Problem 57 - A Complete Resource Book in Chemistry for JEE Main

Question

The equilibrium constant for the reaction, \(\mathrm{SO}_{3}(\mathrm{~g}) \rightleftharpoons \mathrm{SO}_{2}(\mathrm{~g})+1 / 2 \mathrm{O}_{2}(\mathrm{~g})\) is \(\mathrm{K}=4.9 \times 10^{-2}\). The value of \(\mathrm{K}\) for the reaction \(2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{~g})\) will be (a) 416 (b) \(2.40 \times 10^{-3}\) (c) \(9.8 \times 10^{-2}\) (d) \(4.9 \times 10^{-2}\)

Step-by-Step Solution

Answer

The value of \( K \) for the reaction is 416.

Step 1: Analyze Given Reaction

The given equilibrium constant, \( K = 4.9 \times 10^{-2} \), is for the reaction \( \text{SO}_3(\text{g}) \rightleftharpoons \text{SO}_2(\text{g}) + \frac{1}{2} \text{O}_2(\text{g}) \). We note this information for further use.

Step 2: Reverse the Reaction

The reaction of interest is \( 2 \text{SO}_2(\text{g}) + \text{O}_2(\text{g}) \rightleftharpoons 2 \text{SO}_3(\text{g}) \), which is essentially the reverse of the given reaction multiplied by 2. For reversing a reaction, the equilibrium constant \( K \) becomes \( \frac{1}{K} \).

Key Concepts

Understanding Chemical Equilibrium

Chemical equilibrium is a state in a chemical reaction where the concentrations of reactants and products remain constant over time. It doesn't mean that the reactants and products are equal in amount, but that their rates of formation are balanced.
This equilibrium is dynamic, meaning that the reactions continue to occur, but the overall concentrations don't change.
If a reaction has reached equilibrium, any change that disturbs the balance will be adjusted by the system to restore equilibrium.
An important tool to understand chemical equilibrium is the equilibrium constant, often denoted as \( K \).

• A small \( K \) value (less than 1) suggests that reactants are favored.
• A large \( K \) (greater than 1) indicates that products are favored.

This constant is calculated using the concentrations of the products and reactants raised to the power of their coefficients in the balanced equation.

Examining Reaction Kinetics

Reaction kinetics is the study of rates of chemical reactions and the factors that affect these rates.
This includes the concentration of reactants, temperature, the physical state of participants, and presence of a catalyst.
Reaction kinetics is closely related to equilibrium as it determines how quickly a reaction approaches equilibrium.
Understanding the kinetics helps predict how a change in conditions might shift the equilibrium point.
For instance, increasing temperature can increase the speed of a reaction, allowing equilibrium to be reached faster.
It's essential to note that while kinetics tells us how soon a reaction will achieve equilibrium, the equilibrium constant (\( K \)) tells us the ratio of products to reactants when equilibrium is achieved.

Exploring Le Chatelier's Principle

Le Chatelier's Principle helps predict how a system at equilibrium responds to external changes.
This might include changes in concentration, temperature, or pressure.
According to this principle, if a system at equilibrium experiences a disturbance, it will shift in a direction that counteracts the disturbance.
Let's break down how this could happen:

• Increasing the concentration of reactants will shift the equilibrium toward products to use up the added reactants.
• Raising the temperature of an exothermic reaction will shift the equilibrium towards reactants.
• Increasing pressure by decreasing volume will shift equilibrium towards the side with fewer gas molecules.

Understanding Le Chatelier's Principle is crucial as it allows chemists to manipulate reaction conditions to maximize product yield.