When `0.1` mole of an acid is added to `2 L` of a buffer solution, the `P^(H)` of the buffer decreases by `0.5`. The buffer capacity of the solution is

Options

A. 0.6
B. 0.4
C. 0.2
D. 0.1

Answer

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

### Step 1: Understand the definition of buffer capacity
Buffer capacity (β) is defined as the amount of acid or base (in moles) that can be added to a buffer solution per unit change in pH. Mathematically, it can be expressed as:
\[ \beta = \frac{\Delta n}{\Delta \text{pH}} \]
where:
- \(\Delta n\) = number of moles of acid or base added
- \(\Delta \text{pH}\) = change in pH

### Step 2: Identify the values from the problem
From the problem, we know:
- Number of moles of acid added (\(\Delta n\)) = 0.1 moles
- Volume of buffer solution = 2 L
- Change in pH (\(\Delta \text{pH}\)) = 0.5

### Step 3: Calculate the number of moles per liter
Since the volume of the buffer solution is 2 L, we need to convert the number of moles added to a per liter basis:
\[ \text{Moles per liter} = \frac{0.1 \text{ moles}}{2 \text{ L}} = 0.05 \text{ moles/L} \]

### Step 4: Substitute the values into the buffer capacity formula
Now, we can substitute the values into the buffer capacity formula:
\[ \beta = \frac{0.05 \text{ moles/L}}{0.5} = 0.1 \text{ moles/L/pH} \]

### Step 5: Conclusion
Thus, the buffer capacity of the solution is:
\[ \beta = 0.1 \text{ moles/L/pH} \]