A mixture is prepared by mixing 10 gm `H_(2)SO_(4) and 40 gm SO_(3)` calculate mole fraction of `H_(2)SO_(4)`

Answer

To calculate the mole fraction of \( H_2SO_4 \) in the mixture of \( H_2SO_4 \) and \( SO_3 \), we will follow these steps:

### Step 1: Calculate the number of moles of \( H_2SO_4 \)

The formula to calculate the number of moles is:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

For \( H_2SO_4 \):
- Given mass = 10 g
- Molar mass of \( H_2SO_4 = 2 + 32 + (16 \times 4) = 98 \, g/mol \)

Now, we can calculate the moles:

\[ \text{Moles of } H_2SO_4 = \frac{10 \, g}{98 \, g/mol} \approx 0.102 \, moles \]

### Step 2: Calculate the number of moles of \( SO_3 \)

For \( SO_3 \):
- Given mass = 40 g
- Molar mass of \( SO_3 = 32 + (16 \times 3) = 80 \, g/mol \)

Now, we can calculate the moles:

\[ \text{Moles of } SO_3 = \frac{40 \, g}{80 \, g/mol} = 0.5 \, moles \]

### Step 3: Calculate the total number of moles in the mixture

Now, we can find the total number of moles:

\[ \text{Total moles} = \text{Moles of } H_2SO_4 + \text{Moles of } SO_3 \]

\[ \text{Total moles} = 0.102 \, moles + 0.5 \, moles = 0.602 \, moles \]

### Step 4: Calculate the mole fraction of \( H_2SO_4 \)

The mole fraction (\( \chi \)) is given by the formula:

\[ \chi_{H_2SO_4} = \frac{\text{Moles of } H_2SO_4}{\text{Total moles}} \]

Substituting the values we calculated:

\[ \chi_{H_2SO_4} = \frac{0.102 \, moles}{0.602 \, moles} \approx 0.169 \]

### Final Answer

The mole fraction of \( H_2SO_4 \) in the mixture is approximately **0.169**.

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