Benzoic acid undergoes dimerization in benzene. x ~g of benzoic acid (molar mass 122 ~g ~mol ⁻¹ ) is dissolved in 49 g of benzene. The depression in freezing point is 1.12 K. If degree of association of acid is 88 % , what is the value of x ? ( ~K _ f . for benzene .=4.9 ~K ~kg ~mol ⁻¹ )

Step-by-step solution

Given, weight of benzoic acid = xg Molar mass of benzoic acid =122 ~g ~mol ⁻¹ Weight of benzene =49 ~g Molar mass of benzene =78 ~g ~mol ⁻¹ aligned & depression in freezing point ( T _ f )=1.12 k & degree of association ( )=88 % & =0.88 & aligned K _ F for benzene =4.9 ~K ~kg ~mol ⁻¹ aligned & For association, & Van't Hoff factor ( i )=1+ ( 1 n -1 ) & =1+ ( 1 2 -1 ) 0.88 & aligned T _ f = i K _ f m aligned & aligned 1.12=0.56 aligned aligned 1.12=0.56 4.9 x 1000 122 49 [ ~m = weight of solute 100 array l Molecular