Question

A solution of sucrose (molar mass ${\text{ = 342g/mol}}$ ) is prepared by dissolving $68.4$ g of it in per litre of solution, what is its osmotic pressure at 273K? [${\text{R = 0}}{\text{.082Latm}}{{\text{K}}^{{\text{ - 1}}}}{\text{mo}}{{\text{l}}^{{\text{ - 1}}}}$ ]
A. $3.92$ atm
B. $4.48$ atm
C. $5.92$ atm
D. $29.4$ atm

Answer 1

Hint: Osmotic pressure of a solution may be defined as the minimum excess pressure which has to be applied on the solution to prevent the entry of the solvent into the solution through the semipermeable membrane.
The osmotic pressure (${{\pi }}$ ) of a solution is found to be directly proportional to the molar concentration (C) of the solution and its temperature T. Mathematically, this relation can be expressed as ${\text{\pi = CRT}}$ , where R is the gas constant. This equation is also called the van’t Hoff equation for dilute solutions.

Complete step by step answer:
Given that a solution of sucrose (molar mass ${\text{ = 342g/mol}}$ ) is prepared by dissolving $68.4$ g of it in per litre of solution. The temperature is 273 K and the gas constant R is equal to ${\text{0}}{\text{.082Latm}}{{\text{K}}^{{\text{ - 1}}}}{\text{mo}}{{\text{l}}^{{\text{ - 1}}}}$ .
We need to find out the osmotic pressure of the solution of sucrose at 273 K.
From van’t Hoff equation for dilute solutions we have, ${{\pi = CRT}}$ .
But concentration is equal to the number of moles by volume. So, this equation can be rewritten as ${{\pi = }}\dfrac{{\text{n}}}{{\text{V}}}{\text{RT}}$ .
Here, ${{\pi }}$ is the osmotic pressure in atmospheres, n is the number of moles of the solute in V litres of the solution, R is the gas constant in ${\text{Latm}}{{\text{K}}^{{\text{ - 1}}}}{\text{mo}}{{\text{l}}^{{\text{ - 1}}}}$ and T is the temperature in Kelvin.
According to the question, the molar mass of the solute sucrose is ${\text{ = 342g/mol}}$ and the mass of the solute dissolved is $68.4$ g.
So, the number of moles of the solute
 $
  {\text{n = }}\dfrac{{{\text{68}}{\text{.4}}}}{{{\text{342}}}} \\
   \Rightarrow {\text{n = }}0.2 \\
 $
Substitute all the values in the van’t Hoff equation.
$
  {{\pi = }}\dfrac{{\text{n}}}{{\text{V}}}{\text{RT}} \\
\Rightarrow {{\pi = }}\dfrac{{{\text{0}}{\text{.2mol}}}}{{{\text{1L}}}} \times 0.082{\text{Latm}}{{\text{K}}^{{\text{ - 1}}}}{\text{mo}}{{\text{l}}^{{\text{ - 1}}}} \times 273{\text{K}} \\
   \Rightarrow {{\pi = }}4.48{\text{atm}} \\
 $

Thus, the correct option is B.

Note:
In all numerical problems on osmotic pressure, percentage means weight by volume unless density of the solution is given.
Those solutions which have the same osmotic pressure are called isotonic solutions. As ${{\pi = CRT}}$ , if osmotic pressures are equal, then at the same temperature, the concentrations must also be equal.