Question

:If ${\text{1}}{\text{.71}}$ g of sugar (molar mass $ = 342$ ) are dissolved in 500 mL of an aqueous solution at 300 K, what will be its osmotic pressure?

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 ${{\pi = CRT}}$ , 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 sugar (molar mass ${\text{ = 342g/mol}}$ ) is prepared by dissolving ${\text{1}}{\text{.71}}$ g of it in 500 milliliter or $0.5$ litre of solution. The temperature is 300 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 sugar at 300 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 question, molar mass of the solute sucrose is ${\text{ = 342g/mol}}$ and mass of the solute dissolved is ${\text{1}}{\text{.71}}$ g.
So, the number of moles of the solute
$\Rightarrow$ $
  {\text{n = }}\dfrac{{{\text{1}}{\text{.71}}}}{{{\text{342}}}} \\
   \Rightarrow {\text{n = 0}}{\text{.005}} \\
 $
Substitute all the values in the van’t Hoff equation. Thus, the osmotic pressure of the sugar solution at 300K is:
$\Rightarrow$ $
  {{\pi = }}\dfrac{{\text{n}}}{{\text{V}}}{\text{RT}} \\
   \Rightarrow {{\pi = }}\dfrac{{{\text{0}}{\text{.005mol}}}}{{{\text{0}}{\text{.5L}}}} \times 0.082{\text{Latm}}{{\text{K}}^{{\text{ - 1}}}}{\text{mo}}{{\text{l}}^{{\text{ - 1}}}} \times 300{\text{K}} \\
   \Rightarrow {{\pi = 0}}{\text{.25atm}} \\
 $

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.