If X molal solution of a compound is benzene has mole fraction of solute equal to` 0.4`. Then the value of X is

Options

A. 4.2
B. 8.5
C. 3.2
D. 5.1

Answer

To solve the problem, we need to find the value of X (molality) given that the mole fraction of the solute in a benzene solution is 0.4.

### Step-by-Step Solution:

1. **Understanding Molality**:
- Molality (X) is defined as the number of moles of solute per kilogram of solvent.
- In this case, we have X moles of solute in 1 kg (1000 g) of benzene.

2. **Mole Fraction Definition**:
- The mole fraction of the solute (solute mole fraction) is given by the formula:
\[ \text{Mole Fraction of Solute} = \frac{\text{Moles of Solute}}{\text{Moles of Solute} + \text{Moles of Solvent}} \]
- We know that the mole fraction of the solute is 0.4.

3. **Calculating Moles of Solvent**:
- The molecular weight of benzene (C6H6) is 78 g/mol.
- For 1000 g of benzene, the number of moles of benzene (solvent) can be calculated as:
\[ \text{Moles of Benzene} = \frac{1000 \text{ g}}{78 \text{ g/mol}} \approx 12.82 \text{ moles} \]

4. **Setting Up the Equation**:
- Let the number of moles of solute be X. According to the mole fraction formula:
\[ 0.4 = \frac{X}{X + 12.82} \]

5. **Cross-Multiplying to Solve for X**:
- Cross-multiplying gives:
\[ 0.4(X + 12.82) = X \]
- Expanding this:
\[ 0.4X + 5.128 = X \]
- Rearranging the equation:
\[ X - 0.4X = 5.128 \]
\[ 0.6X = 5.128 \]
- Solving for X:
\[ X = \frac{5.128}{0.6} \approx 8.55 \]

6. **Final Answer**:
- The value of X (molality) is approximately 8.5.