3.9 g of benzoic acid dissolved in 49 g of benzene shows a depression in freezing point of 1.62 K. Calculate the van't Hoff factor and predict the nature of solute (associated for dissociated). ("Given : Molar mass of benzoic acid = 122 g mol"^(-1),K_(f)" for benzene = 4.9 K kg mol"^(-1))

3.9 g of benzoic acid dissolved in 49 g of benzene shows a depression

1.	3.9 g of benzoic acid dissolved in 49 g of benzene shows a depression in freezing point of 1.62 K. Calculate the van't Hoff factor and predict the nature of solute (associated for dissociated). ("Given : Molar mass of benzoic acid = 122 g mol"^(-1),K_(f)" for benzene = 4.9 K kg mol"^(-1))
Answer» Solution :`DeltaT_(f)"(calculated)"=(1000K_(f)w_(2))/(w_(1)M_(2))=("1000 g kg"^(-1)xx"4.9 K kg mol"^(-1)xx3.9 g)/(49g xx"122 g mol"^(-1))=3.197K` `""("Mol. mass of BENZOIC acid "C_(6)H_(5)COOH="122 g mol"^(-1))` `i=(Delta_(f)"(observed)")/(DeltaT_(f)"(calculated)")=(1.62)/(3.197)=0.506` Alternatively, MOLALITY `(m)=(3.9)/(122)xx(1)/(49)xx1000=0.652, DeltaT_(f)=iK_(f)m` `"or"i=(DeltaT_(f))/(K_(f)m)=(1.62)/(4.9xx0.652)=0.507.` As i lt 1, solute is associated.