Question

What is the mass of solute (molar mass 39) in 156 g of benzene, if mole fraction of solute in benzene is 0.2? (at wt C=12, H=1, O=16)

• A. 15.8 g
• B. 19.5 g
• C. 22.4 g
• D. 10 g

Hint:

To calculate the mass of solute using mole fraction, first find the moles of solute and solvent, then use the molar mass of the solute.

Answer 1

The Correct Option is B

Step 1: Understanding the mole fraction formula.
The mole fraction (\( X \)) of a solute is given by: \[ X_{\text{solute}} = \frac{n_{\text{solute}}}{n_{\text{solute}} + n_{\text{solvent}}} \] Where \( n_{\text{solute}} \) is the number of moles of solute and \( n_{\text{solvent}} \) is the number of moles of solvent.
Step 2: Calculating the moles of benzene (solvent).
The molar mass of benzene (C\(_6\)H\(_6\)) is: \[ M_{\text{benzene}} = (6 \times 12) + (6 \times 1) = 78 \, \text{g/mol} \] The number of moles of benzene is: \[ n_{\text{benzene}} = \frac{156}{78} = 2 \, \text{mol} \] Step 3: Using the mole fraction.
Given that the mole fraction of the solute is 0.2, we can find the moles of solute: \[ 0.2 = \frac{n_{\text{solute}}}{n_{\text{solute}} + 2} \] Solving for \( n_{\text{solute}} \): \[ n_{\text{solute}} = 0.4 \, \text{mol} \] Step 4: Calculating the mass of solute.
The mass of the solute is given by: \[ \text{Mass of solute} = n_{\text{solute}} \times \text{Molar mass} = 0.4 \times 39 = 15.8 \, \text{g} \] Step 5: Conclusion.
The correct answer is (B) 19.5 g.