Problem 164 - A Complete Resource Book in Chemistry for JEE Main

Question

Consider the following statements (a) The rate of a process is always proportional to its free energy change. (b) The molecularity of an elementary chemical reaction step can be determined by examining its stoichiometry. (c) The first order reactions follow an exponential time course. (d) Energy of activation is inversely proportional to temperature. The correct statement (s) is/are (a) \(1,2,3\) (b) \(1,2,3,4\) (c) 2 and 3 (d) 1 and 3

Step-by-Step Solution

Answer

The correct answer is (c) 2 and 3.

Step 1: Analyze Statement (a)

Statement (a) states that the rate of a process is always proportional to its free energy change. This is incorrect because the rate of a reaction is actually determined by activation energy, not free energy change. Free energy change determines spontaneity, not the rate.

Step 2: Analyze Statement (b)

Statement (b) claims that the molecularity of an elementary chemical reaction step can be determined by examining its stoichiometry. This is generally correct; the stoichiometry of a single-step reaction often reflects its molecularity.

Step 3: Analyze Statement (c)

Statement (c) says that first order reactions follow an exponential time course. This is true, as the concentration of reactants in a first order reaction decreases exponentially over time, as described by the first order rate law equation \( [A] = [A_0] e^{-kt} \).

Step 4: Analyze Statement (d)

Statement (d) claims that the energy of activation is inversely proportional to temperature. This is incorrect; instead, higher temperatures can overcome activation energy more easily, but activation energy itself is not inversely proportional to temperature.

Step 5: Determine Correct Statements

After analyzing each statement, we find statements (b) and (c) to be correct. Thus, the correct option is the one containing statements 2 and 3.

Key Concepts

Rate of Reaction

The rate of reaction refers to the speed at which reactants are converted into products in a chemical reaction. It is a crucial concept in chemical kinetics, as it helps us understand how quickly a reaction proceeds. The rate of reaction can be influenced by various factors, such as:

• Concentration of reactants
• Temperature
• Presence of a catalyst
• Surface area of reactants

Contrary to the misconception that the rate of reaction is proportional to free energy change, it is actually governed by activation energy and collision theory. Activation energy is the minimum energy required for a reaction to occur, while collision theory suggests that particles must collide with sufficient energy and proper orientation for a reaction to take place.
Reaction rates are usually quantified by observing the change in concentration of a reactant or product over time and using that to infer the speed of the reaction.

Molecularity

Molecularity of a reaction is the number of reactant molecules that come together to react in an elementary step of a reaction mechanism. Molecularity can be:

• Unimolecular: Involving one molecule, typically undergoing a change by itself.
• Bimolecular: Involving two molecules colliding and reacting with each other.
• Termolecular: Involving three molecules coming together in the same reaction step, though this is rare due to the low probability of three molecules colliding simultaneously.

Molecularity is determined by the stoichiometry of an elementary reaction step. For instance, if a reaction step involves "A + B → C", the molecularity is two, indicating a bimolecular reaction. Unlike reaction order, which is determined experimentally, molecularity is always a whole number derived directly from the reaction step's stoichiometry.

First Order Reactions

First order reactions are a category of chemical reactions where the rate depends linearly on the concentration of only one reactant. The rate equation for a first order reaction is expressed as:\[ Rate = k[A] \]where \( k \) is the rate constant and \([A]\) is the concentration of the reactant. The characteristic feature of first order reactions is that they follow an exponential decay of reactant concentration over time. This behavior is described by the first order rate law:\[ [A] = [A_0] e^{-kt} \]where \([A_0]\) is the initial concentration of the reactant, \( t \) is time, and \( k \) is the first order rate constant.
First order reactions are common in processes such as radioactive decay and many biological and chemical processes where a single reactant influences the rate.

Activation Energy

Activation energy is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that must be overcome for reactants to be transformed into products. This concept is critical in determining the rate of a reaction. A higher activation energy means that fewer molecules have the necessary energy to react at a given temperature, resulting in a slower reaction rate. Conversely, a lower activation energy leads to a faster reaction.
While temperature does not change the activation energy of a reaction, it influences the fraction of molecules that can overcome this energy barrier. As temperature increases, more molecules have sufficient kinetic energy to surpass the activation energy, typically leading to an increase in the reaction rate. This relationship is quantitatively described by the Arrhenius equation:\[ k = A e^{-E_a/(RT)} \] where \( k \) is the rate constant, \( A \) is the frequency factor, \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.