Buffer pH

1. One of the remarkable properties of buffers is their ability to maintain a stable pH even when diluted.
2. When a buffer solution is diluted, the concentrations of both $[A^{-}]$ and $[HA]$ decrease proportionally.
3. However, since the ratio $[A^{-}]/[HA]$ remains constant, the pH does not change.

Reflection and Practice