100 ml of 0.3 M HCl solution is mixed with 200 ml of 0.3 M `H_(2)SO_(4)` solution. What is the molariyt of `H^(+)` in resultant solution ?

Options

A. `0.9`
B. `0.6`
C. `0.4`
D. `0.5`

Answer

To find the molarity of \( H^+ \) ions in the resultant solution after mixing 100 ml of 0.3 M HCl with 200 ml of 0.3 M \( H_2SO_4 \), we can follow these steps:

### Step 1: Calculate the contribution of \( H^+ \) from HCl
- HCl dissociates completely in solution:
\[ HCl \rightarrow H^+ + Cl^- \]
- Therefore, the concentration of \( H^+ \) from HCl is the same as the concentration of HCl, which is 0.3 M.
- Volume of HCl solution = 100 ml = 0.1 L.
- Moles of \( H^+ \) from HCl:
\[ \text{Moles of } H^+ = \text{Molarity} \times \text{Volume} = 0.3 \, \text{mol/L} \times 0.1 \, \text{L} = 0.03 \, \text{mol} \]

### Step 2: Calculate the contribution of \( H^+ \) from \( H_2SO_4 \)
- \( H_2SO_4 \) dissociates as follows:
\[ H_2SO_4 \rightarrow 2H^+ + SO_4^{2-} \]
- Therefore, for every mole of \( H_2SO_4 \), there are 2 moles of \( H^+ \).
- The concentration of \( H_2SO_4 \) is also 0.3 M.
- Volume of \( H_2SO_4 \) solution = 200 ml = 0.2 L.
- Moles of \( H^+ \) from \( H_2SO_4 \):
\[ \text{Moles of } H^+ = 2 \times \text{Molarity} \times \text{Volume} = 2 \times 0.3 \, \text{mol/L} \times 0.2 \, \text{L} = 0.12 \, \text{mol} \]

### Step 3: Calculate the total moles of \( H^+ \) in the resultant solution
- Total moles of \( H^+ \):
\[ \text{Total moles of } H^+ = \text{Moles from HCl} + \text{Moles from } H_2SO_4 = 0.03 \, \text{mol} + 0.12 \, \text{mol} = 0.15 \, \text{mol} \]

### Step 4: Calculate the total volume of the resultant solution
- Total volume = Volume of HCl + Volume of \( H_2SO_4 \):
\[ \text{Total volume} = 100 \, \text{ml} + 200 \, \text{ml} = 300 \, \text{ml} = 0.3 \, \text{L} \]

### Step 5: Calculate the molarity of \( H^+ \) in the resultant solution
- Molarity of \( H^+ \):
\[ M = \frac{\text{Total moles of } H^+}{\text{Total volume in L}} = \frac{0.15 \, \text{mol}}{0.3 \, \text{L}} = 0.5 \, \text{M} \]

### Final Answer
The molarity of \( H^+ \) in the resultant solution is **0.5 M**.

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