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

(c) lowering the temperature and increasing the pressure.

Step 1: Understand the Reaction Characteristics

The reaction given is an exothermic reaction (since \( \Delta H^{\circ} = -198 \, \mathrm{kJ} \,\ \text{is negative}\)). This means that releasing heat is favored.

Step 2: Apply Le Chatelier's Principle to Temperature

Since the reaction is exothermic, decreasing temperature will shift the equilibrium towards the products (right side), favoring the forward reaction. This is because at lower temperatures, the system will try to produce more heat to counteract the imposed change.

Step 3: Apply Le Chatelier's Principle to Pressure

The reaction involves a decrease in the number of moles of gas (from 3 moles on the left to 2 moles on the right). According to Le Chatelier's principle, increasing pressure will favor the side with fewer gas moles. Hence, increasing pressure shifts the equilibrium towards the products.

Step 4: Combine Temperature and Pressure Effects

Since decreasing temperature and increasing pressure both favor the forward reaction, the condition favorable for the forward reaction is lowering the temperature and increasing the pressure.

Key Concepts

Reaction Equilibrium

In chemistry, reaction equilibrium refers to a state where the rate of the forward reaction equals the rate of the reverse reaction. This means the concentrations of reactants and products remain constant over time, not equal. In our exercise, the balanced reaction equation is:\[2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{~g})\]At equilibrium, the forward process of sulfur dioxide and oxygen forming sulfur trioxide occurs at the same pace as sulfur trioxide decomposes back to sulfur dioxide and oxygen. Importantly, equilibrium is dynamic, meaning the molecular exchange occurs continuously, but concentrations remain stable. Understanding this balance helps us predict and influence chemical processes, especially using Le Chatelier’s Principle, which we'll explore next.

Exothermic Reaction

An exothermic reaction releases heat as it progresses. In our example, the given reaction \( \Delta \mathrm{H}^{\circ}=-198 \mathrm{~kJ} \) indicates it is exothermic because the enthalpy change is negative. During such reactions, energy is transferred from the system to the surroundings, usually as heat, which feels warm to the touch.Le Chatelier's Principle, which concerns how changes in conditions can shift equilibrium, becomes crucial here. For exothermic reactions, lowering the temperature encourages the formation of products, as the system compensates by generating more heat. This knowledge helps chemists and industrial processes maximize yields of desired products efficiently by manipulating environmental conditions.

Effect of Pressure on Equilibrium

Pressure affects reactions involving gases significantly, as described by Le Chatelier's Principle. The principle states that if a change in pressure occurs in a reaction system, the equilibrium will shift to counteract this change. Specifically, if we increase the pressure of a gaseous system, the equilibrium will shift toward the side with fewer moles of gas.In our reaction, the left side has three moles of gas (\(2 \mathrm{SO}_{2} \) and \(1 \mathrm{O}_{2} \)), while the right has two moles (\(2 \mathrm{SO}_{3} \)). Thus, increasing pressure shifts the equilibrium towards the formation of sulfur trioxide (\(\mathrm{SO}_{3}\)), favoring the forward reaction. Understanding this effect allows us to control yield rates by simply adjusting atmospheric conditions, which is widely applied in industrial chemistry.

Effect of Temperature on Equilibrium

Temperature changes impact chemical equilibrium significantly, especially in exothermic reactions. According to Le Chatelier's Principle, if the temperature of a system at equilibrium is lowered, the system will shift to produce more heat, thus favoring the exothermic reaction direction.For our reaction, decreasing the temperature will shift the equilibrium towards the right, resulting in more sulfur trioxide (\(\mathrm{SO}_{3}\)) being produced. This effect is particularly advantageous in industrial processes where the goal is to maximize product formation. Conversely, increasing the temperature would favor the reverse endothermic process, reducing \(\mathrm{SO}_{3}\) yield.Balancing these environmental factors allows chemists to optimize reactions, striking a balance between reaction speed and product yield. Knowing how to manipulate such conditions effectively utilizes energy efficiency in manufacturing and reduces waste production.