Problem 27 - A Complete Resource Book in Chemistry for JEE Main

Question

For equilibrium reaction \(2 \mathrm{NO}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g})+14.6 \mathrm{~J}\), increase in tem- perature would (a) favour the formation of \(\mathrm{N}_{2} \mathrm{O}_{4}\) (b) stop reaction (c) favour the decomposition of \(\mathrm{N}_{2} \mathrm{O}_{4}\) (d) no alter the equilibrium

Step-by-Step Solution

Answer

(c) Increase in temperature favors the decomposition of \(\text{N}_{2}\text{O}_{4}\).

Step 1: Determine the Nature of the Reaction

The given reaction \(2 \text{NO}_{2}(\text{g}) \rightleftharpoons \text{N}_{2}\text{O}_{4}(\text{g}) + 14.6 \text{ J}\) is an exothermic reaction. The positive heat term \(+14.6\text{ J}\) indicates that heat is released as the reaction proceeds to the right towards \(\text{N}_{2}\text{O}_{4}(\text{g})\).

Step 2: Apply Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions (such as temperature), the position of equilibrium will shift to counteract that change. In the case of increased temperature in an exothermic reaction, the equilibrium shifts to the left to absorb the added heat and favor the formation of \(\text{NO}_{2}(\text{g})\).

Step 3: Identify the Correct Option

Given the analysis, increasing the temperature leads to a leftward equilibrium shift, favoring the endothermic reaction, which is the decomposition of \(\text{N}_{2}\text{O}_{4}\) into \(2 \text{NO}_{2}(\text{g})\). This aligns with option (c), which states that the increase in temperature would favor the decomposition of \(\text{N}_{2}\text{O}_{4}\).

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemistry that helps to predict how a change in conditions affects equilibrium in a chemical reaction. When a system at dynamic equilibrium is subjected to a change in concentration, temperature, or pressure, the system will adjust itself to partially counteract the effect of the change and a new equilibrium is established. For example:

• If the concentration of the reactants is increased, the equilibrium will shift towards the products to reduce that effect.
• If the pressure is increased, the equilibrium will move towards the side with fewer gas molecules.
• If the temperature is increased, the equilibrium will shift in the direction that absorbs heat.

For the reaction given, \[2 \mathrm{NO}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{N}_{2}\mathrm{O}_{4}(\mathrm{~g})+14.6 \mathrm{~J}\]increasing the temperature causes a shift towards the endothermic side, favoring the decomposition back to \(\mathrm{NO}_{2}\). This is because the system will attempt to absorb the extra heat, thereby shifting the equilibrium.

Exothermic Reaction

An exothermic reaction is one that releases energy in the form of heat to its surroundings. This is denoted by a positive heat change in thermochemical equations. In these reactions, the energy released when new bonds form in the products is greater than the energy required to break the bonds in the reactants. For instance:

• Combustion reactions, where fuels burn in oxygen to release heat.
• Many oxidation-reduction reactions.
• Neutralization reactions between acids and bases.

The reaction, \[2 \mathrm{NO}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{N}_{2}\mathrm{O}_{4}(\mathrm{~g})+14.6 \mathrm{~J}\]is exothermic since it releases 14.6 J when moving towards \(\mathrm{N}_{2}\mathrm{O}_{4}\). Therefore, the forward reaction, which forms \(\mathrm{N}_{2}\mathrm{O}_{4}\), is exothermic and releases heat.

Dynamic Equilibrium

Dynamic equilibrium occurs in a closed system where the rate of the forward reaction equals the rate of the backward reaction. At this point, the concentrations of reactants and products remain constant though both processes—formation and decomposition—continue. It's important to note:

• The system must be closed to matter but open to heat exchange.
• There is no net change in the concentrations of the reactants and products.
• Dynamic equilibrium can occur in both chemical reactions and physical processes like evaporation and condensation.

For the reaction \[2 \mathrm{NO}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{N}_{2}\mathrm{O}_{4}(\mathrm{~g})+14.6 \mathrm{~J}\],the system is in dynamic equilibrium when the rates of formation of \(\mathrm{N}_{2}\mathrm{O}_{4}\) and its decomposition back to \(\mathrm{NO}_{2}\) are equal. A change in temperature or pressure disturbs this balance, causing the system to adjust.

Temperature Effect on Equilibrium

Temperature is a crucial factor that influences the position of equilibrium in chemical reactions. The effect depends on the nature of the reaction—whether it is exothermic or endothermic. Here's how it works:

• In exothermic reactions, increasing temperature generally shifts the equilibrium to the left, favoring the reactants.
• In endothermic reactions, increasing temperature shifts the equilibrium to the right, favoring the products.

In our example reaction,\[2 \mathrm{NO}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{N}_{2}\mathrm{O}_{4}(\mathrm{~g})+14.6 \mathrm{~J}\],a rise in temperature adds heat to the system. Since the reaction is exothermic, the equilibrium shifts left, promoting the decomposition of \(\mathrm{N}_{2}\mathrm{O}_{4}\) back into \(\mathrm{NO}_{2}\) to absorb the extra heat, as predicted by Le Chatelier's Principle.