Question

At a constant temperature, a solution of glucose $\left({\text{C}}_6{\text{H}}_{12}{\text{O}}_6\right)$ is isotonic with $4\text{g}$ of urea $({\text{NH}}_2-\text{CO}-{\text{NH}}_2)$ per liter of solution. The concentration of glucose is

• A. $4\text{g/L}$
• B. $8\text{g/L}$
• C. $12\text{g/L}$
• D. $14\text{g/L}$

Answer 1

The correct option is C $12\text{g/L}$

$\text{Osmotic preaaure},\pi =CRT$
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=$4\text{g}$
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.
$\therefore C_1=C_2$
$\Rightarrow \frac{n_1}{V}=\frac{n_2}{V}\Rightarrow \frac{4}{60}=\frac{X}{180}$
$\Rightarrow X=12\text{g/L}$