A sugar syrup of weight $214.2 ext{ g}$ contains $34.2 ext{ g}$ of sugar ($ ext{C}_{12} ext{H}

Question

A sugar syrup of weight $214.2 	ext{ g}$ contains $34.2 	ext{ g}$ of sugar ($	ext{C}_{12}	ext{H}_{22}	ext{O}_{11}$). Which of the following statements is/are CORRECT?

Professor PC Thomas Classes · Answer

Molar mass of sugar $= 342 	ext{ g/mol}$. Moles of sugar $= 34.2 / 342 = 0.1 	ext{ mol}$. Mass of water $= 214.2 - 34.2 = 180 	ext{ g} = 0.18 	ext{ kg}$. Moles of water $= 180 / 18 = 10 	ext{ mol}$. 
Molality $= 0.1 	ext{ mol} / 0.18 	ext{ kg} = 0.555 	ext{ m}$ (A is correct). 
Mole fraction of sugar $= 0.1 / (10 + 0.1) = 0.1 / 10.1 \approx 0.0099$ (B is correct). 
Mass percentage of water $= (180 / 214.2) 	imes 100 \approx 84.03\%$ (C is correct). 
Molarity cannot be determined precisely without the density of the solution, so D is incorrect.