Question

If a $100mL$ of urea solution is isotonic with $10\%\left(w/V\right)$ solution of cane sugar , then calculate the weight of urea in the urea solution
Given: The molecular mass of cane sugar is $342gmo{l}^{-1}$ and that of urea is $60gmo{l}^{-1}$.

• A. $1.01g$
• B. $0.54g$
• C. $2.58g$
• D. $1.75g$

Answer 1

The correct option is D $1.75g$

Isotonic solution:
Two solutions having the same osmotic pressure across a semipermeable membrane is referred to as an isotonic solution.
$10\%\left(w/V\right)$ cane sugar solution means, $10g$ of cane sugar is there in $100mL$ of solution.
$\text{Molar concentration of cane sugar}=\frac{w_1}{m_1\times V_1}=\frac{10}{342\times 0.1}$
and
$\text{Molar concentration of urea}=\frac{w_2}{m_2{V}_2}=\frac{w_2}{60\times 0.1}$
Here $V_1$ and $V_2$ are the volumes of solutions in $L$
For isotonic solutions,

$\frac{w_1}{m_1{V}_1}=\frac{w_2}{m_2{V}_2}\frac{10}{342\times 0.1}=\frac{w_2}{60\times 0.1}{w}_2=1.754g$