Question

Solution of glucose (having molar mass 180 g/mol) is isotonic with $12\text{g}$ of urea (having molar mass 60 g/mol) at a constant temperature. Both solutions are one litre each. Then the concentration of glucose is:

• A. $18g/L$
• B. $36g/L$
• C. $12g/L$
• D. $24g/L$

Answer 1

The correct option is B $36g/L$

$\text{Osmotic pressure},\pi =CRT$
Here $\text{C}$ is concentration in molarity.
$\text{R}$ is universal gas constant and $T$ is temperature.
$\text{C}=\frac{n}{V}$
$n=\frac{\text{Given mass}}{\text{Molar mass}}$
Given mass of urea=$12\text{g}$
Volume of each solution =$1\text{L}$
Since both solutions have same osmotic pressure, they have same concentrations also.
Let, the mass of glucose be $X\text{g}$ per liter solution.
$\therefore C_1=C_2$
$\Rightarrow \frac{n_1}{V}=\frac{n_2}{V}\Rightarrow \frac{12}{60}=\frac{X}{180}$
$\Rightarrow X=36\text{g/L}$