Problem 132 - A Complete Resource Book in Chemistry for JEE Main

Question

For the reaction, \(\mathrm{C}_{2} \mathrm{H}_{4}+\mathrm{H}_{2} \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}, \Delta \mathrm{E}^{0}=-30\) kcal. If the reaction is reversible and if the activation energy for the forward reaction is \(28.0 \mathrm{kcal}\) and its drops to \(10.5 \mathrm{kcal}\) in the presence of a catalyst, the activation energies for the uncatalyzed and catalysed reverse reaction are respectively (in kcal) (a) \(58,40.5\) (b) \(-58,-40.5\) (c) \(40.5,58\) (d) \(58.0,-58.0\)

Step-by-Step Solution

Answer

The correct answer is (a) \(58, 40.5\).

Step 1: Understanding Given Data

We are given that the forward reaction \[\mathrm{C}_{2} \mathrm{H}_{4} + \mathrm{H}_{2} \rightarrow \mathrm{C}_{2} \mathrm{H}_{6}\] has an energy change \(\Delta E^{0} = -30\) kcal. The activation energy for the forward uncatalyzed reaction is \(28.0\) kcal. With a catalyst, it decreases to \(10.5\) kcal.

Step 2: Calculate Activation Energy for Reverse Reaction

For any reaction, if \(E_a\) is the activation energy for the forward reaction and \(\Delta E^{0}\) is the change in energy, the activation energy for the reverse reaction \(E_{a, reverse}\) is given by:\[E_{a, reverse} = E_a + \Delta E^{0}\]Substitute the values for the uncatalyzed forward reaction: \[E_{a, reverse} = 28.0 + 30 = 58.0\] kcal.

Step 3: Calculate Activation Energy for Catalyzed Reverse Reaction

For the catalyzed reverse reaction, use the same process with the catalyzed forward activation energy:\[E_{a, reverse, catalyzed} = 10.5 + 30 = 40.5\] kcal. This finds the activation energy for the reverse reaction in the presence of the catalyst.

Step 4: Verify Against Options

Compare the calculated activation energies \(58.0\) kcal (uncatalyzed) and \(40.5\) kcal (catalyzed) with the given options:(a) \(58, 40.5\) (b) \(-58, -40.5\)(c) \(40.5, 58\)(d) \(58.0, -58.0\).The correct choice is (a) \(58, 40.5\).

Key Concepts

Understanding Catalysis

In the world of chemistry, catalysis plays a vital role in facilitating reactions. A catalyst is a substance that increases the rate of a chemical reaction without undergoing permanent changes itself. Its primary effect is on the activation energy: the minimum energy required for a reaction to commence.
Catalysts lower this energy barrier, making it easier for reactants to transform into products.
Consequently, reactions can proceed more rapidly or at lower temperatures.

• Catalysts do not alter the overall energy change (9E) of the reaction; they only affect the speed.
• Both forward and reverse reactions can be enhanced by a catalyst.

In the given problem, with a catalyst, the activation energy for the forward reaction drops from 28.0 kcal to 10.5 kcal. This demonstrates how a catalyst can make the path for the reaction easier, contributing greatly to industrial applications, where energy efficiency is crucial.

Exploring Energy Change

Energy change (9E) is a key concept in thermodynamics and chemistry. It refers to the difference in energy between the reactants and products in a chemical reaction.
In exothermic reactions, like the one in the given exercise, 9E is negative, indicating that the reaction releases energy into the surroundings.
This energy release makes the products more stable than the reactants.

• An exothermic reaction has a 9E less than zero.
• Endothermic reactions, in contrast, absorb energy, with a positive 9E.

Understanding this parameter helps chemists predict reaction behavior and energy dynamics. In calculating activation energies for reactions, 9E provides vital insights. As shown in the exercise, by knowing the 9E of -30 kcal, we can find the activation energy for the reverse reaction.

Insight into Reaction Kinetics

Reaction kinetics explores the rates at which chemical reactions occur and the factors influencing these rates. Several factors, such as temperature, concentration, and catalysts, play significant roles.
Activation energy is central to understanding reaction rates.
It represents the barrier that needs to be overcome for reactants to convert into products.

• Lower activation energies generally mean faster reactions.
• Parameters like temperature can also significantly affect reaction time and speed.

In our problem, the uncatalyzed reaction has an activation energy of 28.0 kcal, while the catalyzed reaction drops significantly to 10.5 kcal, underscoring how catalysts impact reaction kinetics. Consequently, detectors of reaction conditions and kinetics are vital in fields ranging from pharmacology to materials science, allowing for the efficient and safe development of new substances.