The `pK_(a)` value of `NH_(3)` is 5. Calculate the pH of the buffer solution, 1 L of which contains `0.01 M NH_(4)Cl` and `0.10M NH_(4)OH `:

Options

A. 4
B. 6
C. 8
D. 10

Explanation

To solve the problem of calculating the pH of the buffer solution containing 0.01 M NH₄Cl and 0.10 M NH₄OH, we can follow these steps:

### Step 1: Identify the components of the buffer solution
The buffer solution consists of:
- NH₄Cl (ammonium chloride), which is the salt of the weak base NH₄OH (ammonium hydroxide).
- NH₄OH (ammonium hydroxide), which is a weak base.

### Step 2: Use the Henderson-Hasselbalch equation
The Henderson-Hasselbalch equation for a basic buffer is given by:

\[ pH = pK_a + \log \left( \frac{[Base]}{[Acid]} \right) \]

In this case, we need to convert the given pK_b of NH₃ to pK_a of NH₄⁺. The relationship between pK_a and pK_b is:

\[ pK_a + pK_b = 14 \]

Given that pK_b of NH₃ is 5, we can calculate pK_a:

\[ pK_a = 14 - pK_b = 14 - 5 = 9 \]

### Step 3: Substitute the concentrations into the equation
Now we can substitute the values into the Henderson-Hasselbalch equation. Here, [Base] is the concentration of NH₄OH (0.10 M) and [Acid] is the concentration of NH₄Cl (0.01 M):

\[ pH = 9 + \log \left( \frac{0.10}{0.01} \right) \]

### Step 4: Calculate the logarithm
Calculating the logarithm:

\[ \log \left( \frac{0.10}{0.01} \right) = \log(10) = 1 \]

### Step 5: Calculate the pH
Now substitute this value back into the equation:

\[ pH = 9 + 1 = 10 \]

### Conclusion
The pH of the buffer solution is **10**.

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