A solution containing 62 g ethylene glycol in 250 g water is cooled to −10°C. If Kf for water is 1.86 K kg mol⁻¹, the…

Strategy:\n> Find the molality required at -10°C, and then calculate how much water must be remaining to maintain that molality. The difference from the starting water mass gives the amount of ice.\n\nStep 1: Calculate initial moles of ethylene glycol\n- Molar Mass = 62.\n- $n = 62 / 62 = 1.0\\text{ mol}$.\n\nStep 2: Calculate required final molality ($m_{\\text{final}}$)\n$\Delta T_f = 10\\text{ K}, K_f = 1.86$.\n$m_{\\text{final}} = 10 / 1.86 \approx 5.376\\text{ mol/kg}$\n\nStep 3: Solve for remaining water ($m_{w,\\text{remaining}}$)\n$5.376 = 1.0 / m_{w,\\text{remaining}} \implies m_{w,\\text{remaining}} = 1.0 / 5.376 \approx 0.186\\text{ kg} = 186\\text{ g}$\n\nStep 4: Calculate mass of ice\n$\\text{Ice} = 250\\text{ g (initial)} - 186\\text{ g (remaining water)} = 64\\text{ g}$.\n\n$\boxed{\\text{Answer: 64}}$