Question

The relationship between osmotic pressures at 273 K, when 10g glucose $\left(P_1\right)$, 10g urea $\left(P_2\right)$ and 10g sucrose $\left(P_3\right)$ are dissolved in 250 mL of water is:

• A. $P_1>P_2>P_3$
• B. $P_3>P_2>P_1$
• C. $P_2>P_1>P_3$
• D. None of these

Answer 1

The correct option is C $P_2>P_1>P_3$

We know that the osmostic pressure is given by $\Pi =iMRT$

where i is the Van't Hoff factor

M is the molarity

R=0.08206 L-atm mol${}^{-1}$ K${}^{-1}$ is the gas constant

T is the absolute temperature

$\Pi \propto M$

Molarity is inversely proportional to molecular weight.

Molecular weight of glucose=180, urea=60, sucrose=342.

Osmotic pressure is also inversely proportional to molecular weight.

$P_1=$Osmotic pressure of glucose (10 g)

$P_2=$Osmotic pressure of urea (10 g)

$P_3=$Osmotic pressure of sucrose (10 g)

So, $P_2>P_1>P_3$