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. `7.0`
B. `1.04`
C. `12.65`
D. `2.0`

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: Calculate the moles of NaOH and HCl
Assuming we are mixing equal volumes, let’s denote the volume of each solution as \( V \) liters.

- **Moles of NaOH**:
\[ \text{Moles of NaOH} = \text{Concentration} \times \text{Volume} = 0.1 \, \text{M} \times V = 0.1V \]

- **Moles of HCl**:
\[ \text{Moles of HCl} = \text{Concentration} \times \text{Volume} = 0.01 \, \text{M} \times V = 0.01V \]

### Step 2: Determine the limiting reactant
The balanced reaction between NaOH and HCl is:
\[ \text{NaOH} + \text{HCl} \rightarrow \text{NaCl} + \text{H}_2\text{O} \]

From the stoichiometry of the reaction, 1 mole of NaOH reacts with 1 mole of HCl.

- Since \( 0.1V \) moles of NaOH are available and \( 0.01V \) moles of HCl are available, HCl is the limiting reactant.

### Step 3: Calculate the remaining moles of NaOH after the reaction
- Moles of NaOH that react with HCl:
\[ \text{Moles of NaOH reacted} = 0.01V \]

- Remaining moles of NaOH:
\[ \text{Remaining moles of NaOH} = 0.1V - 0.01V = 0.09V \]

### Step 4: Calculate the total volume of the solution
The total volume after mixing both solutions:
\[ \text{Total Volume} = V + V = 2V \]

### Step 5: Calculate the concentration of OH⁻ ions
Since NaOH is a strong base, it completely dissociates in solution:
\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]

The concentration of OH⁻ ions in the total volume:
\[ \text{Concentration of OH}^- = \frac{\text{Moles of NaOH remaining}}{\text{Total Volume}} = \frac{0.09V}{2V} = \frac{0.09}{2} = 0.045 \, \text{M} \]

### Step 6: Calculate pOH
Using the concentration of OH⁻, we can calculate pOH:
\[ \text{pOH} = -\log[\text{OH}^-] = -\log(0.045) \]

Calculating \( \log(0.045) \):
\[ \log(0.045) \approx -1.35 \quad (\text{since } 0.045 = 4.5 \times 10^{-2}) \]
Thus,
\[ \text{pOH} = 1.35 \]

### Step 7: Calculate pH
Using the relationship \( \text{pH} + \text{pOH} = 14 \):
\[ \text{pH} = 14 - \text{pOH} = 14 - 1.35 = 12.65 \]

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

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