The `pK_(a)` of a weak acid is `4.8` . What should be the ratio of [Acid]/[Salt] of a buffer if `pH = 5 .8` is required

Options

A. 10
B. `0.1`
C. 1
D. 2

Answer

To solve the problem, we will use the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the pKa of the weak acid and the ratio of the concentrations of the salt (conjugate base) and the weak acid.

### Step-by-Step Solution:

1. **Write the Henderson-Hasselbalch Equation**:
\[ \text{pH} = \text{pK}_a + \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) \]

2. **Substitute the given values**:
- Given:
- \( \text{pK}_a = 4.8 \)
- \( \text{pH} = 5.8 \)
- Substitute these values into the equation:
\[ 5.8 = 4.8 + \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) \]

3. **Rearrange the equation to isolate the logarithm**:
\[ \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) = 5.8 - 4.8 \]
\[ \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) = 1 \]

4. **Convert the logarithmic equation to its exponential form**:
\[ \frac{[\text{Salt}]}{[\text{Acid}]} = 10^1 = 10 \]

5. **Find the ratio of [Acid] to [Salt]**:
- We need the ratio of [Acid] to [Salt]:
\[ \frac{[\text{Acid}]}{[\text{Salt}]} = \frac{1}{10} = 0.1 \]

### Final Answer:
The ratio of [Acid] to [Salt] required for the buffer solution when the pH is 5.8 is **0.1**.

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