The dissociation constant of a weak acid is `1 xx 10^(-4)`. In order of prepare a buffer solution with a pH =5 the [Salt]/[Acid] ratio should be

Options

A. `1:10`
B. `4:5`
C. `10:1`
D. `5:4`

Answer

To find the ratio of salt to acid in a buffer solution with a given pH, we can use the Henderson-Hasselbalch equation, which relates pH, pKa, and the concentrations of the acid and its salt.

### Step-by-step Solution:

1. **Identify the given values**:
- Dissociation constant (Ka) of the weak acid = \(1 \times 10^{-4}\)
- Desired pH of the buffer solution = 5

2. **Calculate pKa**:
- The relationship between Ka and pKa is given by:
\[ pKa = -\log(Ka) \]
- Substituting the value of Ka:
\[ pKa = -\log(1 \times 10^{-4}) = 4 \]

3. **Use the Henderson-Hasselbalch equation**:
- The equation is:
\[ pH = pKa + \log\left(\frac{[Salt]}{[Acid]}\right) \]
- Substituting the known values:
\[ 5 = 4 + \log\left(\frac{[Salt]}{[Acid]}\right) \]

4. **Rearrange the equation to find the log ratio**:
- Subtract pKa from both sides:
\[ 5 - 4 = \log\left(\frac{[Salt]}{[Acid]}\right) \]
- This simplifies to:
\[ 1 = \log\left(\frac{[Salt]}{[Acid]}\right) \]

5. **Convert the log ratio to a regular ratio**:
- To eliminate the logarithm, we exponentiate both sides:
\[ \frac{[Salt]}{[Acid]} = 10^1 = 10 \]

6. **Express the ratio**:
- The ratio of salt to acid is:
\[ \frac{[Salt]}{[Acid]} = 10:1 \]

### Final Answer:
The ratio of salt to acid should be \(10:1\).

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