Question

Van’t Hoff factor is:
(a) More than one in case of association
(b) Less than one in case of dissociation
(c) \[\dfrac{{normal\,molecular\,mass}}{{observed\,molecular\,mass}}\]
(d) \[\dfrac{{observed\,molecular\,mass}}{{normal\,molecular\,mass}}\]

Answer 1

Hint: If we assume that we could simply multiply the molar concentration of a solute by the number of ions per formula unit to obtain the actual concentration of dissolved particles in a solution, it would mean that same concentration of different solution will have same elevation in boiling point but we see that this is not the case. Here the concept of Van’t Hoff factor comes into play.

Complete step by step solution:
The relationship between the actual number of moles of solute added to form a solution and the apparent number as determined by colligative properties is called the Van’t Hoff factor.
This can be better understood with the help of the following equation:
\[i = \dfrac{{apparent\,no.\,of\,particles\,in\,solution}}{{no.\,of\,moles\,of\,solute\,dissolved}}\]
Thus, the Van't Hoff factor is actually the measure of deviation from ideal behavior. It offers insight on the effect of solutes on the colligative properties of solutions.
We can also define Van’t Hoff factor as the ratio of normal molecular mass to observed molecular mass.
In case of association, we see that the observed molecular mass is more than the normal, the factor i has a value less than 1. But in case of dissociation, the Van’t Hoff’s factor is more than 1 because the observed molecular mass has a lesser value than the normal molecular mass. Hence, both the options A and B provided here are incorrect.
We can hereby conclude that the correct answer is Option (C) \[\dfrac{{normal\,molecular\,mass}}{{observed\,molecular\,mass}}\]

Additional information:
When a nonelectrolyte is dissolved in water, no dissociation takes place and the Van’t Hoff factor is 1.

Note: We should keep in mind that the Van't Hoff factor is essential for calculating and comparing colligative properties of solutions like osmotic pressure, relative lowering of vapor pressure, elevation in boiling point and depression in freezing point.
It is also important to calculate the degree of association and dissociation before proceeding to calculate the Van’t Hoff factor.