Final answer:
The molality of a sodium chloride solution with a freezing point of -5.5 °C can be calculated using the formula for freezing point depression. The correct answer is approximately 1.5 mol/kg, which is option (a).
Step-by-step explanation:
To calculate the molality of a sodium chloride solution with a freezing point of -5.5 °C, we use the formula for freezing point depression: ΔT_f = i * K_f * m. Here, ΔT_f is the freezing point depression, i is the van't Hoff factor (which is 2 for NaCl, because it dissociates into two ions, Na+ and Cl-), K_f is the freezing point depression constant for water (1.86 °C/m), and m is the molality of the solution. For water, a freezing point depression of 1 °C corresponds to a 1 m solution of a non-electrolyte, meaning 1 mole of solute per kilogram of solvent (원리전). Because sodium chloride dissociates into two particles, its effect is doubled. Therefore, using the equation with the given freezing point depression (-5.5 °C), we have:
ΔT_f = -5.5 °C = 2m * 1.86 °C/kg. Solving for m gives us m = -5.5 /(2 * 1.86) which yields approximately 1.479 mol/kg. The closest answer choice is (a) 1.5 mol/kg.