Problem 175 - A Complete Resource Book in Chemistry for JEE Main

Question

In a hypothetical reaction \(\mathrm{X} \rightarrow \mathrm{Y}\), the activation energy for the forward and backward reaction is 15 and \(9 \mathrm{~kJ}\) \(\mathrm{mol}^{-1}\) respectively. The potential energy of \(\mathrm{X}\) is \(10 \mathrm{~kJ}\) \(\mathrm{mol}^{-1}\). Identify the correct statement(s). (a) The threshold energy of the reaction is \(25 \mathrm{~kJ}\). (b) The potential energy \(\mathrm{f} \mathrm{Y}\) is \(16 \mathrm{~kJ}\) (c) Heat of reaction is \(6 \mathrm{~kJ}\). (d) The reaction is endothermic.

Step-by-Step Solution

Answer

Statements (a) and (d) are correct.

Step 1: Calculate Threshold Energy

The threshold energy is the amount of energy required for the reaction to occur. For the forward reaction, it is the sum of the activation energy and the potential energy of the reactants. We calculate it as follows: \[ \text{Threshold Energy} = \text{Activation Energy} + \text{Potential Energy of } X \]\[ = 15\, \text{kJ/mol} + 10\, \text{kJ/mol} = 25\, \text{kJ/mol} \]Thus, statement (a) is correct.

Step 2: Calculate Potential Energy of Y

To find the potential energy of Y, we first calculate the change in potential energy using the backward activation energy.Since the activation energy of the backward reaction is given and it transitions from Y to X:\[ \text{Potential Energy of } Y = \text{Potential Energy of } X + \text{Activation Energy of backward reaction} \]\[ = 10\, \text{kJ/mol} + 9\, \text{kJ/mol} = 19\, \text{kJ/mol} \]Thus, statement (b) is incorrect as it states \(16 \, \text{kJ/mol}\).

Step 3: Determine Heat of Reaction

The heat of reaction (\(\Delta H\)) is the difference in potential energy between products and reactants. Using the potential energies calculated:\[ \Delta H = \text{Potential Energy of Y} - \text{Potential Energy of X} \]\[ = 19\, \text{kJ/mol} - 10\, \text{kJ/mol} = 9\, \text{kJ/mol} \]Therefore, statement (c) is incorrect as it states \(6 \, \text{kJ/mol}\).

Step 4: Determine if Reaction is Endothermic or Exothermic

A reaction is endothermic if the products have higher potential energy than the reactants, resulting in \(\Delta H > 0\). Here, the potential energy of Y is greater than X:\[ \Delta H = 9\, \text{kJ/mol} > 0 \]Therefore, the reaction is endothermic, confirming that statement (d) is correct.

Key Concepts

Activation Energy

Activation energy is a crucial concept in understanding chemical reactions. It refers to the minimum amount of energy required for reactants to convert into products in a chemical reaction.
Without sufficient activation energy, the reactants will not have the energy needed to overcome the energy barrier to start the reaction.

• In the hypothetical reaction from the exercise (\(\mathrm{X} \rightarrow \mathrm{Y}\)), the activation energy for the forward reaction is given as 15 kJ/mol.
• This means that 15 kJ/mol of energy is needed for substance X to change into Y.
• The backward reaction, which turns Y back into X, requires 9 kJ/mol of activation energy.

These values tell us about the energy landscape of the reaction and how easily or difficultly it can occur.

Potential Energy

The potential energy of a substance in a chemical reaction tells us about the inherent energy present within the molecules due to chemical bonds and interactions.
In our example, the potential energy of X is given as 10 kJ/mol.

• This value represents the stored energy within the chemical bonds of substance X.
• The potential energy of Y can be calculated by adding the backward activation energy (9 kJ/mol) to the potential energy of X.
• This calculation yields a potential energy of 19 kJ/mol for Y, indicating stored energy in the bonds and molecular structure of Y.

Understanding potential energy helps us comprehend how energy transitions in chemical processes.

Endothermic Reaction

An endothermic reaction is one that absorbs energy from its surroundings, typically in the form of heat. This occurs when the energy required to break the reactants' bonds is greater than the energy released in forming the products' bonds.
In the given exercise:

• The reaction \(\mathrm{X} \rightarrow \mathrm{Y}\) is endothermic.
• This is because the potential energy of the products (Y) is higher than that of the reactants (X).
• The calculated heat of reaction (\(\Delta H = 9 \, \text{kJ/mol}\)) is positive, confirming endothermic behavior.

Endothermic reactions typically feel cold to the touch, as they absorb heat to proceed.

Heat of Reaction

The heat of reaction, represented as \(\Delta H\), is a measure of the total energy change during a chemical reaction.
It reflects the difference in potential energy between the products and reactants.

• In the hypothetical reaction, the heat of reaction is calculated as \(19 \, \text{kJ/mol} - 10 \, \text{kJ/mol} = 9 \, \text{kJ/mol}\).
• This positive value indicates that the products have higher energy than the reactants.
• This also tells us that the reaction absorbs energy, consistent with its endothermic nature.

The heat of reaction is central to predicting the thermal properties of chemical processes.