In a solution of benzene in chlorofrom `(CHCl_(3))` , the mole fraction on benzene is 0.45. Calculate its percentage by weight in the mixture .

Explanation

To calculate the percentage by weight of benzene in a solution of benzene in chloroform (CHCl₃) with a mole fraction of benzene equal to 0.45, we can follow these steps:

### Step 1: Understand the Definitions
- **Mole Fraction (X)**: The mole fraction of benzene is given as 0.45. This means that the moles of benzene divided by the total moles of the solution equals 0.45.
- **Percentage by Weight**: This is defined as the mass of the solute (benzene) divided by the mass of the solution, multiplied by 100.

### Step 2: Assume a Total Mass of Solution
Assume the total mass of the solution is 100 grams. This makes calculations easier since we can directly relate the mass of benzene to its percentage by weight.

### Step 3: Express Mass of Benzene and Chloroform
Let:
- Mass of benzene = X grams
- Mass of chloroform = 100 - X grams

### Step 4: Calculate Moles of Benzene and Chloroform
- **Molecular Mass of Benzene (C₆H₆)**: 78 g/mol
- **Molecular Mass of Chloroform (CHCl₃)**: 119.5 g/mol

Now calculate the number of moles:
- Moles of benzene = \( \frac{X}{78} \)
- Moles of chloroform = \( \frac{100 - X}{119.5} \)

### Step 5: Set Up the Mole Fraction Equation
Using the mole fraction formula:
\[ \text{Mole Fraction of Benzene} = \frac{\text{Moles of Benzene}}{\text{Moles of Benzene} + \text{Moles of Chloroform}} = 0.45 \]
Substituting the values:
\[ 0.45 = \frac{\frac{X}{78}}{\frac{X}{78} + \frac{100 - X}{119.5}} \]

### Step 6: Solve the Equation
Cross-multiply to eliminate the fraction:
\[ 0.45 \left( \frac{X}{78} + \frac{100 - X}{119.5} \right) = \frac{X}{78} \]
Expanding and simplifying gives:
\[ 0.45 \cdot \frac{X}{78} + 0.45 \cdot \frac{100 - X}{119.5} = \frac{X}{78} \]
Rearranging and solving for X will yield:
\[ 3510 = 119.5X - 18.675X \]
\[ X = \frac{3510}{100.825} \approx 34.8 \]

### Step 7: Calculate Percentage by Weight
Now that we have the mass of benzene (X ≈ 34.8 grams), we can find the percentage by weight:
\[ \text{Percentage by Weight} = \left( \frac{X}{100} \right) \times 100 = 34.8\% \]

### Final Answer
The percentage by weight of benzene in the mixture is **34.8%**.

---