Problem 70 - A Complete Resource Book in Chemistry for JEE Main

Question

Consider the following statements: (1) rate of a process is directly proportional to its free energy change (2) the order of an elementary reaction step can be determined by examining the stoichiometry (3) the first-order reaction describe exponential time course. Of the statements (a) 1 and 2 are correct (b) 1 and 3 are correct (c) 2 and 3 are correct (d) 1,2 and 3 are correct

Step-by-Step Solution

Answer

(c) 2 and 3 are correct.

Step 1: Analyze Statement (1)

Statement 1 claims that the rate of a process is directly proportional to its free energy change. In chemical kinetics and thermodynamics, the rate of a reaction is actually independent of the free energy change. The rate is more directly affected by activation energy, catalysts, and concentration of reactants, not directly by free energy change. Thus, statement (1) is incorrect.

Step 2: Analyze Statement (2)

Statement 2 claims that the order of an elementary reaction step can be determined by examining the stoichiometry. In elementary reactions, the reaction order is equal to the stoichiometric coefficients of the reactants in the balanced equation, so this statement is correct.

Step 3: Analyze Statement (3)

Statement 3 claims that a first-order reaction describes an exponential time course. This is true, as the rate of a first-order reaction can be expressed as \( \frac{d[A]}{dt} = -k[A] \), which integrates to \( [A] = [A]_0 e^{-kt} \), showing an exponential decrease over time. So, statement (3) is correct.

Step 4: Conclusion

After analyzing each statement: (1) is incorrect, (2) is correct, and (3) is correct. Thus, the correct option that matches our finding is option (c) 2 and 3 are correct.

Key Concepts

Reaction Rate

In chemical kinetics, the **reaction rate** refers to how fast or slow a reaction occurs. It is crucial to understand that reaction rates are primarily influenced by factors such as reactant concentration, temperature, and catalysts, rather than by the free energy change, which often confuses students.

Some key influences on reaction rates include:

• **Concentration of Reactants:** A higher concentration usually increases the reaction rate because there are more particles available to collide.
• **Temperature:** Increasing temperature generally speeds up a reaction. Higher temperatures provide molecules with more energy to surpass the activation energy barrier.
• **Catalysts:** These substances can significantly increase reaction rates by providing an alternative pathway with a lower activation energy.

Understanding these factors and their effects on reaction rate is vital for predicting and controlling how fast a reaction proceeds.

Elementary Reaction

An **elementary reaction** is a single-step process where reactants convert directly to products. This type of reaction is straightforward because it typically displays a 1-to-1 correspondence between reactant molecules colliding and forming products.

In an elementary reaction, the reaction order is determined by examining the stoichiometry of the balanced equation. This means that the coefficients in the chemical equation tell us how many molecules participate in the process and that is usually how we classify the order of reactions.

For instance, if an elementary reaction is written as \( A + B \rightarrow C \), then it's considered first order with respect to each reactant \( A \) and \( B \), and second order overall because the sum of the stoichiometric coefficients (1 for \( A \) and 1 for \( B \)) adds up to 2. Elementary reactions are unique in that they represent the simplest reactive units and give insights into the step-by-step mechanism of complex reactions.

First-order Reaction

A **first-order reaction** is an important concept in chemical kinetics where the rate of reaction depends on the concentration of a single reactant. This is often represented with a rate law of the form: \[\frac{d[A]}{dt} = -k[A]\]where \([A]\) is the concentration of the reactant, \(\frac{d[A]}{dt}\) is the rate of change of concentration with time, and \(k\) is the rate constant.

The integrated form of this rate law is: \[[A] = [A]_0 e^{-kt}\]This equation shows that the concentration of reactant \([A]\) decreases exponentially over time, confirming the exponential time-course trajectory.

First-order reactions are especially common in radioactive decay and some simple chemical decompositions. Understanding their characteristics helps in determining half-lives and predicting the behavior of reactions over time.