Ammonium acetate which is 0.01 M , is hydrolysed to 0.001 M concentration . Calculate the change in pH in 0.001 M solution , if initially pH = `pK_(a)`

Options

A. 5
B. 10
C. 100
D. 1

Answer

To solve the problem, we need to follow these steps:

### Step 1: Understand the Hydrolysis of Ammonium Acetate
Ammonium acetate (CH₃COONH₄) is a salt formed from a weak acid (acetic acid, CH₃COOH) and a weak base (ammonium hydroxide, NH₄OH). When it hydrolyzes, it can be represented as:
\[ \text{CH}_3\text{COONH}_4 + \text{H}_2\text{O} \rightleftharpoons \text{CH}_3\text{COOH} + \text{NH}_4\text{OH} \]

### Step 2: Initial Conditions
We are given that the initial concentration of ammonium acetate is 0.01 M and it is hydrolyzed to 0.001 M. The initial pH is equal to the pKa of acetic acid.

### Step 3: Use the Henderson-Hasselbalch Equation
The Henderson-Hasselbalch equation is:
\[ \text{pH} = \text{pKa} + \log \left( \frac{[\text{Salt}]}{[\text{Acid}]} \right) \]

In this case:
- The salt is ammonium acetate (CH₃COONH₄).
- The acid is acetic acid (CH₃COOH).

### Step 4: Calculate the pH for 0.01 M Ammonium Acetate
Initially, when the concentration is 0.01 M:
\[ \text{pH}_{\text{initial}} = \text{pKa} + \log \left( \frac{0.01}{0} \right) \]
Since the concentration of the acid is negligible, we can consider it as:
\[ \text{pH}_{\text{initial}} = \text{pKa} + \log(10) \]
Given that \(\log(10) = 1\):
\[ \text{pH}_{\text{initial}} = \text{pKa} + 1 \]

### Step 5: Calculate the pH for 0.001 M Ammonium Acetate
Now, for the concentration of 0.001 M:
\[ \text{pH}_{\text{final}} = \text{pKa} + \log \left( \frac{0.001}{0.001} \right) \]
This simplifies to:
\[ \text{pH}_{\text{final}} = \text{pKa} + \log(1) \]
Since \(\log(1) = 0\):
\[ \text{pH}_{\text{final}} = \text{pKa} \]

### Step 6: Calculate the Change in pH
Now, we can find the change in pH:
\[ \Delta \text{pH} = \text{pH}_{\text{final}} - \text{pH}_{\text{initial}} \]
Substituting the values:
\[ \Delta \text{pH} = \text{pKa} - (\text{pKa} + 1) \]
\[ \Delta \text{pH} = -1 \]

### Final Answer
The change in pH when the concentration of ammonium acetate is reduced from 0.01 M to 0.001 M is -1.

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