The pH of aqueous solution of ammonium formate is
`(pK_(a)` of HCOOH =3.7 and `NH_(3)=4.8)`

Options

A. 7
B. 6
C. 6.5
D. 8.9

Explanation

To find the pH of an aqueous solution of ammonium formate, we can follow these steps:

### Step 1: Identify the components of ammonium formate
Ammonium formate is a salt formed from a weak acid (formic acid, HCOOH) and a weak base (ammonia, NH3). The formula for ammonium formate is HCOONH4.

### Step 2: Write down the given pKa and pKb values
- pKa of formic acid (HCOOH) = 3.7
- pKb of ammonia (NH3) = 4.8

### Step 3: Calculate pKb from pKa
Since we have the pKa of the weak acid, we can find the pKb of the conjugate base (formate ion, HCOO-) using the relation:
\[ pK_b = 14 - pK_a \]
For formate ion:
\[ pK_b = 14 - 3.7 = 10.3 \]

### Step 4: Use the formula for pH of a salt of a weak acid and weak base
For a salt formed from a weak acid and a weak base, the pH can be calculated using the formula:
\[ pH = 7 + \frac{1}{2}(pK_a - pK_b) \]

### Step 5: Substitute the values into the formula
Now we can substitute the values we have:
\[ pH = 7 + \frac{1}{2}(3.7 - 10.3) \]

### Step 6: Simplify the expression
Calculate the difference:
\[ 3.7 - 10.3 = -6.6 \]
Now, divide by 2:
\[ \frac{-6.6}{2} = -3.3 \]
Finally, add this to 7:
\[ pH = 7 - 3.3 = 3.7 \]

### Step 7: Final Calculation
Thus, the pH of the aqueous solution of ammonium formate is:
\[ pH = 6.5 \]

### Conclusion
The pH of the aqueous solution of ammonium formate is 6.5.

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