Question

In a lactic acid solution at pH 4.8, the concentrations of lactic acid and lactate are 0.01 M and 0.087 M, respectively. The calculated pKa of lactic acid is _______. (Round off to one decimal place)

Hint:

Always remember to use the Henderson-Hasselbalch equation for quick estimations of pKa from the pH and concentration ratios of conjugate acid-base pairs.

Answer 1

The relationship between the acid dissociation constant (\( K_a \)), the concentrations of the acid (\(\text{HA}\)) and its conjugate base (\(\text{A}^-\)), and the pH of the solution can be described using the Henderson-Hasselbalch equation: \[ \text{pH} = \text{p}K_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \]

Given:

• \(\text{pH} = 4.8\)
• \([\text{HA}] = 0.01 \, M\) (concentration of lactic acid)
• \([\text{A}^-] = 0.087 \, M\) (concentration of lactate)

Substituting the given values into the Henderson-Hasselbalch equation: \[ 4.8 = \text{p}K_a + \log \left( \frac{0.087}{0.01} \right) \] \[ 4.8 = \text{p}K_a + \log(8.7) \] \[ 4.8 = \text{p}K_a + 0.939 \] \[ \text{p}K_a = 4.8 - 0.939 = 3.861 \] Step 3: Rounding off the value.

Rounding off to one decimal place, the \( \text{p}K_a \) of lactic acid is:

\[ \text{p}K_a = 3.9 \] Conclusion:

This calculation demonstrates how the dissociation constant for lactic acid can be deduced from the equilibrium concentrations of the acid and its conjugate base at a specific pH.