`K_a` for `CH_3COOH` is `1.8xx10^(-5)` and `K_b` for `NH_4OH` is `1.8xx10^(-5)` The pH of ammonium acetate will be :

Options

A. 7.005
B. 4.75
C. `7.0`
D. between 6 and 7

Explanation

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

### Step 1: Understand the Components
Ammonium acetate is formed from acetic acid (CH₃COOH) and ammonium hydroxide (NH₄OH). We have the dissociation constants (Kₐ and K_b) for these compounds.

### Step 2: Identify Given Values
- \( K_a \) for acetic acid (CH₃COOH) = \( 1.8 \times 10^{-5} \)
- \( K_b \) for ammonium hydroxide (NH₄OH) = \( 1.8 \times 10^{-5} \)

### Step 3: Calculate pKₐ and pK_b
To find pKₐ and pK_b, we use the formula:
\[ pK = -\log(K) \]

#### Calculate pKₐ:
\[ pK_a = -\log(1.8 \times 10^{-5}) \]
Using a calculator, we find:
\[ pK_a \approx 4.74 \]

#### Calculate pK_b:
\[ pK_b = -\log(1.8 \times 10^{-5}) \]
Similarly, we find:
\[ pK_b \approx 4.74 \]

### Step 4: Use the pH Formula for Weak Acid and Weak Base
For a solution of 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 Values
Since \( pK_a \) and \( pK_b \) are equal:
\[ pH = 7 + \frac{1}{2}(4.74 - 4.74) \]
This simplifies to:
\[ pH = 7 + \frac{1}{2}(0) = 7 \]

### Conclusion
The pH of ammonium acetate is **7**.

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