Problem 208 - A Complete Resource Book in Chemistry for JEE Main

Question

Consider an endothermic reaction \(\mathrm{X} \longrightarrow \mathrm{Y}\) with the activation energies \(\mathrm{E}_{b}\) and \(\mathrm{E}_{\mathrm{f}}\) for the backward and forward reactions respectively. In general, (a) \(\mathrm{E}_{b}<\mathrm{E}_{f}\) (b) \(E_{h}>E_{f}\) (c) \(\mathrm{E}_{b}-\mathrm{E}_{f}\) (d) there is no definite relation between \(\mathrm{E}_{\mathrm{b}}\) and \(\mathrm{E}_{\mathrm{t}}\)

Step-by-Step Solution

Answer

Generally, (a) \(E_b < E_f\) is true for an endothermic reaction.

Step 1: Understanding Activation Energies

Activation energy is the minimum energy required for a reaction to occur. For an endothermic reaction, the forward reaction (A to B) absorbs heat, meaning the activation energy of the forward reaction, \(E_f\), is typically higher than that of the backward reaction, \(E_b\), because energy must be added for the forward reaction to proceed.

Step 2: Comparing Forward and Backward Activation Energies

In an endothermic reaction, the activation energy for the forward reaction, \(E_f\), is greater than for the backward reaction, \(E_b\), because more energy is required to convert reactants to products than to reverse the process. Thus, option (a), \(E_b < E_f\), is generally true for endothermic reactions.

Step 3: Assessing the Reactions

Option (b), \(E_h > E_f\), is incorrect because \(E_h\) (the heat of reaction) is not related to activation energy comparison. Option (c), \(E_b-E_f\), suggests a calculation rather than a comparison and does not provide a valid true/false proposition within this context. Similarly, option (d) implies a comparison with \(E_t\), but no such defined condition exists in the problem.

Key Concepts

Endothermic Reaction

An endothermic reaction is one where the system absorbs energy, typically in the form of heat, from its surroundings during the process. This happens because the products have a higher energy level than the reactants. In chemical terms, energy is required to break the bonds of the reactants, and because the products have stronger bonds, additional energy must be input. This energy is absorbed, and that's why these reactions feel cold to the touch.

Key points to remember about endothermic reactions include:

• The surrounding environment experiences a drop in temperature during the reaction, as heat is absorbed into the system.
• Endothermic reactions are characterized by a positive enthalpy change ( ΔH > 0 ), indicating an overall gain in energy by the system.
• Examples of endothermic reactions include photosynthesis and the reaction of barium hydroxide octahydrate with ammonium thiocyanate.

Understanding these basics will help provide insight into why certain activation energies compare the way they do.

Forward and Backward Reaction

In reversible reactions, both forward and backward pathways are possible. Understanding these reactions involves analyzing how molecules in reactants convert to products and vice-versa. This process is crucial in determining activation energy ( E_f for forward reaction and E_b for backward reaction).

For endothermic reactions: the forward reaction absorbs energy (heat). This means overcoming a higher energy barrier, resulting in E_f being greater than E_b . Why? Because to move from reactants to higher-energy products, additional energy must be supplied.

Conversely, the backward reaction involves going from higher-energy products back to low-energy reactants, requiring less extra energy input (hence a lower E_b ). This dynamic helps understand why endothermic reactions function as they do.

• The forward reaction often has a higher energy activation threshold ( E_f > E_b ).
• Backward reactions, going from products to reactants, encounter lower energy demands.

This concept is vital for predicting how reactions will proceed under different conditions.

Energy Comparison

Energy comparison plays a pivotal role in dissecting reactions, particularly in assessing the relationship between various energies involved. In the context of activation energies, this means looking closely at the energy required to initiate a reaction ( E_f and E_b ).

In endothermic reactions, E_f surpasses E_b as more energy input is needed to reach the forward transition state from reactants to products. Comparatively, the backward process is easier energy-wise, with lower barriers ( E_b < E_f ). This differential highlights the nature of endothermic reactions and outlines how energy influences their direction.

• Activation energies depend on the direction of the reaction, influencing reaction rates.
• Comparative values give insights into reaction dynamics and feasibility under certain circumstances.

Such insights help chemists design conditions that favor desired reactions or equilibria. Grasping these distinctions clarifies why certain options in exercises are true or false.