The Henderson-Hasselbalch equation relates the pH of a buffer to the relative concentrations of the buffer components. According to this equation, under which conditions is pH = pKa?
The Correct Answer and Explanation is:
Correct Answer:
The pH equals the pKa when the concentrations of the conjugate base and the weak acid in a buffer solution are equal.
Explanation
The Henderson-Hasselbalch equation is a formula used to estimate the pH of a buffer solution. It is expressed as: pH=pKa+log([A−][HA])\text{pH} = \text{pKa} + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)
Where:
- pH is the measure of acidity/basicity,
- pKa is the acid dissociation constant (a measure of acid strength),
- [A⁻] is the concentration of the conjugate base,
- [HA] is the concentration of the weak acid.
This equation highlights how pH is influenced by the ratio of base to acid in the buffer.
The condition pH = pKa occurs when the log term in the equation becomes zero. This happens when the ratio of [A−][A^-] to [HA][HA] is 1: log([A−][HA])=log(1)=0\log\left(\frac{[A^-]}{[HA]}\right) = \log(1) = 0
Thus, under the condition [A⁻] = [HA], the equation simplifies to: pH=pKa\text{pH} = \text{pKa}
This point is known as the half-equivalence point in a titration of a weak acid with a strong base. At this stage, exactly half of the acid has been neutralized to form its conjugate base.
This condition is important in buffer chemistry because when [A−]=[HA][A^-] = [HA], the buffer is most effective. It resists changes in pH upon the addition of small amounts of acid or base. This is because the system contains equal ability to neutralize added H⁺ (with A⁻) or OH⁻ (with HA).
In practical applications, choosing a buffer with a pKa close to the desired pH ensures maximum buffering capacity, especially when the concentrations of acid and conjugate base are equal.
Thus, pH = pKa when [conjugate base] = [acid].
