Which of the following solutions containing weak acid and salt of its conjugate base has maximum buffer capaity?

Options

A. `["Salt"] lt ["Acid"]`
B. `["Salt"] =["Acid"]`
C. `["Salt"] gt ["Acid"]`
D. `["Salt"] + ["Acid"]` is minimum

Explanation

To determine which solution containing a weak acid and the salt of its conjugate base has the maximum buffer capacity, we can follow these steps:

### Step 1: Understand Buffer Capacity
Buffer capacity refers to the ability of a solution to resist changes in pH upon the addition of small amounts of acid or base. A buffer solution is typically made from a weak acid and its conjugate base (salt).

### Step 2: Identify the Condition for Maximum Buffer Capacity
The maximum buffer capacity occurs when the pH of the solution is equal to the pKa of the weak acid. This is derived from the Henderson-Hasselbalch equation:
\[ \text{pH} = \text{pKa} + \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) \]

### Step 3: Set Up the Equation for Maximum Buffer Capacity
For maximum buffer capacity, we want:
\[ \text{pH} = \text{pKa} \]
This implies:
\[ \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) = 0 \]

### Step 4: Solve the Logarithmic Equation
If the logarithm equals zero, then:
\[ \frac{[\text{Salt}]}{[\text{Acid}]} = 10^0 = 1 \]
This means that the concentrations of the salt and the acid must be equal for maximum buffer capacity.

### Step 5: Analyze the Given Options
Now, we need to look at the options provided in the question. We will check which solution has equal concentrations of the weak acid and its conjugate base (salt).

### Step 6: Conclusion
The correct option will be the one where the concentration of the weak acid is equal to the concentration of its salt. This condition ensures that the buffer capacity is maximized.

### Final Answer
The correct option for maximum buffer capacity is **Option B** (assuming Option B is the one with equal concentrations of the weak acid and its salt).

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