The freezing point of a diluted milk sample is found to be −0.2°C, while it should have been −0.5°C for pure milk. How…

Strategy:\n> Freezing point depression is proportional to the concentration of the solute. When milk is diluted with water, the concentration decreases, and the magnitude of the freezing point depression decreases proportionally.\n\nStep 1: Analyze the concentration ratio\n- Pure milk: $\Delta T_f = 0.5\\text{ K}$\n- Diluted milk: $\Delta T_f = 0.2\\text{ K}$\n$\\frac{\\text{Concentration}_{\\text{diluted}}}{\\text{Concentration}_{\\text{pure}}} = \\frac{0.2}{0.5} = \\frac{2}{5}$\n\nStep 2: Determine the dilution ratio\nLet $V_m$ be the volume of pure milk and $V_w$ be the volume of added water.\nThe concentration is inversely proportional to volume:\n$\\frac{V_m}{V_m + V_w} = \\frac{2}{5} \implies 5 V_m = 2 V_m + 2 V_w$\n$3 V_m = 2 V_w \implies \\frac{V_w}{V_m} = \\frac{3}{2}$\nSo, 3 cups of water were added to every 2 cups of pure milk.\n\n$\boxed{\\text{Answer: (2)}}$