When `0.002mol` of acid is added to `250 mL` of a buffer solution, `pH` decreases by `0.02`units. The buffer capacity of the system is

Options

A. (a) `0.1`
B. (b) `0.2`
C. (c) `0.3`
D. (d) `0.4`

Explanation

To find the buffer capacity of the system, we can follow these steps:

### Step 1: Understand the definition of buffer capacity
Buffer capacity is defined as the number of moles of acid or base added to 1 liter of buffer solution divided by the change in pH that is observed.

### Step 2: Identify the given values
- Moles of acid added = 0.002 mol
- Volume of buffer solution = 250 mL
- Change in pH = 0.02 units

### Step 3: Convert the volume of the buffer solution to liters
Since buffer capacity is expressed per liter, we need to convert the volume of the buffer solution from milliliters to liters:
\[ 250 \, \text{mL} = 0.250 \, \text{L} \]

### Step 4: Calculate the number of moles of acid added per liter
To find the number of moles of acid added per liter, we can use the formula:
\[ \text{Moles of acid per liter} = \frac{\text{Moles of acid added}}{\text{Volume of buffer in liters}} \]
Substituting the values:
\[ \text{Moles of acid per liter} = \frac{0.002 \, \text{mol}}{0.250 \, \text{L}} = 0.008 \, \text{mol/L} \]

### Step 5: Calculate the buffer capacity
Now that we have the moles of acid added per liter, we can use the formula for buffer capacity:
\[ \text{Buffer Capacity} = \frac{\text{Moles of acid per liter}}{\text{Change in pH}} \]
Substituting the values:
\[ \text{Buffer Capacity} = \frac{0.008 \, \text{mol/L}}{0.02} \]
Calculating this gives:
\[ \text{Buffer Capacity} = 0.4 \, \text{mol/L} \]

### Final Answer
The buffer capacity of the solution is **0.4 mol/L**.

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