Question

Calculate the molality of a solution that contains 51.2 g of naphthalene (C$_{10}$H$_8$), in 500 mL of carbon tetrachloride. The density of CCl$_4$ is 1.60 g/mL.

• A. 0.250 m
• B. 0.500 m
• C. 0.750 m
• D. 0.840 m
• E. 1.69 m

Hint:

Always convert solvent mass into kg for molality.

Answer 1

The Correct Option is B

Concept: Molality
\[ m = \frac{\text{moles of solute}}{\text{kg of solvent}} \] ---

Step 1: Molar mass of naphthalene
\[ C_{10}H_8 = 10(12) + 8(1) = 128 \text{ g/mol} \] ---

Step 2: Moles of solute
\[ \frac{51.2}{128} = 0.4 \text{ mol} \] ---

Step 3: Mass of solvent
\[ \text{Volume} = 500 \text{ mL} \] \[ \text{Mass} = 500 \times 1.60 = 800 \text{ g} = 0.8 \text{ kg} \] ---

Step 4: Molality
\[ m = \frac{0.4}{0.8} = 0.5 \] --- Final Answer: \[ \boxed{0.500 \, m} \]