Calculate the `pH` of solution obtained by mixing `10 ml` of `0.1 M HCl` and `40 ml` of `0.2 M H_(2)SO_(4)`

Options

A. `0.3685`
B. `0.4685`
C. `1.3685`
D. `1.4684`

Explanation

To calculate the pH of the solution obtained by mixing 10 mL of 0.1 M HCl and 40 mL of 0.2 M H₂SO₄, we can follow these steps:

### Step 1: Calculate the number of moles of H⁺ from HCl
- **Volume of HCl solution** = 10 mL = 0.01 L
- **Concentration of HCl** = 0.1 M

Using the formula for moles:
\[ \text{Moles of HCl} = \text{Concentration} \times \text{Volume} = 0.1 \, \text{mol/L} \times 0.01 \, \text{L} = 0.001 \, \text{mol} \]

Since HCl is a strong acid, it fully dissociates:
\[ \text{Moles of H⁺ from HCl} = 0.001 \, \text{mol} \]

### Step 2: Calculate the number of moles of H⁺ from H₂SO₄
- **Volume of H₂SO₄ solution** = 40 mL = 0.04 L
- **Concentration of H₂SO₄** = 0.2 M

Using the formula for moles:
\[ \text{Moles of H₂SO₄} = \text{Concentration} \times \text{Volume} = 0.2 \, \text{mol/L} \times 0.04 \, \text{L} = 0.008 \, \text{mol} \]

H₂SO₄ is a diprotic acid, meaning it can donate two protons:
\[ \text{Moles of H⁺ from H₂SO₄} = 0.008 \, \text{mol} \times 2 = 0.016 \, \text{mol} \]

### Step 3: Calculate the total moles of H⁺
\[ \text{Total moles of H⁺} = \text{Moles of H⁺ from HCl} + \text{Moles of H⁺ from H₂SO₄} = 0.001 \, \text{mol} + 0.016 \, \text{mol} = 0.017 \, \text{mol} \]

### Step 4: Calculate the total volume of the mixed solution
\[ \text{Total volume} = 10 \, \text{mL} + 40 \, \text{mL} = 50 \, \text{mL} = 0.050 \, \text{L} \]

### Step 5: Calculate the concentration of H⁺ in the mixed solution
\[ \text{Concentration of H⁺} = \frac{\text{Total moles of H⁺}}{\text{Total volume}} = \frac{0.017 \, \text{mol}}{0.050 \, \text{L}} = 0.34 \, \text{M} \]

### Step 6: Calculate the pH of the solution
Using the formula for pH:
\[ \text{pH} = -\log[\text{H⁺}] = -\log(0.34) \]

Calculating the logarithm:
\[ \text{pH} \approx 0.47 \]

### Final Answer
The pH of the solution obtained by mixing 10 mL of 0.1 M HCl and 40 mL of 0.2 M H₂SO₄ is approximately **0.47**.

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