2.21    Two elements A and B form compounds having formula AB2 and AB4 . When dissolved in 20 g of benzene (C_{6}H_{6}), 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.

Answers (1)

In this question we will use the formula :

                                                              \Delta T_f = k_f \times m

Firstly for compound AB2  :-  

                                                M_B = \frac{K_f\times W_b \times 1000}{w_A\times \Delta T_f}

or                                                       = \frac{5.1\times 1 \times 1000}{20\times 2.3} = 110.87\ g/mol

Similarly for compound AB4 :- 

                                                 M_B= \frac{5.1\times 1 \times 1000}{20\times 1.3} = 196\ g/mol

If we assume atomic weight of element A to be x and of element B to be y, then we have :- 

                                         x + 2y = 110.87                               -----------------   (i)

                                         x + 4y = 196                                    -----------------   (ii)

Solving both the equations, we get :- 

          x  =  25.59  ;    y =  42.6

Hence atomic mass of element A is 25.59u and atomic mass of element B is 42.6u.

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