Question

\(3.42 \times 10^{-2}\ \text{kg}\) sugar (molar mass = 342) is dissolved in water to produce \(234.2\ \text{g}\) of sugar syrup. What is the molality of sugar syrup?

• A. \(0.50\ \text{mol kg}^{-1}\)
• B. \(0.76\ \text{mol kg}^{-1}\)
• C. \(0.67\ \text{mol kg}^{-1}\)
• D. \(0.85\ \text{mol kg}^{-1}\)

Hint:

Molality depends only on mass, so it is independent of temperature.

Answer 1

The Correct Option is A

Step 1: Calculate moles of sugar.
Mass of sugar \(= 3.42 \times 10^{-2}\ \text{kg} = 34.2\ \text{g}\)
\[ \text{Moles of sugar} = \frac{34.2}{342} = 0.1\ \text{mol} \]

Step 2: Calculate mass of solvent.
Mass of solution \(= 234.2\ \text{g}\)
Mass of solvent \(= 234.2 - 34.2 = 200\ \text{g} = 0.2\ \text{kg}\)

Step 3: Apply molality formula.
\[ \text{Molality} = \frac{\text{moles of solute}}{\text{mass of solvent (kg)}} = \frac{0.1}{0.2} = 0.50\ \text{mol kg}^{-1} \]

Step 4: Conclusion.
The molality of the sugar syrup is \(0.50\ \text{mol kg}^{-1}\).