Question

The Van’t Hoff factor for Sulphur solution is?
A) $i = 1$
B) $i = 1/6$
C) $i = 1/2$
D) $i = 1/8$

Answer 1

Van’t Hoff Factor is a measure of the effect of solute on various colligative properties like relative lowering of vapour pressure, depression in freezing point, elevation in boiling point, osmotic pressure. Colligative properties are directly proportional to the quantity of solute in the solution. The Van't Hoff factor is generally the ratio between actual concentration of particles when it is dissolved in the solvent to the concentration of substance from its molar mass. The Van’t Hoff factor is denoted by ‘I’.

Complete Step By Step Answer:
The Van’t Hoff factor is used to measure the change in the colligative properties of the solution. The different formulas for Van’t Hoff Factor are:
$i = \dfrac{{Observed{\text{ }}colligative{\text{ }}property}}{{Theoretical{\text{ }}Colligative{\text{ }}Property}}$
$i = \dfrac{{Normal{\text{ }}Molar{\text{ }}Mass}}{{Observed{\text{ }}Molar{\text{ }}Mass}}$
$i = \dfrac{{Actua\operatorname{l} {\text{ }}number{\text{ }}of{\text{ }}particles}}{{Expected{\text{ }}number{\text{ }}of{\text{ }}particles}}$
The Van’t Hoff Factor ‘I’ is basically the number of particles formed after splitting or forming of the solute. It is the ratio of the actual concentration of the substance to the calculated concentration of the substance.
Here we are given sulphur. Initially we have 8 atoms of sulphur which are associated to form a single molecule of Sulphur with chemical formula ${S_8}$ . The reaction of the association of particles to form a molecule can be given as:
$8S \rightleftharpoons {S_8}$

T=0	1	0
T=equilibrium	0	1/8

Initially we have 1 mole of sulphur atom and zero moles of ${S_8}$ Molecule. At equilibrium we have 1/8 moles of ${S_8}$ molecule.
To find the Van't Hoff Factor we can use the formula: $i = \dfrac{{tota\operatorname{l} {\text{ }}no.of{\text{ }}moles{\text{ }}at{\text{ }}equilibrium}}{{initial{\text{ }}moles}}$
Substituting the values we get; $i = \dfrac{{0 + 1/8}}{{1 + 0}} = \dfrac{1}{8}$
Hence the Van’t Hoff Factor for Sulphur Solution is $1/8$ .
The correct option is Option (D).

Note:
The Van’t Hoff Factor for dissociation can be also given by the formula $i = 1 + \alpha (n - 1)$ where I is the van't Hoff factor, $\alpha$ is the dissociation constant and n is the no. of moles formed after dissociation. Similarly, for association the Van’t Hoff Factor can be found out by the formula:
$i = 1 - \left( {1 - \dfrac{1}{n}} \right)\alpha$ where $\alpha$ , I and n have the same meanings.