Elevation in boiling point for 1.5 molal solution of glucose in water is 4 K. The depression in freezing point for 4.5…

Strategy:\n> Determine the constants $K_b$ and $K_f$ separately using the respective molalities and elevations/depressions. Then, find the ratio $K_b/K_f$.\n\nStep 1: Calculate $K_b$\n$\Delta T_b = 4\ \\text{K}$ for $1.5\ \\text{molal}$ glucose solution.\n$K_b = \\frac{\Delta T_b}{m_1} = \\frac{4}{1.5} = \\frac{8}{3}\ \\text{K kg/mol}$\n\nStep 2: Calculate $K_f$\n$\Delta T_f = 4\ \\text{K}$ for $4.5\ \\text{molal}$ glucose solution.\n$K_f = \\frac{\Delta T_f}{m_2} = \\frac{4}{4.5} = \\frac{8}{9}\ \\text{K kg/mol}$\n\nStep 3: Find the ratio $K_b/K_f$\n$\\frac{K_b}{K_f} = \\frac{8/3}{8/9} = \\frac{8}{3} \\times \\frac{9}{8} = 3$\nComparing with the options: 1/2, 1/4, 1/3, 3/1. The value is 3, which corresponds to option (4). Note: Some sources mistakenly index $1/3$, but the math yields 3.\n$\boxed{\\text{Answer: (4) 3 : 1}}$