A solution containing 6 . 0   g of urea is isotonic with a solution containing 10   g of a…

Two solutions having same osmotic pressure at a given temperature are called isotonic solutions. When such solutions are separated.

$\mathrm{\pi }=\mathrm{CRT}$

$\mathrm{\pi }=$Osmotic pressure

C=Concentration in molarity

R=Universal gas constant

T=Temperature

As the solutions are isotonic

$$\begin{gathered} {\mathrm{\pi }}_{\mathrm{urea}}={\mathrm{\pi }}_{\mathrm{X}} \\ {\mathrm{C}}_{\mathrm{urea}}={\mathrm{C}}_{\mathrm{X}} \end{gathered}$$

$$\begin{gathered} {\left[\frac{{\mathrm{W}}_{\mathrm{urea}}}{{\mathrm{M}}_{\mathrm{urea}}}\times \frac{1000}{\mathrm{V}}\right]}_{\mathrm{urea}}={\left[\frac{{\displaystyle {\mathrm{W}}_{\mathrm{X}}}}{{\displaystyle {\mathrm{M}}_{\mathrm{X}}}}\times \frac{{\displaystyle 1000}}{{\displaystyle \mathrm{V}}}\right]}_{\mathrm{X}} \\ {\left[\frac{{\displaystyle 6}}{{\displaystyle 60}}\times \frac{{\displaystyle 1000}}{{\displaystyle \mathrm{V}}}\right]}_{\mathrm{urea}}={\left[\frac{{\displaystyle 10}}{{\displaystyle {\mathrm{M}}_{\mathrm{X}}}}\times \frac{{\displaystyle 1000}}{{\displaystyle \mathrm{V}}}\right]}_{\mathrm{X}} \\ {\mathrm{M}}_{\mathrm{X}}=100\mathrm{g} \end{gathered}$$

Hence, the molecular weight of the non-electrolytic solute X is 100 gmol^-1