A certain endothermic reaction: Ato Product, DeltaH=+ve proceeds ina sequence of three elementary steps with the rate constant K_(1),K_(2) and K_(3) and each one having energy of activation E_(1),E_(2) and E_(3) respectively at 25^(@)C. The observed rate constannt for the reaction is equal to K_(3)sqrt((K_(1))/(K_(2))). A_(1),A_(2) and A_(3) are Arrhenius parameters respectively. Presence of a catalyst decreasesthe energy of activation of each path by half the value of E_(1). Assuming the other factors same, the observed energy of activation would be

A certain endothermic reaction: Ato Product, DeltaH=+ve proceeds ina s

1.	A certain endothermic reaction: Ato Product, DeltaH=+ve proceeds ina sequence of three elementary steps with the rate constant K_(1),K_(2) and K_(3) and each one having energy of activation E_(1),E_(2) and E_(3) respectively at 25^(@)C. The observed rate constannt for the reaction is equal to K_(3)sqrt((K_(1))/(K_(2))). A_(1),A_(2) and A_(3) are Arrhenius parameters respectively. Presence of a catalyst decreasesthe energy of activation of each path by half the value of E_(1). Assuming the other factors same, the observed energy of activation would be
Answer» `E_(3)-(E_(2))/2` `2E_(3)-E_(2)` `E_(2)-(E_(3))/2` `(E_(1))/2+(E_(2))/2+E_(3)` Solution :`E^(1)=[(2(epsilon_(3)-(epsilon_(1))/2)+(epsilon_(1)-(epsilon_(1))/2)-(epsilon_(2)-(epsilon_(1))/2))/2]=(2((2epsilon_(3)-epsilon_(1))/2)+((2epsilon_(1)-epsilon_(1))/1)-((2epsilon_(2)-epsilon_(1))/2))/2` `=(4epsilon_(3)-2epsilon_(1)+epsilon_(1)-2epsilon_(2)+epsilon_(1))/(2xx2),EPSILON^(1)=((4epsilon_(3)-2epsilon_(2)))/4,epsilon^(1)=(epsilon_(3)-(epsilon_(2))/2)`