What is the `pH` of the resulting solution when equal volumes of `0.1 M NaOH` and `0.01 M HCl` are mixed?

Options

A. (a) `12.65`
B. (b) `2.0`
C. (c) `7.0`
D. (d) `1.04`

Explanation

To find the pH of the resulting solution when equal volumes of 0.1 M NaOH and 0.01 M HCl are mixed, we can follow these steps:

### Step 1: Determine the number of moles of NaOH and HCl
- **Volume of NaOH = 1 L** (0.1 M)
- **Number of moles of NaOH = Concentration × Volume = 0.1 mol/L × 1 L = 0.1 moles**

- **Volume of HCl = 1 L** (0.01 M)
- **Number of moles of HCl = Concentration × Volume = 0.01 mol/L × 1 L = 0.01 moles**

### Step 2: Identify the limiting reactant
- The reaction between NaOH and HCl is:
\[ \text{NaOH} + \text{HCl} \rightarrow \text{NaCl} + \text{H}_2\text{O} \]
- Since 0.01 moles of HCl will react with 0.01 moles of NaOH, we subtract these from the initial moles:
- Moles of NaOH remaining = 0.1 moles - 0.01 moles = 0.09 moles
- Moles of HCl remaining = 0.01 moles - 0.01 moles = 0 moles

### Step 3: Calculate the total volume of the solution
- Total volume = Volume of NaOH + Volume of HCl = 1 L + 1 L = 2 L

### Step 4: Calculate the concentration of NaOH in the resulting solution
- Concentration of NaOH = Moles of NaOH remaining / Total volume
\[ \text{Concentration of NaOH} = \frac{0.09 \text{ moles}}{2 \text{ L}} = 0.045 \text{ M} \]

### Step 5: Calculate the concentration of OH⁻ ions
- Since NaOH completely dissociates in solution, the concentration of OH⁻ ions is also 0.045 M.

### Step 6: Calculate pOH
- Use the formula:
\[ \text{pOH} = -\log[\text{OH}^-] = -\log(0.045) \]
- Calculating this gives:
\[ \text{pOH} \approx 1.35 \]

### Step 7: Calculate pH
- Use the relationship between pH and pOH:
\[ \text{pH} = 14 - \text{pOH} = 14 - 1.35 = 12.65 \]

### Final Answer
- The pH of the resulting solution is **12.65**.