`pK_(a)` of `NH_(4)^(+)` is 9.26. Hence, effective range for `NH_(4)OH-NH_(4)Cl` buffer is about pH:

Options

A. 8.26 to 10.26
B. 4.74 to 5.74
C. 3.74 to 5.74
D. 8.26 to 9.26

Answer

To find the effective pH range for the buffer solution made from ammonium hydroxide (NH₄OH) and ammonium chloride (NH₄Cl), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given data**:
- The \( pK_a \) of the ammonium ion (\( NH_4^+ \)) is given as 9.26.

2. **Calculate \( pK_b \)**:
- Since \( pK_a + pK_b = 14 \) (this is a fundamental relationship in acid-base chemistry), we can calculate \( pK_b \) for ammonium hydroxide:
\[ pK_b = 14 - pK_a = 14 - 9.26 = 4.74 \]

3. **Determine the effective pOH range**:
- The effective range for a buffer is typically \( pK_b \pm 1 \). Therefore, we calculate:
\[ \text{Effective pOH range} = pK_b \pm 1 = 4.74 \pm 1 \]
- This gives us:
\[ \text{Lower limit} = 4.74 - 1 = 3.74 \]
\[ \text{Upper limit} = 4.74 + 1 = 5.74 \]

4. **Convert pOH range to pH range**:
- We use the relationship \( pH + pOH = 14 \) to find the corresponding pH values:
\[ \text{Lower pH limit} = 14 - 5.74 = 8.26 \]
\[ \text{Upper pH limit} = 14 - 3.74 = 10.26 \]

5. **State the effective pH range**:
- Therefore, the effective pH range for the ammonium hydroxide and ammonium chloride buffer is:
\[ \text{Effective pH range} = 8.26 \text{ to } 10.26 \]

### Final Answer:
The effective pH range for the \( NH_4OH - NH_4Cl \) buffer is **8.26 to 10.26**.

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