Problem 192 - A Complete Resource Book in Chemistry for JEE Main

Question

In gaseous reactions important for understanding the upper atmosphere, \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{O}\) react bimolecularly to form two OH radicals. \(\Delta \mathrm{H}\) for this reaction is \(72 \mathrm{~kJ}\) at \(500 \mathrm{~K}\) and \(\mathrm{Ea}=77 \mathrm{~kJ} \mathrm{~mol}^{-1}\), then \(\mathrm{E}_{9}\) for the bimolecu- lar recombination of \(2 \mathrm{OH}\) radicals to form \(\mathrm{H}_{2} \mathrm{O} \& \mathrm{O}\) at \(500 \mathrm{~K}\) is

Step-by-Step Solution

Answer

The activation energy for the reverse reaction is 5 kJ/mol.

Step 1: Understanding Given Data

We are given the following information: the enthalpy change for the reaction forming 2 OH radicals is \( \Delta H = 72 \text{ kJ/mol} \), the activation energy \( E_a \) for this process is \( 77 \text{ kJ/mol} \). We need to find the activation energy for the reverse reaction, which is the recombination of 2 OH radicals to form \( \mathrm{H}_2\mathrm{O} \) and \( \mathrm{O} \).

Step 2: Using the Relationship between Forward and Reverse Reactions

For a reversible reaction, the relationship between the activation energies of the forward \( E_a^{forward} \) and reverse \( E_a^{reverse} \) reactions is given by: \[ E_a^{reverse} = E_a^{forward} - \Delta H \]

Step 3: Substitute and Calculate

Using the formula from the previous step, substitute:\[ E_a^{reverse} = 77 \text{ kJ/mol} - 72 \text{ kJ/mol} \],which simplifies to \[ E_a^{reverse} = 5 \text{ kJ/mol} \].

Key Concepts

Bimolecular Reaction

A bimolecular reaction involves two reactant molecules coming together to form products. In this scenario, the reaction involves gaseous \[ \text{H}_2\text{O} \text{ and } \text{O} \]molecules reacting to produce two OH radicals. Such reactions are quite common in the gas phase due to the higher energy and motion of the molecules involved. The frequency of collisions between molecules is vital in a bimolecular reaction. The likelihood of a successful reaction depends on whether these molecules collide with sufficient energy and proper orientation. Bimolecular reactions are a fundamental concept for understanding atmospheric chemistry, such as how radicals are formed and consumed, influencing various processes in the environment.
Understanding the dynamics of these reactions helps explain many atmospheric phenomena, particularly those related to pollution and climate change.

Enthalpy Change

The enthalpy change, denoted as \( \Delta H \), represents the heat absorbed or released during a chemical reaction at constant pressure. For the reaction of \[ \text{H}_2\text{O} + \text{O} \rightarrow 2 \text{OH} \]\( \Delta H \) is given as \(72 \text{ kJ/mol}\). This positive value indicates the reaction is endothermic, meaning it absorbs heat from its surroundings. Enthalpy change is crucial for understanding the energy profile of a reaction. While a positive \( \Delta H \) suggests the reactants must absorb energy to react, a negative \( \Delta H \) would indicate energy release, typical in exothermic reactions.In practical terms, knowing \( \Delta H \) allows for energy management in chemical processes, including industrial applications where specific heat conditions are crucial for efficiency and safety.
It also plays a critical role in thermodynamic calculations, helping scientists predict how a reaction will proceed under different conditions.

Reversible Reaction

Reversible reactions can proceed in both forward and backward directions, given the appropriate conditions. In this exercise, the forward reaction forms OH radicals from \[ \text{H}_2\text{O} \text{ and } \text{O} \],while the reverse reaction recombines OH radicals back into water and oxygen. Understanding reversible reactions is key in chemical equilibrium studies, where the rate of the forward reaction equals the rate of the backward reaction, resulting in a stable mixture of reactants and products. These reactions are fundamental in processes like the Haber process for ammonia synthesis or the catalytic converters in automobiles, where achieving a dynamic balance is critical for optimal performance.Addressing the activation energy difference between forward and reverse reactions helps us deduce which direction the reaction favors under given conditions. This is important in designing reactions to maximize yields and minimize energy consumption.

OH Radicals

OH radicals, or hydroxyl radicals, are highly reactive species formed during many atmospheric reactions. In the given reaction, they are produced from water vapor and oxygen \[ \text{H}_2\text{O} + \text{O} \rightarrow 2 \text{OH} \].These radicals play a critical role as

• Cleansing agents in the atmosphere, breaking down pollutants.
• Initiators of various chain reactions that impact air quality.
• Key components in the understanding of chemical kinetics and dynamics.

Their high reactivity stems from their unpaired electron, making them effective in oxidizing numerous organic and inorganic compounds. OH radicals significantly influence the rates of chemical reactions in the atmosphere, determining the persistence of pollutants and affecting climate models.
Studying OH radicals helps scientists develop strategies for mitigating adverse environmental effects and enhancing air quality by understanding how these small, but powerful radicals interact with various atmospheric substances.