Calculate the mole fraction of benzene in solution containing `30%` by mass in carbon tetrachloride.

Explanation

To calculate the mole fraction of benzene in a solution containing 30% by mass of benzene in carbon tetrachloride, we can follow these steps:

### Step 1: Define the mass of the solution
Assume we have 100 g of the solution for simplicity. Since the solution contains 30% benzene by mass, we can calculate the mass of benzene and carbon tetrachloride.

- Mass of benzene = 30% of 100 g = 30 g
- Mass of carbon tetrachloride = 100 g - 30 g = 70 g

### Step 2: Calculate the number of moles of benzene and carbon tetrachloride
Next, we need to find the number of moles of each component using their molar masses.

- Molar mass of benzene (C₆H₆) = 78 g/mol
- Molar mass of carbon tetrachloride (CCl₄) = 153.8 g/mol

Now, we can calculate the number of moles:

- Moles of benzene = Mass of benzene / Molar mass of benzene
\[ \text{Moles of benzene} = \frac{30 \text{ g}}{78 \text{ g/mol}} \approx 0.3846 \text{ moles} \]

- Moles of carbon tetrachloride = Mass of carbon tetrachloride / Molar mass of carbon tetrachloride
\[ \text{Moles of carbon tetrachloride} = \frac{70 \text{ g}}{153.8 \text{ g/mol}} \approx 0.4540 \text{ moles} \]

### Step 3: Calculate the total number of moles in the solution
Now, we can find the total number of moles in the solution:

\[ \text{Total moles} = \text{Moles of benzene} + \text{Moles of carbon tetrachloride} \]
\[ \text{Total moles} = 0.3846 + 0.4540 \approx 0.8386 \text{ moles} \]

### Step 4: Calculate the mole fraction of benzene
The mole fraction of benzene (X_benzene) is given by the formula:

\[ X_{\text{benzene}} = \frac{\text{Moles of benzene}}{\text{Total moles}} \]
\[ X_{\text{benzene}} = \frac{0.3846}{0.8386} \approx 0.458 \]

### Final Answer
The mole fraction of benzene in the solution is approximately **0.458**.

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