Read the passage given below and answer based it.

The rate of a reaction is concerned with decrease in concentration of reactants or increase in concentration of products per unit time. It can be expressed as instantaneous rate at a particular instant of time and average rate over a large interval of time. A number of factors such as temperature, concentration of reactants, catalyst, affect the rate of a reaction. Mathematical representation of rate of a reaction is given by rate law. It has to be determined experimentally and cannot be predicted. Order of a reaction with respect to a reactant is the power of its concentration which appears in the rate law equation. Molecularity is defined only for an elementary reaction. Molecularity and order of an elementary reaction are same.

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.

Let us go through each statement in detail to understand their validity.

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

Free Energy Change (ΔG): The free energy change of a reaction tells us about the spontaneity of the process. A negative ΔG indicates a spontaneous process, whereas a positive ΔG indicates a non-spontaneous process. However, ΔG does not give information about how fast the reaction proceeds.

Reaction Rate: The rate of a reaction depends on the activation energy (Ea) and the temperature, among other factors. The relationship between the rate constant (k) and activation energy is described by the Arrhenius equation:

\( k = A e^{-\frac{E_a}{RT}} \)

Here, \( A \) is the pre-exponential factor, \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature.

Therefore, the rate of a reaction is more closely related to the activation energy than to the free energy change. The free energy change determines the equilibrium position of the reaction but not the rate at which equilibrium is achieved.

Conclusion: This statement is incorrect.

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

Elementary Reaction: An elementary reaction is a single-step process with no intermediates. The stoichiometry of an elementary reaction directly reflects the number of molecules or atoms involved in the transition state.

Reaction Order: For an elementary reaction, the order with respect to each reactant is equal to its stoichiometric coefficient in the balanced equation. For example, for the elementary reaction:

\( aA + bB \rightarrow \text{products} \)

The rate law is:

\(\text{Rate} = k[A]^a[B]^b \)

Here, \( a \) and \( b \) are the stoichiometric coefficients and also the orders with respect to \( A \) and \( B \), respectively.

Conclusion: This statement is correct.

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

First-Order Reaction: A first-order reaction is one where the rate depends linearly on the concentration of a single reactant.

\( \text{Rate} = k[A] \)

Exponential Decay: The integrated rate law for a first-order reaction shows how the concentration of the reactant decreases over time:

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

Here, \([A]_0\) is the initial concentration of the reactant, \( k \) is the rate constant, and \( t \) is time. This equation describes an exponential decrease in the concentration of \( A \) over time.

Conclusion: This statement is correct.

Summary:

Statement (A): Incorrect. The rate of a reaction is not directly proportional to the free energy change but to the activation energy.

Statement (B): Correct. The order of an elementary reaction can be determined by its stoichiometry.

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

Therefore, the correct conclusion is B and C are correct.