Question

A 2 molal solution of sodium chloride in water causes an elevation in the boiling point of water by 1.88K. What is the value of Van't Hoff factor? What does it signify?
$\text{ }\!\![\!\!\text{ }{{\text{K}}_{b}}\text{ = 0}\text{.52K kg mo}{{\text{l}}^{-1}}]$

Answer 1

Hint: Elevation in boiling point is a colligative property. The formula to calculate elevation is multiplied by a term called the Van't Hoff factor keeping in mind the increase in the number of particles after dissociation of an ionic compound.

Complete step by step solution:
Colligative properties are the properties of solutions that depend on the ratio of the number of solute particles to the number of solvent molecules in a solution, and not on the nature of the chemical species present.
The number ratio can be related to the various units for the concentration of a solution, for example, molarity, molality, normality etc.

The colligative properties are:
Relative lowering of vapour pressure
Elevation of boiling point
Depression of freezing point
Osmotic pressure

The boiling point of a liquid at a given external pressure is the temperature (\[{{T}_{b}}\]) at which the vapour pressure of the liquid equals the external pressure. The normal boiling point is the boiling point at a pressure equal to 1 atm.
The boiling point of a pure solvent is increased when a non-volatile solute to the solvent and the elevation can be measured by ebullioscopy. It is found that
$\Delta {{T}_{b}}\text{ = }{{\text{T}}_{b}}(solution)-{{T}_{b}}(solvent)\text{ = i }\text{. }{{\text{K}}_{b}}\text{. m}$
Here i is the van 't Hoff factor as above, ${{K}_{b}}$ is the ebullioscopic constant of the solvent (0.512 K kg $\text{mo}{{\text{l}}^{-1}}$ for water), and m is the molality of the solution.
We will now substitute the values in the equation given below to find the Van't Hoff factor for sodium chloride.
$1.88\text{ = i }\text{. (0}\text{.52) }\text{. 2}$
$\text{i = 1}\text{.8}$

Hence the Van't Hoff factor for the solution is 1.8.

Note: Van't Hoff factor is the ratio between the actual concentration of particles produced when the substance is dissolved and the concentration of a substance as per its mass. The value of the Van't Hoff factor is greater than 1 for dissociation of ionic compounds. In the above question we discussed the value of Van't Hoff factor for dissociation of non-volatile solute. However, some solutes can undergo association when added to a solvent. For e.g. Benzoic acid undergoes association when added to the solvent benzene. For association, the value of the Van't Hoff factor is less than 1.