Chemistry - Liquid Solution Question with Solution | TestHub

For isotonic solutions, the osmotic pressures are equal, ${\pi }_1={\pi }_2$.

Since both glycerin and glucose are non-electrolytes, their van't Hoff factors are $i=1$. Therefore, their molar concentrations are equal, $C_1=C_2$.

Let the molar mass of glycerin be $M$. A $1.02\%$ solution of glycerin contains $1.02\text{ g}$ in $100\text{ mL}$ of solution, and a $2\%$ solution of glucose contains $2\text{ g}$ in $100\text{ mL}$ of solution.

Concentration of glycerin, $C_1=\frac{1.02}{M\times 0.1}$

Concentration of glucose, $C_2=\frac{2}{180\times 0.1}$

Equating $C_1$ and $C_2$:

$\frac{1.02}{M}=\frac{2}{180}$

$M=\frac{1.02\times 180}{2}$

$M=1.02\times 90=91.8\text{ g/mol}$

Answer: 91.8