Factors Affecting Buffer pH
Note
- In this article, we use Henderson-Hasselbalch equation to reason the intuition behind buffer pH.
- In IB Chemistry (First Examination 2025), you don't have to remember this equation.
- However, according to the syllabus, it is essential to understand that the pH of a buffer solution depends on both:
- the $pK_a$ or $pK_b$ of its acid or base
- the ratio of the concentration of acid or base to the concentration of the conjugate base or
acid.
The Henderson-Hasselbalch Equation: A Tool for Predicting Buffer pH
- 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.
- 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.
Note
This equation highlights two critical factors influencing buffer pH:
- The $ \text{pKa} $ of the weak acid.
- The ratio of the concentrations of the conjugate base $[A^-]$ to the weak acid $[HA]$.
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 $[A^-] = [HA]$.
Example
Selecting a Buffer for pH 4.8
- To prepare a buffer with a pH of 4.8, choose a weak acid with a $ \text{pKa} $ value near 4.8, such as ethanoic acid $ \text{pKa} = 4.76 $.
- By adjusting the ratio of $[A^-]$ (ethanoate ion) to $[HA]$ (ethanoic acid), you can fine-tune the pH to 4.8.
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} $.
Tip
- To prepare a buffer with a specific pH, calculate the required $[A^-]/[HA]$ ratio using the Henderson-Hasselbalch equation.
- This ensures accuracy in achieving the desired pH.
Self review
If a buffer has a pH of 6.2 and the $ \text{pKa} $ of the weak acid is 6.0, is $[A^-]$ greater than or less than $[HA]$?
Effect of Dilution on Buffer pH
- One of the remarkable properties of buffers is their ability to maintain a stable pH even when diluted.
- When a buffer solution is diluted, the concentrations of both $[A^-]$ and $[HA]$ decrease proportionally.
- However, since the ratio $[A^-]/[HA]$ remains constant, the pH does not change.
Example
Diluting a Buffer
- Consider a buffer with $[A^-] = 0.1 \, \text{mol dm}^{-3}$ and $[HA] = 0.2 \, \text{mol dm}^{-3}$.
- The ratio $[A^-]/[HA] = 0.5$.
- If the solution is diluted tenfold, $[A^-]$ becomes $0.01 \, \text{mol dm}^{-3}$ and $[HA]$ becomes $0.02 \, \text{mol dm}^{-3}$.
- The ratio remains 0.5, so the pH stays the same.
Note
While dilution does not affect pH, it reduces the buffer capacity, the ability of the buffer to resist pH changes when acids or bases are added.
