The standard free energy of activation of a reaction A is 78.2 kJ mol–1 (18.7 kcal mol–1) at 298 K. Reaction B is ten million times faster than reaction A at the same temperature. The products of each reaction are 10.0 kJ mol–1 (2.39 kcal mol–1) more stable than the reactants.

Is there a question here? I don't see one.

The questions are as follows: What is the standard free energy activation of B? What is the standard free energy activation of the reverse of reaction A? What is the standard free energy activation of the reverse of reaction B?To think two years later same exact problem, no answer. I have absolutely no idea how to calculate these things.

To understand the concept of activation energy and how it relates to reaction rates, let's break down the given information and equations.

1. The standard free energy of activation of reaction A is 78.2 kJ mol–1 (18.7 kcal mol–1) at 298 K.
This indicates that for reaction A to occur, the reactants need to overcome an energy barrier of 78.2 kJ mol–1. Activation energy is the minimum amount of energy required to initiate a chemical reaction. It determines the speed or rate at which a reaction takes place.

2. Reaction B is ten million times faster than reaction A at the same temperature.
This statement implies that reaction B has a lower activation energy compared to reaction A. A lower activation energy allows reactant molecules to overcome the energy barrier more easily, resulting in a faster reaction rate.

3. The products of each reaction are 10.0 kJ mol–1 (2.39 kcal mol–1) more stable than the reactants.
This information suggests that the products have a lower energy content than the reactants. A negative value for the energy change indicates an exothermic reaction, where energy is released as heat during the formation of products.

In summary, reaction B is faster than reaction A because it has a lower activation energy. Additionally, both reactions result in more stable products compared to the reactants.

To calculate the actual rate constant or reaction rate for each reaction, we need quantitative information such as the rate equation or rate constant value. Since that information is not provided, we cannot determine the exact rate of the reactions.