Question

The substance A, when dissolved in solvent B, shows the molecular mass corresponding to \[{A_3}\] . The Van’t Hoff factor will be:
A.1
B.2
C.3
D.$\dfrac{1}{3}$

Answer 1

Hint: Van’t Hoff factor is a correction factor which is used to account for this increase in the number of solute particles dissociated. The Van’t Hoff factor for a given solution is equal to the number of particles the given solute dissociates into.

Complete Step-by-Step Answer:
Before we move forward with the solution of the given question, let us first discuss some important basic concepts.
When covalent compounds are dissolved in a solvent, a molecule of the covalent compound dissolves as a whole. But in the case of an ionic compound, once the compound is added to the solvent, it tends to dissociate into its constituent ions. This means that the number of ions dissociated depends on the number of ions that are present in the first place. What this does is, it increases the number of constituent particles in the solution. This in turn increases the concentration of the solution.
Now the formulae used for calculating these colligative properties do not account for this error. Another way to calculate the Van’t Hoff factor is:
 \[i = 1 - \alpha \] , where i is the Van’t Hoff factor and \[\alpha \] is the degree of dissociation.
Now, moving to the question, converting the given data in the form of a chemical equation, we get:
\[3A \to {A_3}\]

	[A]	\[[{A_3}]\]
\[t = 0\]	1	0
\[t = t\]	\[1 - \alpha \]	\[\alpha \]

Hence, the Van’t Hoff factor can be calculated as:
 \[i = 1 - [\dfrac{\alpha }{3} - \alpha ]\]
Since the solute is completely dissolved, then \[\alpha = 100\% = 1\]
 \[i = 1 - [\dfrac{1}{3} - 1] = \dfrac{1}{3}\]
Hence, Option D is the correct option

Note: Colligative properties can be described as the properties of the solution which depend only on the concentration of the solute particles. There are 4 basic colligative properties, viz. vapor pressure, boiling point, freezing point and osmotic pressure. The concentration of the solution remains constant if the solute used is a covalent compound. But in the situation where an ionic solute is used, things change a little.