Question

The relationship between osmotic pressures at $273K$ when $10g$ glucose $\left( {{P}_{1}} \right)$ $10g$ urea $\left( {{P}_{2}} \right)$ and $10g$ sucrose $\left( {{P}_{3}} \right)$ are dissolved in $250mL$ 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

Hint: Osmotic pressure follows the direct relationship with molarity. Molarity is defined as the number of moles of substance present per unit volume. Osmotic pressure depends on the molecular weight inversely.

Complete Step by Step Answer:
The formula for osmotic pressure is given as follows:
\[\pi =iMRT\]

Here $i$ is the van't hoff’s factor.
$M$ is the molarity of the solution.
$R$ is the Rydberg constant and $T$ is the temperature.

From the above relation we can say that osmotic pressure is directly proportional to molarity again molarity is inversely proportional to molecular weight. Thus osmotic pressure is also inversely proportional to molecular weight.

The molecular weight of sugar cane is $342$ grams.
The molecular weight of glucose is $180$ grams.
The molecular weight of urea is $60$ grams.
Thus the osmotic pressure of urea will be higher followed by glucose and cane sugar.
So, the correct relation is \[{{P}_{2}}>{{P}_{1}}>{{P}_{3}}\].
Thus the correct option is C.

Note: The molecular weight of a compound can be determined using osmotic pressure. Osmotic pressure is also widely used in the desalination and purification of seawater, which involves the process of reverse osmosis. Osmotic pressure can be measured in terms of concentration of solution.