The pH of an aqueous solution of 1.0M ammonium formate will be `(pk_a of formic acid = 3.8 and pK_a, of ammonium hydroxide = 4.8)`

Options

A. 5.5
B. 7.5
C. 6.1
D. 6.5

Answer

To find the pH of a 1.0 M aqueous solution of ammonium formate, we can use the Henderson-Hasselbalch equation, which is applicable for buffer solutions. Ammonium formate is a salt of a weak acid (formic acid) and a weak base (ammonium hydroxide).

### Step-by-Step Solution:

1. **Identify the Components**:
- Ammonium formate (NH4HCOO) is the salt of formic acid (HCOOH) and ammonium hydroxide (NH4OH).
- The pKa of formic acid (HCOOH) is given as 3.8.
- The pKa of ammonium hydroxide (NH4OH) is given as 4.8.

2. **Calculate the pKa of the Conjugate Acid and Base**:
- The pKa of formic acid is 3.8.
- The pKb of ammonium hydroxide can be calculated using the relation:
\[ pK_a + pK_b = 14 \]
Thus,
\[ pK_b = 14 - pK_a = 14 - 4.8 = 9.2 \]

3. **Use the Henderson-Hasselbalch Equation**:
The Henderson-Hasselbalch equation is:
\[ pH = pK_a + \log \left( \frac{[A^-]}{[HA]} \right) \]
Where:
- [A^-] is the concentration of the base (NH4^+ from ammonium formate).
- [HA] is the concentration of the acid (HCOOH).

4. **Determine the Concentrations**:
In this case, since we have a 1.0 M solution of ammonium formate, we can assume:
- [NH4^+] = 1.0 M (conjugate acid)
- [HCOO^-] = 1.0 M (conjugate base)

5. **Substitute into the Equation**:
\[ pH = 3.8 + \log \left( \frac{1.0}{1.0} \right) \]
Since \(\log(1) = 0\):
\[ pH = 3.8 + 0 = 3.8 \]

6. **Final Answer**:
The pH of the 1.0 M ammonium formate solution is **3.8**.