Elevation in boiling point for 1.5 molal solution of glucose in water is 4 K. The depression in freezing point for 4.5 molal solution of glucose in water is 4 K. The ratio of molal elevation constant to molal depression constant (K b /K f ) is _________.

Solution

Chemistry ma’am · 3 steps

Same 4 K change from both sides, so each constant is just 4 divided by its own molality.

1. Glucose stays whole. Glucose is a non-electrolyte, so i = 1. That gives Δ T_b = K_b m and Δ T_f = K_f m with no extra factor.
2. Find each constant. K_b = 4/1.5 K kg mol⁻¹ and K_f = 4/4.5 K kg mol⁻¹.

   K_b/K_f = (4/1.5)/(4/4.5) = 4.5/1.5 = 3

3. So. The 4 K cancels, and the ratio K_b/K_f is 3.

The common slip: 0.33. Writing the ratio as 1.5/4.5 gives K_f/K_b = 0.33, the upside-down answer.

The idea to keep. When the temperature change is the same, the constant is inversely proportional to the molality needed. The smaller molality belongs to the larger constant.

Answer from the NTA final answer key. Solution by PrepWiser.