The `pK_(a)` of acetic acid and `pK_(b)` of `NH_(4)OH` are 4.75 and 4.75 respectively. Find the pH of ammonium acetate solution?

Answer

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

### Step 1: Understand the Components
We have acetic acid (CH₃COOH) and ammonium hydroxide (NH₄OH). The given values are:
- pKₐ of acetic acid = 4.75
- pKᵦ of ammonium hydroxide = 4.75

### Step 2: Identify the Salt Formed
When acetic acid reacts with ammonium hydroxide, they form ammonium acetate (CH₃COONH₄), which is a salt of a weak acid and a weak base.

### Step 3: Use the pH Formula for Weak Acid and Weak Base
For a solution of a salt formed from a weak acid and a weak base, the pH can be calculated using the formula:
\[ \text{pH} = \frac{1}{2} (\text{pK}_a - \text{pK}_b) + 7 \]

### Step 4: Substitute the Values
Now, substitute the given values into the formula:
\[ \text{pH} = \frac{1}{2} (4.75 - 4.75) + 7 \]

### Step 5: Simplify the Equation
Calculating the expression inside the parentheses:
\[ \text{pH} = \frac{1}{2} (0) + 7 \]
This simplifies to:
\[ \text{pH} = 0 + 7 = 7 \]

### Conclusion
Thus, the pH of the ammonium acetate solution is 7.

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