How does the Henderson-Hasselbalch equation enable the prediction of the pH of a buffer solution when given the concentrations of the weak acid and its conjugate base?
The correct answer and explanation is:
Correct Answer:
The Henderson-Hasselbalch equation allows the prediction of the pH of a buffer solution by relating the pH to the pKa of the weak acid and the ratio of the concentrations of the conjugate base to the weak acid.
Equation: pH=pKa+log([A−][HA])\text{pH} = \text{pKa} + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)
Where:
- pH = the hydrogen ion concentration of the solution
- pKa = the acid dissociation constant of the weak acid
- [A−][A^-] = concentration of the conjugate base
- [HA][HA] = concentration of the weak acid
Explanation (300 words):
The Henderson-Hasselbalch equation is a crucial tool in chemistry for estimating the pH of buffer solutions, which are mixtures of a weak acid and its conjugate base (or a weak base and its conjugate acid). A buffer resists changes in pH when small amounts of acid or base are added, making it essential in biological and chemical systems.
This equation stems from the rearrangement of the acid dissociation constant (Ka) expression: Ka=[H+][A−][HA]Ka = \frac{[H^+][A^-]}{[HA]}
Taking the negative logarithm of both sides and solving for pH leads to the Henderson-Hasselbalch form: pH=pKa+log([A−][HA])\text{pH} = \text{pKa} + \log\left(\frac{[A^-]}{[HA]}\right)
This formula shows that the pH of a buffer depends on two key components: the pKa of the weak acid and the ratio of conjugate base to acid. If the concentrations of the acid and base are equal, the log term becomes zero, and pH equals pKa. If the base concentration is higher, the pH increases; if the acid concentration is higher, the pH decreases.
The beauty of this equation is its simplicity and predictive power. Given any two of the three variables (pH, pKa, and concentration ratio), you can solve for the third. This makes it especially useful in designing buffer systems with a desired pH. Moreover, since pKa values are known constants, the equation enables quick adjustments by simply altering the concentrations of buffer components.