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 \(28.0\) kcal and its drops to \(10.5\) 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: Understand Reaction Energies

For the reaction, ΔE° = -30 kcal indicates the energy difference between the products and reactants. This means the reverse reaction's energy change will be +30 kcal.

Step 2: Determine Uncatalyzed Reverse Activation Energy

For the uncatalyzed forward reaction, Ea_forward = 28 kcal. The activation energy of the uncatalyzed reverse reaction Ea_reverse can be found using the relation: \[ E_{a, ext{reverse}} = E_{a, ext{forward}} + ext{ΔE}^0 = 28 + 30 = 58 \text{ kcal} \]

Step 3: Calculate Catalyzed Reverse Activation Energy

With the catalyst, the forward activation energy drops to 10.5 kcal. We similarly adjust the reverse activation energy: \[ E_{a, ext{reverse, catalyzed}} = E_{a, ext{forward, catalyzed}} + ext{ΔE}^0 = 10.5 + 30 = 40.5 \text{ kcal} \]

Step 4: Match with Given Options

The activation energies calculated for uncatalyzed and catalyzed reactions are 58 kcal and 40.5 kcal respectively, which corresponds to option (a).

Key Concepts

Activation Energy

Activation energy is an essential concept in chemical kinetics. It refers to the minimum energy required for a chemical reaction to occur. Think of it as the energy barrier that reactants must overcome to form products. Higher activation energy means a slower reaction rate, as fewer molecules possess enough energy to overcome the barrier.
This "energy hill" must be climbed by reactants before they can transform into products. In our exercise, the forward reaction has an activation energy of 28 kcal without a catalyst. This value signifies the energy needed for ethylene (\(\mathrm{C}_{2} \mathrm{H}_{4}\) ) and hydrogen (\(\mathrm{H}_{2}\) ) to combine into ethane (\(\mathrm{C}_{2} \mathrm{H}_{6}\) ).

• High activation energy: Slows the reaction.
• Low activation energy: Speeds up the reaction.

Understanding activation energy helps in manipulating reactions to control rates by changing conditions such as temperature or introducing a catalyst.

Catalysis

Catalysis is a fascinating process where a substance called a catalyst modifies the rate of a reaction without being consumed in the process. Catalysts work by providing an alternative reaction pathway with a lower activation energy.
For the forward reaction in our exercise, the catalyst reduces the activation energy from 28 kcal to 10.5 kcal, making the reaction proceed faster. The reduced energy barrier means that more molecules have the necessary energy to react at a given temperature.
Some key points include:

• Catalysts lower the activation energy, increasing reaction speed.
• They are not consumed, hence can be reused multiple times.
• They do not alter the \(\Delta E^0\) of a reaction, only the rate of reaching equilibrium.

Catalysts are widely used in industrial and biological processes, where reaction speed and efficiency are critical.

Reaction Mechanism

The reaction mechanism is the step-by-step sequence of elementary reactions by which overall chemical change occurs. It provides insight into the pathway taken by reactants as they transform into products.
Understanding the mechanism allows chemists to determine where energy barriers exist and how a catalyst can affect these barriers. For the reaction given, the mechanism without a catalyst involves the reactants overcoming a high energy barrier. With the catalyst, the pathway is altered to lower the barrier, enabling the reaction to speed up.
Some critical aspects of reaction mechanisms include:

• The sequence of steps, each with their own rate laws and activation energies.
• The role of intermediate species that may form and decay within the process.

In the exercise example, knowing the mechanism helps us calculate the reverse reaction's activation energies by considering the effect of energy changes and catalyst inclusion. Understanding mechanisms helps scientists and engineers to devise strategies for controlling reaction rates in various chemical processes.