Two elements A and B form compounds having formula AB2 and AB4. When dissolved in 20 g of benzene (C6H6), 1 g of AB2 lowers the freezing point by 2.3 K whereas 1.0 g of AB4 lowers it by 1.3 K. The molar depression constant for benzene is 5.1 K kg mol–1. Calculate atomic masses of A and B.

Two elements A and B form compounds having formula AB2 and AB4. When dissolved in 20 g of benzene (C6H6), 1 g of AB2 lowers the freezing point by 2.3 K whereas 1.0 g of AB4 lowers it by 1.3 K. The molar depression constant for benzene is 5.1 K kg mol–1. Calculate atomic masses of A and B.

Solution:

Weight of component AB2 = 1 g

Weight of benzene = 20 g

Molar despression costant, Kf = 5.1 K

Delta Tf = 2.3 K

Use formula of Molar mass 

Mass of M_AB2 =Atomic weight of A + 2 × Atomic weight of B

        A + 2B = 110.87     ...(1)

Similarly,   

Mass of M_AB4 = =Atomic weight of A + 4 × Atomic weight of B

        A + 4B = 196.15     ...(2)

Subtracting equation (2) from (1), we get

2B = 196.15 - 110.87 = 85.28

Divide by 2

B = 42.64

Atomic mass of element B = 42.64 g atom^-1.

Plug the value in equation (1) we get

A + 2B  = 110.87 

A= (110.87 - 2 × 42.64)

  = 25.59 g atom^-1.

Atomic mass of element a = 25.59 g atom^-1