A food technology student is developing a sports drink. She dissolves a non-volatile, non-electrolyte carbohydrate (molar mass = 180 g mol⁻¹) in water to study its colligative properties before finalising the formulation.
A food technology student is developing a sports drink. She dissolves a non-volatile, non-electrolyte carbohydrate (molar mass = 180 g mol⁻¹) in water. She prepares Solution P by dissolving 9.0 g of this carbohydrate in 500 g of water, and Solution Q by dissolving 9.0 g of the same carbohydrate in 250 g of water.
(a) Calculate the boiling point elevation (ΔT_b) of Solution P. (K_b for water = 0.52 K kg mol⁻¹) [2 marks]
(b) Without further calculation, predict how the boiling point elevation of Solution Q compares with that of Solution P. Give one reason for your answer. [1 mark]
(c) The student later adds a small amount of NaCl (van't Hoff factor i = 2) to Solution Q to improve conductivity. State with reason whether the osmotic pressure of the resulting solution would increase, decrease, or remain the same compared to Solution Q (before NaCl addition), assuming volume remains constant. [1 mark]
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The governing formula for boiling point elevation is:
ΔT_b = K_b × m
where m = molality = (mass of solute / molar mass of solute) / (mass of solvent in kg)
Moles of carbohydrate = 9.0 / 180 = 0.05 mol
Mass of solvent (water) = 500 g = 0.500 kg
m = 0.05 / 0.500 = 0.1 mol kg⁻¹
ΔT_b = 0.52 × 0.1 = 0.052 K
∴ Boiling point elevation of Solution P = 0.052 K
(b) The boiling point elevation of Solution Q will be greater (double) than that of Solution P.
Reason: Solution Q contains the same mass of solute (9.0 g, same moles = 0.05 mol) dissolved in half the mass of solvent (250 g = 0.250 kg), giving double the molality (m = 0.2 mol kg⁻¹). Since ΔT_b = K_b × m, a higher molality produces a greater boiling point elevation. (ΔT_b of Q = 0.104 K)
(c) The osmotic pressure of the resulting solution would increase.
Reason: Osmotic pressure is given by π = i·C·R·T. Adding NaCl (i = 2) increases the total effective concentration of solute particles (ionic species Na⁺ and Cl⁻) in the solution. Since volume is constant and temperature is unchanged, the total particle concentration (C_effective) increases, and therefore π increases.