Question

The relationship between osmotic pressures $({\pi }_{glucose},{\pi }_{urea}and{\pi }_{sucrose})$ at a definite temperature when $1g$ glucose, $1g$ urea and $1g$ sucrose are dissloved in $1litre$ of water is:
(Assume $\text{Vant Hoff factor}\left(i\right)=1$ for all):
Molecular masses for urea, glucose and sucrose are $60g/mol,180g/mol\&342g/mol$ respectively

• A. ${\pi }_{glcose}>{\pi }_{urea}>{\pi }_{sucrose}$
• B. ${\pi }_{sucrose}>{\pi }_{glucose}>{\pi }_{urea}$
• C. ${\pi }_{urea}>{\pi }_{glucose}>{\pi }_{sucrose}$
• D. ${\pi }_{sucrose}>{\pi }_{urea}>{\pi }_{glucose}$

Answer 1

The correct option is C ${\pi }_{urea}>{\pi }_{glucose}>{\pi }_{sucrose}$

Osmotic pressure: $\left(\pi \right)$
$\pi =i\times C\times R\times T$
Here
$i=\text{Vant Hoff factor}$
$C\text{is concentration (Molarity)}{\text{(mol L}}^{-1}\left)R\text{is ideal gas constant}{\text{(L atm mol}}^{-1}{\text{K}}^{-1}\right)T\text{is temperature (K)}$
At a given temperature
$\pi \propto C$
Since volume , and mass of solute is constant
$\pi \propto \frac{1}{\text{Molecular mass}}$
Since,

$M_{urea}<M_{glucose}<M_{sucrose}$

$\therefore {\pi }_{urea}>{\pi }_{glucose}>{\pi }_{sucrose}$