Final answer:
The van't Hoff factor (i) for benzoic acid in benzene, when considering dimerization, can be understood as i = (1 + x/2), where x is the degree of association. This factor accounts for the fact that dimerization reduces the number of particles in solution from what would be expected from the stoichiometry of benzoic acid alone.
Step-by-step explanation:
The relationship between the van't Hoff factor (i) and the degree of association (a) during the dimerization of benzoic acid in benzene solution can be understood through the concept of particles in solution. The van't Hoff factor is used to represent the ratio of the actual number of particles in solution to the number expected based on the substance's chemical formula, reflecting deviations from ideal behavior due to molecular associations or dissociations.
For benzoic acid, which dimerizes in benzene, the expected ratio of benzoic acid formula units to particles in solution would be 1:1 if there were no association. However, dimerization leads to fewer particles than formula units. Assuming x represents the degree of association of benzoic acid (where x is the fraction of molecules that are dimerized), the van't Hoff factor is calculated as i = (1 + x/2). This equation reflects that for every two benzoic acid molecules that dimerize, there is one less particle in solution.