Question

10 gm of solute A and 20 gm of solute B are both dissolved in 500 ml water. The solution has the same osmotic pressure as 6.67 gm of A and 30 gm of B dissolved in the same amount of water at the same temperature. What is the ratio of molar masses of A and B?

• A. $1$
• B. $0.33$
• C. $3$
• D. $0.66$

Answer 1

The correct option is B $0.33$

Let $M_A$ and $M_B$ be the molar masses of solutes $A$ and $B$ respectively.

Osmotic pressure is a colligative property and is directly proportional to the concentration.

Hence,

$\frac{10}{M_A}+\frac{20}{M_B}=\frac{6.67}{M_A}+\frac{30}{M_B}$

$\frac{10M_B+20M_A}{M_A{M}_B}=\frac{6.67M_B+30M_A}{M_A{M}_B}$

$10M_B+20M_A=6.67M_B+30M_A$

$3.33M_B=10M_A$

$\frac{M_A}{M_B}=\frac{3.33}{10}=0.33$