Question

The pKa of a buffer solution with pH of 5, consisting of 0.4 M sodium acetate and 0.04 M acetic acid, is ____. (Answer in integer)

Hint:

The Henderson-Hasselbalch equation is crucial for estimating the pKa from buffer compositions and their pH, facilitating effective buffer design in practical applications.

Answer 1

Step 1: Understanding the Buffer System

The buffer system consists of acetic acid (weak acid) and sodium acetate (its conjugate base). The pH of the buffer solution and the concentrations of the acid and its conjugate base are given.

Step 2: Using the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is used to calculate the \( \text{p}K_a \) of a buffer solution:

\[ \text{pH} = \text{p}K_a + \log\left(\frac{[\text{Conjugate Base}]}{[\text{Acid}]}\right) \] Step 3: Inserting the Given Values

Given that the pH is **5**, the concentration of the conjugate base (sodium acetate) is **0.4 M**, and the concentration of the acid (acetic acid) is **0.04 M**, we substitute these values into the equation:

\[ 5 = \text{p}K_a + \log\left(\frac{0.4}{0.04}\right) \] \[ 5 = \text{p}K_a + \log(10) \] \[ 5 = \text{p}K_a + 1 \] Step 4: Solving for \( \text{p}K_a \) \[ \text{p}K_a = 5 - 1 \] \[ \text{p}K_a = 4 \] Conclusion:

Explanation: The calculated \( \text{p}K_a \) value is **4**, indicating the acid dissociation constant of acetic acid under the conditions of the buffer system provided.