Two elements A and B form compounds having molecular formula AB_(2) and AB_(4). When dissolved in 20 g of benzene (C_(6)H_(6)), 1 g of AB_(2) lowers the freezing point by 2.4 K whereas 1.0 g of AB_(4) lowers it by 1.3 K. The molal depression constant of benzene is "5.1 K kg mol"^(-1). Calculate atomic masses of A and B.

Two elements A and B form compounds having molecular formula AB_(2) an

1.	Two elements A and B form compounds having molecular formula AB_(2) and AB_(4). When dissolved in 20 g of benzene (C_(6)H_(6)), 1 g of AB_(2) lowers the freezing point by 2.4 K whereas 1.0 g of AB_(4) lowers it by 1.3 K. The molal depression constant of benzene is "5.1 K kg mol"^(-1). Calculate atomic masses of A and B.
Answer» Solution :Applying the formula, `M_(2)=(1000K_(F)w_(2))/(w_(1)xxDeltaT_(f))` `M_(AB_(2))=(1000xx5.1xx1)/(20xx2.3)"110.87 g mol"^(1),M_(AB_(4))= (1000xx5.1xx1)/(20xx1.3)= "196.15 g mol"^(-1)` Suppose atomic masses of A and B are 'a' and 'b' RESPECTIVELY. Then Molar mass of `AB_(2)=a+2b=110.87" g mol"^(-1)"...(i)"` Molar mass of `AB_(4)=a+4b="196.15 g mol"^(-1)"...(ii)"` EQN. (ii) - Eqn. (i) gives 2 b = 85.28 or b = 42.64 SUBSTITUTING in eqn. (i), we GET `a+2xx42.64=110.87 or a=25.59` Thus, Atomic mass of A = 25.59 u, `""` Atomic mass of B = 42.64 u