What will be the pH of an aqueous solution of 1.0 M ammonium formate?
Given :`pK_(a)=3.8 and pK_(b)=4.8`

Options

A. `7.5`
B. `3.4`
C. `6.5`
D. `10.2`

Answer

To find the pH of a 1.0 M aqueous solution of ammonium formate (NH4HCO2), we can use the formula for the pH of a salt formed from a weak acid and a weak base:

**Step 1: Identify the components of ammonium formate.**
Ammonium formate is a salt derived from the weak acid formic acid (HCOOH) and the weak base ammonium hydroxide (NH4OH).

**Step 2: Use the given pKa and pKb values.**
We are given:
- pKa = 3.8 (for formic acid)
- pKb = 4.8 (for ammonium ion)

**Step 3: Apply the formula for pH.**
The formula to calculate the pH of a salt solution made from a weak acid and a weak base is:

\[ \text{pH} = 7 + \frac{1}{2}(\text{pKa} - \text{pKb}) \]

**Step 4: Substitute the values into the formula.**
Substituting the given values into the formula:

\[ \text{pH} = 7 + \frac{1}{2}(3.8 - 4.8) \]

**Step 5: Calculate the difference.**
Calculate the difference between pKa and pKb:

\[ 3.8 - 4.8 = -1.0 \]

**Step 6: Calculate half of the difference.**
Now, calculate half of this difference:

\[ \frac{1}{2}(-1.0) = -0.5 \]

**Step 7: Add this to 7.**
Now, add this value to 7 to find the pH:

\[ \text{pH} = 7 - 0.5 = 6.5 \]

**Final Answer:**
The pH of the 1.0 M aqueous solution of ammonium formate is **6.5**.

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