An endothermic reaction A------B has an activation energy of 15kcal/mol and the energy of the reaction is 5kcal/mol.what is the activation energy of the reaction B------ A?

Activation energy is the amount of energy require to reach the transition state from reactant. Let the transition state is at C, then energy difference between A to C (C-A) is 15 Kcal/mol.
Energy of reaction = energy gap between A to B. Since the reaction is endothermic ,product have higher energy than reactant. the energy gap B-A = 5 Kcal/mol.

Now in reverse reaction B have to achieve the transition state C (= activation energy of reverse reaction). So the energy barrier between B to C can be calculated using following relations:
B-A =5 Kcal/mol
C-A = 15 Kcal/mol
​So C-B = (C-A)-(B-A) = 15 - 5 = 10 Kcal/mol
 

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