An aqueous mixture at room temperature is 0.1 M with respect to ammonium chloride and 0.01 M with respect to `NH_4 OH,pK_b ` of aqueous ammonia as base is 5. The pH of the mixture is nearly

Options

A. 7.5
B. 6.8
C. 6.5
D. `8.0`

Answer

To find the pH of the aqueous mixture containing ammonium chloride and ammonium hydroxide, we can follow these steps:

### Step 1: Identify the components
We have:
- Ammonium chloride (NH4Cl) which is a salt formed from a strong acid (HCl) and a weak base (NH4OH).
- Ammonium hydroxide (NH4OH) which is a weak base.

### Step 2: Understand the buffer system
The solution acts as a basic buffer because it consists of a weak base (NH4OH) and its conjugate acid (NH4Cl).

### Step 3: Use the Henderson-Hasselbalch equation
For a basic buffer, the pH can be calculated using the formula:
\[ \text{pH} = 14 - pK_b - \log\left(\frac{[\text{Salt}]}{[\text{Base}]}\right) \]
Where:
- \( pK_b \) is given as 5.
- The concentration of salt (NH4Cl) is 0.1 M.
- The concentration of base (NH4OH) is 0.01 M.

### Step 4: Substitute the values into the equation
Substituting the values into the formula:
\[ \text{pH} = 14 - 5 - \log\left(\frac{0.1}{0.01}\right) \]

### Step 5: Calculate the logarithm
Calculate the ratio:
\[ \frac{0.1}{0.01} = 10 \]
Then, calculate the logarithm:
\[ \log(10) = 1 \]

### Step 6: Final calculation
Now substitute back into the pH equation:
\[ \text{pH} = 14 - 5 - 1 = 8 \]

### Conclusion
The pH of the mixture is approximately 8.

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