if equal volumes of 0.1 M `H_2SO_4` and 0.1 M HCl are mixed then the pH of resulting solution will be (log 15 = 1.176)

Options

A. 0.82
B. 1.64
C. 2.82
D. 1.82

Answer

To solve the problem of finding the pH of a solution formed by mixing equal volumes of 0.1 M H₂SO₄ and 0.1 M HCl, we can follow these steps:

### Step 1: Determine the moles of H₂SO₄ and HCl
Since we are mixing equal volumes, let's assume we are mixing 1 liter of each solution.

- Moles of H₂SO₄:
\[ \text{Moles of H₂SO₄} = \text{Molarity} \times \text{Volume} = 0.1 \, \text{M} \times 1 \, \text{L} = 0.1 \, \text{moles} \]

- Moles of HCl:
\[ \text{Moles of HCl} = \text{Molarity} \times \text{Volume} = 0.1 \, \text{M} \times 1 \, \text{L} = 0.1 \, \text{moles} \]

### Step 2: Calculate the contribution of H⁺ ions from H₂SO₄
H₂SO₄ is a strong acid that dissociates completely in solution:
\[ \text{H₂SO₄} \rightarrow 2 \text{H}^+ + \text{SO₄}^{2-} \]
From 0.1 moles of H₂SO₄, the moles of H⁺ produced will be:
\[ \text{Moles of H}^+ \text{ from H₂SO₄} = 0.1 \, \text{moles} \times 2 = 0.2 \, \text{moles} \]

### Step 3: Calculate the contribution of H⁺ ions from HCl
HCl also dissociates completely:
\[ \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \]
From 0.1 moles of HCl, the moles of H⁺ produced will be:
\[ \text{Moles of H}^+ \text{ from HCl} = 0.1 \, \text{moles} \]

### Step 4: Calculate total moles of H⁺ ions
Now, we can find the total moles of H⁺ ions in the solution:
\[ \text{Total moles of H}^+ = 0.2 \, \text{moles (from H₂SO₄)} + 0.1 \, \text{moles (from HCl)} = 0.3 \, \text{moles} \]

### Step 5: Calculate the total volume of the solution
Since we mixed 1 liter of H₂SO₄ and 1 liter of HCl, the total volume is:
\[ \text{Total volume} = 1 \, \text{L} + 1 \, \text{L} = 2 \, \text{L} \]

### Step 6: Calculate the concentration of H⁺ ions
Now, we can calculate the concentration of H⁺ ions in the resulting solution:
\[ \text{Concentration of H}^+ = \frac{\text{Total moles of H}^+}{\text{Total volume}} = \frac{0.3 \, \text{moles}}{2 \, \text{L}} = 0.15 \, \text{M} \]

### Step 7: Calculate the pH of the solution
The pH is calculated using the formula:
\[ \text{pH} = -\log[\text{H}^+] \]
Substituting the concentration:
\[ \text{pH} = -\log(0.15) \]
Using the logarithmic property:
\[ \text{pH} = -\log(15) + 2 \quad (\text{since } 0.15 = 1.5 \times 10^{-1} = 10^{-1} \times 10^{-0.176}) \]
Given that \(\log(15) = 1.176\):
\[ \text{pH} = -1.176 + 2 = 0.824 \]

Thus, the pH of the resulting solution is approximately **0.82**.