an endothermic reaction a to b has an activation energy of 15 kcal per mol and heat of reaction 5 kcal per mol the activation energy for the reaction b to a will be ?

10kcal: it absorbs 5kcal and gives off 15kcal

To determine the activation energy for the reverse reaction, we can use the concept of the Arrhenius equation. The Arrhenius equation relates the rate constant, activation energy, temperature, and pre-exponential factor of a chemical reaction:

k = A * exp(-Ea/RT)

Where:
- k is the rate constant
- A is the pre-exponential factor (or frequency factor)
- Ea is the activation energy
- R is the gas constant (8.314 J/(mol*K))
- T is the temperature in Kelvin

In this case, we have an endothermic reaction A to B with an activation energy of 15 kcal/mol and a heat of reaction (enthalpy change) of 5 kcal/mol. Since the reaction is endothermic, the products (B) are higher in energy compared to the reactants (A), thus requiring an input of energy during the reaction.

Now, to find the activation energy for the reverse reaction (B to A), we need to take into account the enthalpy change. The enthalpy change for the reverse reaction will be the negative of the enthalpy change for the forward reaction, so it will be -5 kcal/mol. This means that the reverse reaction is exothermic.

Now, to find the activation energy for the reverse reaction, we need to consider that the activation energy represents the energy barrier that the reactants must overcome to reach the transition state. Since the reverse reaction has a lower energy barrier compared to the forward reaction (due to it being exothermic), the activation energy for the reverse reaction will be less than 15 kcal/mol.

Unfortunately, without more information about the specific reaction, it is difficult to provide an exact value for the activation energy of the reverse reaction. The activation energy can vary depending on the reaction mechanism, reactants, and specific conditions.