$\pi_{1}, \pi_{2}, \pi_{3}$ and $\pi_{4}$ atm are the osmotic pressures of $5 \%$ (mass/volume) solutions of…

$\pi_{1}, \pi_{2}, \pi_{3}$ and $\pi_{4}$ atm are the osmotic pressures of $5 \%$ (mass/volume) solutions of urea, fructose, sucrose and $\mathrm{KCl}$ respectively at certain temperature. The correct order of their magnitudes is :
  1. $\pi_{1}>\pi_{4}>\pi_{2}>\pi_{3}$
  2. $\pi_{1}<\pi_{4}<\pi_{2}<\pi_{3}$
  3. $\pi_{4}>\pi_{1}>\pi_{2}>\pi_{3}$
  4. $\pi_{4}>\pi_{1}>\pi_{3}>\pi_{2}$

Solution

Moles of urea $=\frac{ 5}{60}$;
moles of fructose $=\frac{5}{180}$
$\mathrm{C}_{\text {urea }}=\frac{0.08 \times 1000}{100} \Rightarrow 0.833$
moles of sucrose $=\frac{5}{342}$
$\mathrm{C}_{\text {sucrose }}=0.0146 \times \frac{1000}{100}=0.146$
moles of $\mathrm{KCl}$ (effective)
$=2 \times \frac{5}{74.5}=\frac{5}{37.25} ; \frac{0.134 \times 1000}{100}=1.34$
$\pi \propto \mathrm{C}$
this order is $\pi_{4}>\pi_{1}>\pi_{2}>\pi_{3}$ /

Asked in: JEE-TOPICTESTS-CHEMISTRY

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