What is the pH of a solution obtained by mixing 10 mL of 0.1 M HCl and 40 mL 0.2 M `H_(2)SO_(4)` ?

Options

A. 0.74
B. 7.4
C. 4.68
D. 0.468

Explanation

To find 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 moles of HCl
- **Volume of HCl** = 10 mL = 0.010 L
- **Concentration of HCl** = 0.1 M

Using the formula for moles:
\[ \text{Moles of HCl} = \text{Concentration} \times \text{Volume} = 0.1 \, \text{mol/L} \times 0.010 \, \text{L} = 0.001 \, \text{mol} \]

### Step 2: Calculate the moles of H₂SO₄
- **Volume of H₂SO₄** = 40 mL = 0.040 L
- **Concentration of H₂SO₄** = 0.2 M

Using the formula for moles:
\[ \text{Moles of H₂SO₄} = \text{Concentration} \times \text{Volume} = 0.2 \, \text{mol/L} \times 0.040 \, \text{L} = 0.008 \, \text{mol} \]

### Step 3: Determine the total moles of H⁺ ions
H₂SO₄ is a strong acid that dissociates completely in two steps:
1. H₂SO₄ → H⁺ + HSO₄⁻ (1 mole of H₂SO₄ produces 1 mole of H⁺)
2. HSO₄⁻ → H⁺ + SO₄²⁻ (1 mole of HSO₄⁻ produces 1 mole of H⁺)

From 0.008 moles of H₂SO₄, we get:
- From the first dissociation: 0.008 moles of H⁺
- From the second dissociation: 0.008 moles of H⁺

Thus, the total moles of H⁺ from H₂SO₄ = 0.008 + 0.008 = 0.016 moles.

Now, adding the moles of H⁺ from HCl:
\[ \text{Total moles of H⁺} = 0.001 \, \text{(from HCl)} + 0.016 \, \text{(from H₂SO₄)} = 0.017 \, \text{mol} \]

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

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

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

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

### 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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