question_answer 33)

The elements A and B form purely covalent compounds having molecular formulae AB2 and AB4. When dissolved in 20 g of benzene, 1 g of AB2 lowers the freezing point by 2.3 K, whereas 1g of AB4 lowers it by 1.3 K. The molal depression constant for benzene is 5.1 K kg mol–1, calculate the atomic mass of A and atomic mass of B.

Answer:

Step I. Calculation of the molecular masses of the two compounds For the compound AB2: = 110.87 g mol?1. For the compound ; W2 = 1 g ; w1 = 20 g = 0.02 kg ; Tf = 1.3 K; Kf = 5.1 K kg mol?1 = 196.15 g mol?I Step II.  Calculation of the atomic masses of elements A and B Let the atomic mass of element A = a Let the atomic mass of element B = b Molecular mass of AB2 = a + 2b Molecular mass of AB4 = a + 4b According to available information a + 2b = 110.87  ... (i) a + 4b = 196.15  ... (ii) Subtract equation (i) from (ii), we get 2b = (196.15 ? 110.87) = 85.28 or b = 85.28/2= 42.64 Substituting the value of ?b? in equation a + 2 (42.64) = 110.87 or a = 110.87 ? 85.28 = 25.59 Thus, Atomic mass of element A = 25.59               Atomic mass of element B = 42.64