Consider the following statements:

(A) Rate of a process is directly proportional to its free energy change

(B) The order of an elementary reaction step can be determined by examining the stoichiometry

(C) The first-order reaction describes an exponential time course.

Of the statements:

B and C are correct

The correct answer is option 3. B and C are correct.

Statement A: Rate of a process is directly proportional to its free energy change

The rate of a reaction is primarily determined by its activation energy, not its free energy change. Activation energy (Ea) is the energy barrier that reactants must overcome to be transformed into products. The Arrhenius equation, \( k = A e^{-E_a/RT} \), shows that the rate constant \( k \) depends on Ea. Free energy change (ΔG) tells us whether a reaction is spontaneous (ΔG < 0) or non-spontaneous (ΔG > 0), but it does not directly dictate the reaction rate.

Statement B: The order of an elementary reaction step can be determined by examining the stoichiometry

For elementary reactions (reactions that occur in a single step), the reaction order with respect to each reactant is equal to its stoichiometric coefficient in the balanced equation. For example, in the reaction \( A + B → \text{products} \), if it is an elementary step, it is second order overall, first order with respect to A, and first order with respect to B. This is because the rate law for an elementary reaction is directly derived from its stoichiometric coefficients.

Statement C: The first-order reaction describes an exponential time course

For a first-order reaction, the concentration of the reactant decreases exponentially over time. The integrated rate law for a first-order reaction is:

\([A]_t = [A]_0 e^{-kt}\)

Here, \( [A]_t \) is the concentration at time \( t \), \( [A]_0 \) is the initial concentration, and \( k \) is the rate constant. This exponential decay reflects how the concentration decreases rapidly initially and then more slowly as the reaction progresses

Conclusion

Statement A is incorrect because the rate is not directly proportional to free energy change. Statements B and C are correct because they accurately describe how reaction order is related to stoichiometry and how the concentration changes over time for a first-order reaction.