Question

A 5.25% solution of a substance is isotonic with a 1.5% solution of urea (molar mass = 60 g mol${}^{-1}$) in the same solvent. If the densities of both the solutions are assumed to be equal to 1.0 gcm${}^{-3}$, molar mass of the substance will be :

• A. 90.0g mol${}^{-1}$
• B. 115.0g mol${}^{-1}$
• C. 105.0g mol${}^{-1}$
• D. 210.0 g mol${}^{-1}$

Answer 1

Answer: (D)

210.0 g mol${}^{-1}$

For isotonic solutions, the osmotic pressure is the same.
When solutions do not associate or dissociate, $\Pi =CRT$ and isotonic solutions will have the same concentration.

Let the molar mass of substance be M. It's molar concentration will be $\frac{52.5}{M\times 1000}$. The molar concentration of urea solution is $\frac{15}{60\times 1000}$

According to question,

$\frac{52.5}{M\times 1000}=\frac{15}{60\times 1000}$

$M=\frac{52.5}{15}\times 60=210.0g/mol$.

Hence, the molar mass of the substance is 210.0 g/mol.