Problem 188 - A Complete Resource Book in Chemistry for JEE Main

Question

Consider the reaction equilibrium, \(2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{~g}) ; \Delta \mathrm{H}^{\circ}=-198 \mathrm{~kJ}\) on the basis of Le Chatelier's principle, the condition favourable for the forward reaction is (a) lowering of temperature as well as pressure (b) increasing temperature as well as pressure (c) lowering the temperature and increasing the pressure (d) any value of temperature and pressure

Step-by-Step Solution

Answer

The favorable condition is (c) lowering the temperature and increasing the pressure.

Step 1: Understand the Reaction

The given chemical reaction is \(2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{~g})\). This is a dynamic equilibrium that can be influenced by temperature and pressure changes.

Step 2: Examine the Effect of Temperature

The reaction is exothermic as indicated by \( \Delta \mathrm{H}^{\circ}=-198 \mathrm{~kJ}\). According to Le Chatelier's principle, decreasing the temperature will favor the forward reaction, shifting the equilibrium to produce more \( \mathrm{SO}_{3} \).

Step 3: Examine the Effect of Pressure

The reaction involves 3 moles of gas on the reactant side and 2 moles of gas on the product side. Increasing the pressure will shift the equilibrium to the side with fewer gas moles, favoring the formation of \( \mathrm{SO}_{3} \).

Step 4: Determine the Best Condition

Both cooling the reaction (lowering temperature) and increasing pressure shift the equilibrium toward producing more \( \mathrm{SO}_{3} \), favoring the forward reaction according to Le Chatelier's principle. Therefore, the condition favorable for the forward reaction is lowering the temperature and increasing the pressure.

Key Concepts

Chemical Equilibrium

Chemical equilibrium is a fascinating concept where reactions occur simultaneously in both directions at the same rate. Imagine it as a busy crossroads where traffic flows equally in both directions, keeping the overall number of cars constant on each side.
This happens because the rates of the forward and reverse reactions are equal, so even though reactants are constantly converting into products, and vice versa, their concentrations remain stable.
A unique feature of chemical equilibrium is that it's dynamic, meaning that molecules are in a constant state of transition, despite the steady "appearance" of the system at large. This balance can be affected by variations in conditions like temperature and pressure, as we'll explore further.

• At equilibrium, no net change in concentration of reactants and products happens over time.
• The position of equilibrium can shift if conditions change.
• It is described by the equilibrium constant ( K_e")).

Exothermic Reaction

Exothermic reactions are akin to a cozy campfire on a chilly night. They release heat, making the surroundings warmer, which is why \( \Delta \mathrm{H}^{\circ}\) is negative. In this particular reaction, \(2 \mathrm{SO}_{2} + \mathrm{O}_{2} \rightarrow 2 \mathrm{SO}_{3}\), 198 kJ of energy is released.
When a reaction releases energy, it generally does so because forming the products releases more energy than is needed to break the reactants apart. This excess energy gets released into the environment as heat.
According to Le Chatelier’s Principle, lowering the temperature tends to favor an exothermic reaction because it helps to "use up" the additional energy. Conversely, increasing the temperature will supply more energy to the system, which can encourage shifting backward to absorb that excess energy.

• Exothermic reactions make the surroundings warmer.
• They have a negative heat change (\(\Delta \mathrm{H} < 0\)).
• Favoured by lowering external temperatures.

Effect of Temperature and Pressure on Equilibrium

The balance of equilibrium can be shifted by changing temperature or pressure, much like how you might prompt water to flow downhill by lifting one side of a container.
In context of an exothermic reaction, like the production of \(\mathrm{SO}_{3}\), reducing the temperature would encourage the formation of products, which is shifting equilibrium toward the forward reaction.
On the other hand, altering the pressure affects reactions that involve gases, due to changes in volume that affect gas concentrations. For the reaction \(2\mathrm{SO}_{2} + \mathrm{O}_{2} \rightarrow 2\mathrm{SO}_{3}\), increasing the pressure favors the side with fewer moles of gas, here being the products side.

• Lower temperature favors exothermic reactions.
• Increased pressure favors side with fewer gas molecules.
• Both changes can shift equilibrium, impacting product yield.

By understanding these principles, we can manipulate reactions to obtain the desired amount of product.