Question

An aqueous solution contains 0.4% urea and 3.42% sucrose by mass. Calculate the osmotic pressure of the solution at 27 $^\circ C$ ?

Answer 1

Hint : Osmotic pressure is the minimum pressure which needs to be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane. It is also defined as the measure of the tendency of a solution to take in a pure solvent by osmosis. Potential osmotic pressure is the maximum osmotic pressure that could develop in a solution if it were separated from its pure solvent by a semipermeable membrane.

Complete Step By Step Answer:
Osmosis occurs when two solutions containing different concentrations of solute are separated by a selectively permeable membrane. Solvent molecules pass preferentially through the membrane from the low-concentration solution to the solution with higher solute concentration. The transfer of solvent molecules will continue until equilibrium is attained. Jacobus van 't Hoff found a quantitative relationship between osmotic pressure and solute concentration, expressed in the following equation: $\pi = iCRT$ $\pi$ is osmotic pressure, i is the dimensionless van 't Hoff index, c is the molar concentration of solute, R is the ideal gas constant, and T is the temperature in kelvins. This formula applies when the solute concentration is sufficiently low that the solution can be treated as an ideal solution. The proportionality to concentration means that osmotic pressure is a colligative property. Note the similarity of this formula to the ideal gas law in the $PV = nRT$ where n is the total number of moles of gas molecules in the volume V, and n/V is the molar concentration of gas molecules. Osmotic pressure= $i \times C \times R \times T$ ,
where, $C$ =concentration of solute(in terms of Molarity) $R$ = Gas constant=0.082 $L\left( {atm} \right){\left( {mol} \right)^{ - 1}}{K^{ - 1}}$
T=temperature (in Kelvin)
i=Van’t-Hoff factor (1 for non-electrolyte)
0.4% urea solution means 0.4g urea is present in 100ml of solution.
mole of urea=weight given/Molecular weight of urea
= 0.4/60=1/120
Hence Concentration( $C$ ) of urea (in terms of Molarity)
= (mole of urea( $n$ )/Volume of solution) $\times$ 1000
= \left\\{ {\left( {\dfrac{1}{{120}}} \right) \div 100} \right\\} \times 1000 \\\ = \dfrac{1}{{12}}
Hence Osmotic pressure $(\pi )$ = $1 \times \dfrac{1}{{12}} \times 0.082 \times 300 = 2.05atm$ .

Note :
The semipermeable membrane only allows the movement of solvent molecules through it – solute particles cannot pass through it.If sufficient pressure is applied to the solution side of the semipermeable membrane, the process of osmosis is halted. The minimum amount of pressure required to nullify the process of osmosis is called osmotic pressure.