pH of a buffer solution decreases by 0.02 units when 0.12 g of acetic acid is added to 250 mL of a buffer solution of acetic and potassium acetate at `27^(@)C`. The buffer capacity of the solution is

Options

A. 0.1
B. 10
C. 1
D. 0.4

Answer

To find the buffer capacity of the solution, we will follow these steps:

### Step 1: Calculate the mass of acetic acid in 1 liter of buffer solution.
Given that 0.12 g of acetic acid is added to 250 mL of the buffer solution, we can find the equivalent mass in 1 liter (1000 mL) using the unitary method.

\[ \text{Mass in 1 L} = \frac{0.12 \, \text{g}}{250 \, \text{mL}} \times 1000 \, \text{mL} = 0.48 \, \text{g} \]

### Step 2: Calculate the number of moles of acetic acid.
To find the number of moles, we use the formula:

\[ \text{Number of moles} = \frac{\text{Given weight}}{\text{Molar mass}} \]

The molar mass of acetic acid (CH₃COOH) is approximately 60 g/mol. Thus, substituting the values:

\[ \text{Number of moles} = \frac{0.48 \, \text{g}}{60 \, \text{g/mol}} = 0.008 \, \text{mol} \]

### Step 3: Calculate the buffer capacity.
Buffer capacity (β) is defined as the number of moles of acid or base added per unit change in pH. The formula for buffer capacity is:

\[ \beta = \frac{\Delta n}{\Delta \text{pH}} \]

Where:
- \(\Delta n\) is the number of moles of acetic acid added (0.008 mol).
- \(\Delta \text{pH}\) is the change in pH (0.02).

Substituting the values:

\[ \beta = \frac{0.008 \, \text{mol}}{0.02} = 0.4 \, \text{mol/L/pH unit} \]

### Conclusion:
The buffer capacity of the solution is 0.4 mol/L/pH unit.

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