If the bond dissociation energies of $XY, X_2 and Y_2$ (all diatomic molecules) are in the ratio of 1 : 1 : 0.5 and OH for the formation of XY is $ – 200 KJ mol^{–1} $ . The bond dissociation energy of $ X_2$ will be
$ Let the bond dissociation energy of XY, X_2 and Y_2 be x,x and x, KJ/mol respectively,$ $ { 1 \over 2 } X_2 + { 1 \over 2 } Y_2 \rightarrow XY ; \triangle Hf = -200 KJ mol ^ { -1} $ $ \triangle Hreaction = [(sum of bond dissociation energy of all reactants) – (sum of bond dissociation energy ofproduct)] $ $ = \left [ { { 1 \over 2 } \triangle H_ {x2} + { 1 \over 2} \triangle H_ {y2} - \triangle H_ {xy} } \right] = { x \over 2 } + { 0.5 x \over 2 } - x = - 200 $ $ \therefore x = 800 KJ mol ^ { -1} $ Second Method $ XY \rightarrow X_{(g) } + Y \triangle H _{(g)} = a + kJ / mole ; ...(i) $ $ X_2 \rightarrow 2 X \triangle H = a+kJ / mole ......(ii) $ $ Y_2 \rightarrow 2 Y \triangle H = 0.5 a kJ / mole ; ......(iii) $ $ { 1 \over 2} \times (ii) + {1 \over 2} \times (iii) - (i) , gives { 1 \over 2} X_2 + { 1 \over 2 } Y_2 \rightarrow XY ; $