The ionization constant of fromic acid is `1.8xx10^(-4)`. Calculate the ratio of sodium formate and formic acid in a buffer of pH 4.25 .

Explanation

To solve the problem of calculating the ratio of sodium formate to formic acid in a buffer solution with a given pH, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Given Information:**
- Ionization constant of formic acid (Ka) = \(1.8 \times 10^{-4}\)
- pH of the buffer solution = 4.25

2. **Calculate pKa:**
- The relationship between Ka and pKa is given by:
\[ pKa = -\log(Ka) \]
- Substitute the value of Ka:
\[ pKa = -\log(1.8 \times 10^{-4}) \]
- Using a calculator, we find:
\[ pKa \approx 3.74 \]

3. **Use the Henderson-Hasselbalch Equation:**
- The Henderson-Hasselbalch equation is:
\[ pH = pKa + \log\left(\frac{[A^-]}{[HA]}\right) \]
- Where \([A^-]\) is the concentration of the salt (sodium formate) and \([HA]\) is the concentration of the acid (formic acid).

4. **Rearrange the Equation to Find the Ratio:**
- Rearranging the equation gives:
\[ \log\left(\frac{[A^-]}{[HA]}\right) = pH - pKa \]
- Substitute the known values:
\[ \log\left(\frac{[A^-]}{[HA]}\right) = 4.25 - 3.74 \]
- Calculate the difference:
\[ \log\left(\frac{[A^-]}{[HA]}\right) = 0.51 \]

5. **Convert from Logarithmic to Linear Form:**
- To find the ratio, we take the antilogarithm:
\[ \frac{[A^-]}{[HA]} = 10^{0.51} \]
- Calculate \(10^{0.51}\):
\[ \frac{[A^-]}{[HA]} \approx 3.24 \]

6. **Conclusion:**
- The ratio of sodium formate to formic acid in the buffer solution is approximately 3.24.