Final answer:
Reaction B is faster than reaction A because it has a lower standard free energy of activation, implying it requires less energy to reach the transition state. An exact factor of the rate difference cannot be determined without additional information.
Step-by-step explanation:
The question asks by what factor one reaction is faster than the other given two different standard free energies of activation, assuming a temperature of 298 K and 1 M concentration. The standard free energy of activation for reaction A is 87.40 KJ mol-1, and for reaction B, it is 78.60 KJ mol-1. Using the Arrhenius equation, which is not provided but known in chemistry, we can see that a lower standard free energy of activation corresponds to a faster rate of reaction because less energy is required to reach the transition state. Hence, reaction B is faster because it has a lower energy barrier.
To estimate the factor by which one reaction is faster than the other, we would typically use the Arrhenius equation: k = A e(-Ea/RT). However, sufficient information to calculate the rate constants (k) directly was not provided in the question, so an exact numerical factor cannot be determined without additional data. Yet qualitatively, we can be sure that reaction B would occur at a faster rate than reaction A.