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 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: \(\text{pK}_a = 4.8\)
- Required: \(\text{pH} = 5.8\)
\[ 5.8 = 4.8 + \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) \]

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

4. **Convert from Logarithmic to Exponential Form:**
\[ \frac{[\text{Salt}]}{[\text{Acid}]} = 10^1 = 10 \]

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

### Final Answer:
The ratio of \([\text{Acid}]/[\text{Salt}]\) is \(0.1\).