Final answer:
The increase in boiling point of a solution is calculated with the formula 
 where 
 is the boiling point elevation i is the van't Hoff factor, Kb is the boiling point elevation constant, and m is the molality.
Step-by-step explanation:
The increase in boiling point temperature of a solution compared to the pure solvent can be derived using the boiling point elevation expression which includes the van't Hoff factor (i). The boiling point elevation 
 is given by the formula 
 where 
 is the increase in boiling point Kb is the boiling point elevation constant and m is the molality of the solution. 
The van't Hoff factor, i represents the number of particles a solute forms in solution and is crucial for calculating the correct boiling point elevation, particularly for ionic compounds that dissociate into multiple particles.