Question

A $5$% solution of cane sugar (Mol wt. $=342$) is isotonic with $1$% solution of substance $X$. The molecular weight of $X$ is:

• A. $171.2$
• B. $68.4$
• C. $34.2$
• D. $136.2$

Answer 1

The correct option is B $68.4$

Two solutions are isotonic when they have the same osmotic pressure. This is possible if they have the same molar concentration.

A $5$% solution of cane sugar means 100 g of the solution will have 5 g of cane sugar. For dilute solutions, 100 g is approximately equal to 100 mL.

Hence, molarity of cane sugar $=\frac{\text{5 g}}{\text{342 g/mol}\times \text{100 mL}}\times \frac{\text{1000 mL}}{\text{1 L}}=\text{0.146 M}$......(1)

A $1$% solution of substance $X$ means 100 g of the solution will have 1 g of substance $X$. For dilute solutions, 100 g is approximately equal to 100 mL.

Hence, molarity of substance $X$ $=\frac{\text{1 g}}{\text{M g/mol}\times \text{100 mL}}\times \frac{\text{1000 mL}}{\text{1 L}}=\frac{10}{M}\text{M}$......(2)

But (1) $=$ (2)

$\frac{10}{M}=0.146$

$M=\frac{10}{0.146}=68.4$

The molecular weight of $X$ is 68.4 g/mol.