2 g of a non-volatile non-electrolyte solute is dissolved in 200 g of two different solvents A and B whose ebullioscopic constants are in the ratio of 1 : 8. The elevation in boiling points of A and B are in the ratio x/y (x : y). The value of y is ______________. (Nearest integer)

Solution

Chemistry ma’am · 3 steps

Same solute, same masses, so the molality is equal and the elevations follow the K_b ratio.

1. Δ T_b = K_b × m

2. Molality is equal. Both solutions have 2 g of the same solute in 200 g of solvent. So the moles of solute and the kilograms of solvent are the same, and the molality m is the same in A and B.
3. Take the ratio. With m equal, it cancels: (Δ T_b(A))/(Δ T_b(B)) = K_b(A)/K_b(B) = 1/8. The solute is a non-electrolyte, so i = 1 for both and nothing else changes.
4. So. The elevations are in the ratio x : y = 1 : 8, which gives y = 8.

The common slip: 1. Writing Δ T_b ∝ 1/K_b flips the ratio to 8 : 1 and gives 1, not 8.

The idea to keep. When the molality is the same in two solvents, the elevation in boiling point is directly proportional to K_b. You never need the molar mass to compare them.

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