If 250 cm³ of an aqueous solution containing 0.73 g of a protein A is isotonic with one litre of another aqueous solution containing 1.65 g of a protein B, at 298 K, the ratio of the molecular masses of A and B is ______ × 10 –2 (to the nearest integer).

Solution

Chemistry ma’am · 3 steps

Isotonic means equal molar concentration, so set moles per litre of A equal to that of B.

1. Isotonic means equal. Osmotic pressure is π = CRT. Both solutions are at 298 K and have the same π, so their molar concentrations C must be equal. R and T cancel.

   (0.73 / M_A)/(0.25 L) = (1.65 / M_B)/(1 L)

2. Volume in litres. 250 cm³ = 0.25 L. Rearranging gives M_A/M_B = 0.73/(0.25 × 1.65) = 0.73/0.4125 = 1.7697.
3. So. M_A/M_B = 1.7697 = 176.97 × 10⁻², which rounds to 177.

The common slip: 44. Ignoring the two different volumes and taking 0.73/1.65 directly gives 0.44, that is 44, not 177. Concentration needs the volume of each solution.

The idea to keep. Isotonic solutions at the same temperature have the same molarity. Write moles over litres for each solution, set them equal, and the gas constant never enters the sum.

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