Question

The mole fraction of an unknown solute in \( 1560 \) g of Benzene is \( 0.5 \). What is the molality of the solution? (Molar mass of Benzene: \( 78 \))

• A. 12.8
• B. 10.3
• C. 3.25
• D. 16.9

Hint:

If mole fraction of solute is 0.5, then moles of solute = moles of solventAlways convert solvent mass into kg for molality.

Answer 1

The Correct Option is A

Step 1: Write mole fraction relation.
\[ x_{\text{solute}} = \frac{n_{\text{solute}}}{n_{\text{solute}} + n_{\text{solvent}}} \]
Given:
\[ x_{\text{solute}} = 0.5 \]

Step 2: Use condition \( x_{\text{solute}} = 0.5 \).
\[ 0.5 = \frac{n_{\text{solute}}}{n_{\text{solute}} + n_{\text{solvent}}} \]
This implies:
\[ n_{\text{solute}} = n_{\text{solvent}} \]

Step 3: Calculate moles of benzene.
\[ n_{\text{solvent}} = \frac{1560}{78} = 20 \, \text{moles} \]
So:
\[ n_{\text{solute}} = 20 \, \text{moles} \]

Step 4: Write molality formula.
\[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \]

Step 5: Convert mass to kg.
\[ 1560 \, \text{g} = 1.56 \, \text{kg} \]

Step 6: Calculate molality.
\[ m = \frac{20}{1.56} \]
\[ m \approx 12.82 \]

Step 7: Final conclusion.
\[ \boxed{12.8} \]