The `pK_b` value of ammonium hydroxide is 4.75. An aqueous solution of ammonium hydroxide is titrated with HCl. The pH of the ammonium hydroxide has been neutralized will be

Options

A. 9.25
B. 8.25
C. `7.50`
D. 4.75

Answer

To solve the problem, we need to determine the pH of an aqueous solution of ammonium hydroxide after it has been neutralized with hydrochloric acid (HCl). Here are the steps to arrive at the solution:

### Step 1: Understand the Reaction
Ammonium hydroxide (NH4OH) is a weak base, and hydrochloric acid (HCl) is a strong acid. When they react, they form ammonium chloride (NH4Cl) and water (H2O).

**Reaction:**
\[ \text{NH}_4\text{OH} + \text{HCl} \rightarrow \text{NH}_4\text{Cl} + \text{H}_2\text{O} \]

### Step 2: Identify the pK_b Value
The pK_b value of ammonium hydroxide is given as 4.75. This value is crucial for calculating the pOH of the solution after neutralization.

### Step 3: Use the Henderson-Hasselbalch Equation
At the neutralization point, the concentrations of the weak base (NH4OH) and its conjugate acid (NH4Cl) are equal. Therefore, we can use the Henderson-Hasselbalch equation in the form suitable for bases:

\[ \text{pOH} = \text{pK}_b + \log\left(\frac{[\text{Conjugate Acid}]}{[\text{Base}]}\right) \]

Since at neutralization, the concentrations of the conjugate acid and base are equal, the ratio becomes 1:

\[ \text{pOH} = \text{pK}_b + \log(1) \]

### Step 4: Calculate pOH
The logarithm of 1 is 0, so:

\[ \text{pOH} = \text{pK}_b + 0 = 4.75 \]

### Step 5: Calculate pH from pOH
We know that:

\[ \text{pH} + \text{pOH} = 14 \]

Substituting the value of pOH:

\[ \text{pH} = 14 - \text{pOH} \]
\[ \text{pH} = 14 - 4.75 = 9.25 \]

### Conclusion
The pH of the ammonium hydroxide solution after it has been neutralized with HCl is **9.25**.