The ionization constant of a certain weak acid is `10^(-4)`. What should be the [salt] to [acid] ratio if we have to prepare a buffer with `pH = 5` using this acid and one of the salts

Options

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

Answer

To solve the problem of determining the salt to acid ratio needed to prepare a buffer with a pH of 5 using a weak acid with an ionization constant (Ka) of \(10^{-4}\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Ionization constant of the weak acid, \(K_a = 10^{-4}\)
- Desired pH of the buffer, \(pH = 5\)

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

3. **Use the Henderson-Hasselbalch Equation:**
- The Henderson-Hasselbalch equation for a buffer solution is:
\[ pH = pK_a + \log\left(\frac{[salt]}{[acid]}\right) \]
- Substituting the known values into the equation:
\[ 5 = 4 + \log\left(\frac{[salt]}{[acid]}\right) \]

4. **Rearranging the Equation:**
- To isolate the logarithmic term:
\[ \log\left(\frac{[salt]}{[acid]}\right) = 5 - 4 = 1 \]

5. **Convert from Logarithmic to Ratio Form:**
- By exponentiating both sides, we can eliminate the logarithm:
\[ \frac{[salt]}{[acid]} = 10^1 = 10 \]

6. **Final Ratio:**
- Therefore, the ratio of salt to acid is:
\[ [salt] : [acid] = 10 : 1 \]

### Conclusion:
To prepare a buffer with a pH of 5 using the weak acid with an ionization constant of \(10^{-4}\), the salt to acid ratio should be **10:1**.