Question

A decimolar solution of ${ K }_{ 4 }[Fe{ (CN) }_{ 6 }]$ is 50% dissociated at 300K. Calculate the osmotic pressure of the solution.

Answer 1

Hint: A decimolar solution is also known as 0.1M solution. Now just recall the formula of osmotic pressure to determine the value of osmotic pressure.

Complete step by step answer:

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.
Dissociation reaction of potassium ferrocyanide is
${ K }_{ 4 }[Fe{ (CN) }_{ 6 }] \rightleftharpoons 4K⁺ + { [Fe{ (CN) }_{ 6 }] }^{ 4- }$
Van’t Hoff’s factor for dissociation is always greater than 1 and higher values of colligative properties are observed. For example, higher osmotic pressure and boiling point.
So, van't Hoff's factor , i = 1 - $\alpha + n\alpha$
van't Hoff's factor , i = 1 - $\alpha + 5\alpha = 1 + 4\alpha$
But α is given 50%
So, $\alpha$ = 0.5
Now, i = 1 + 4 $\alpha$ = 1 + 4 × 0.5 = 1 + 2 = 3
Given,
Concentration , C = decimolar = 0.1M
Temperature , T = 300K
Gas constant , R = 0.082 atm.L/Kmol
Now, Osmotic pressure , $\Pi \quad =\quad iCRT$
= 3 × 0.1 × 0.082 × 300
= 900 × 0.0082
= 7.38 atm
Hence, the correct answer for this question is Osmotic pressure = 7.38 atm

Note: The Van’t Hoff factor offers insight on the effect of solutes on the colligative properties of solutions. It is denoted by the symbol ‘i’. The extent to which a substance associates or dissociates in a solution is described by the Van’t Hoff factor.
For example, when a non-electrolytic substance is dissolved in water, the value of i is generally 1.
However, when an ionic compound forms a solution in water, the value of i is equal to the total number of ions present in one formula unit of the substance.
So, never forget to use this for those compounds, which shows association and dissociation in solution.