Concentration of `NH_4Cl and NH_4OH` in buffer solution are in the ratio of `1 : 1 ,K_b " for " NH_4OH ` is ` 10 ^(-10 ) ` The pH of the buffer is

Options

A. ` 4`
B. ` 5`
C. ` 9`
D. ` 11`

Answer

To solve the problem, we need to calculate the pH of a buffer solution containing NH4Cl and NH4OH, given that their concentrations are in the ratio of 1:1 and that the Kb for NH4OH is \(10^{-10}\).

### Step-by-Step Solution:

1. **Identify the Components of the Buffer:**
- The buffer solution consists of NH4Cl (a salt) and NH4OH (a weak base).
- The concentration ratio of NH4Cl to NH4OH is 1:1.

2. **Calculate pKb:**
- We know that \(K_b\) for NH4OH is \(10^{-10}\).
- To find \(pK_b\), we use the formula:
\[ pK_b = -\log(K_b) \]
- Substituting the value:
\[ pK_b = -\log(10^{-10}) = 10 \]

3. **Use the Formula for pOH:**
- For a basic buffer, the formula to calculate pOH is:
\[ pOH = pK_b + \log\left(\frac{[\text{Salt}]}{[\text{Base}]}\right) \]
- Since the concentrations of NH4Cl and NH4OH are equal (1:1 ratio), we can substitute:
\[ pOH = 10 + \log\left(\frac{1}{1}\right) \]
- The logarithm of 1 is 0:
\[ pOH = 10 + 0 = 10 \]

4. **Calculate pH from pOH:**
- We know that:
\[ pH + pOH = 14 \]
- Therefore, we can find pH:
\[ pH = 14 - pOH = 14 - 10 = 4 \]

5. **Final Answer:**
- The pH of the buffer solution is 4.