Question

Van’t Hoff factor of centi molal solution of ${K_3}[Fe{(CN)_6}]$ is $3.333$. Calculate the percent dissociation of ${K_3}[Fe{(CN)_6}]$.
(A) $33.33$
(B) $0.78$
(C) $78$
(D) $23.33$

Answer 1

Hint:As we know that Van’t Hoff factor is a measure of solute effect on some colligative properties like osmotic pressure, freezing point depression, boiling point elevation and relative lowering of vapour pressure. It is the ratio of actual concentration when compound dissolves to the concentration as calculated from its mass.

Complete answer:
We already know that the Van't Hoff factor is the ratio of experimental value of the colligative property to the calculated value of the colligative property or the ratio of concentration of particles when the compound dissolves to the concentration as calculated from its mass.
We can also say that it is the total number of moles of all the species produced from one mole of the solute in solution.
Now we are given that the Van't Hoff factor of the centi molal solution of Potassium ferricyanide ${K_3}[Fe{(CN)_6}]$ is $i = 3.333$.
After dissociation, potassium ferricyanide would give three potassium ions and a ferricyanide ion. We can show this dissociation through an equation:
${K_3}[Fe{(CN)_6}] \to 3{K^ + } + {[Fe{(CN)_6}]^{3 - }}$
So we got total number of ions $ = 4$
We all know that, since colligative property is proportional to the number of moles of solutes present in solution, therefore the Van’t Hoff factor is given as:
$\alpha = \dfrac{{i - 1}}{{n - 1}}$, where $\alpha $, is the dissociation degree fraction of solute, $n$is number of ions formed and $i$ is the Van’t Hoff Factor.
Putting all the values:
$\Rightarrow \alpha = \dfrac{{3.333 - 1}}{{4 - 1}}$
$\Rightarrow \alpha = \dfrac{{2.333}}{3}$
$\Rightarrow \alpha = 0.7776 \approx 0.78$
Percentage of the dissociation is $0.78 \times 100 = 78\% $

Therefore, the correct answer is (C).

Additional information:
Van’t Hoff Factor is related to the osmotic coefficient $g$ by the reaction $i = ng$

Note:
When Van’t Hoff factor is equivalent to one the solution is in equilibrium neither association nor dissociation has taken place, for example- glucose in water. When its value is more than one, it depicts the dissociation condition like sodium chloride in water and when it is less than one it suggests that the association has taken place like carboxylic acids like acetic acid forms dimers in benzene.