in a solvent 50% of benzoic acid dimerises while the rest ionises. determine molar mass of acid which is observed and also its van't hoff factor.

Your friend is correct.
Formula to calculate i ( Van't haff factor) using α (degree of ionizaion) is as follows:
i = (​1-α) + αn
Here, 
α = 50/100 = 0.5
n ​= 2 (dimerisation)
i = (1.0-0.5) + 0.5/2
 = 0.75

i = Observed molar massActual Molar mass

0.75 = Observed molar mass122 g/mol

Observed Molar mass = 0.75 x 122 g/mol
                                  = 91.5 g/mol

 

  • -35

alpha = 50/100 = 0.5 put in formula i = 1 - 0.5 + 0.5/2 here 2 is the dimerization or dissociation as its dissociated to 2 ions so i = 0.5 + 0.25 = 0.75 now for mass put in the equation i = observed mass/normal mass = 0.75 = x/122 = x = 91.5 so mass is 91.5 grams observed

  • -20
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