Question

A solution containing 10 g/dm${}^3$ of urea (molecular mass = 60 g mol${}^{-1}$) is isotonic with a 5% solution of a nonvolatile solute. The molecular mass of this nonvolatile solution is:

• A. 250 g/mol
• B. 300 g/mol
• C. 350 g/mol
• D. 200 g/mol

Answer 1

The correct option is B 300 g/mol

$\pi =CRT$

where $\pi$ is the osmotic pressure of the solution

$C=$ Molarity of dissolved solute

$R=$ Universal Gas constant

$T=$ Temperature in Kelvin

For two solutions to be isotonic, their osmotic pressures have to be equal.

$\Rightarrow {\pi }_1={\pi }_2$

$\Rightarrow C_{1}R{T}_1=C_{2}R{T}_2$

Here, $T_1=T_2$

$\Rightarrow C_1=C_2$

Here, $C_1=\frac{10}{60}$

and $C_2=\frac{5}{M\times 100}\times 1000$

Equating $C_1=C_2$ and solving for $M$ we get,

$M=300g/mol$

Hence, the correct option is $\text{B}.$