Problem 43 - A Complete Resource Book in Chemistry for JEE Main

Question

In which of the following cases does the reaction go farthest to completion? (a) \(\mathrm{K}=1\) (b) \(\mathrm{K}=10\) (c) \(\mathrm{K}=10^{-2}\) (d) \(\mathrm{K}=10^{2}\)

Step-by-Step Solution

Answer

The reaction goes farthest to completion in case (d) where \(K = 10^{2}\).

Step 1: Understanding the Equilibrium Constant

The equilibrium constant, denoted as \(K\), indicates the extent to which a reaction proceeds to completion. A large \(K\) value (\(K > 1\)) means that the products are favored at equilibrium, while a small \(K\) value (\(K < 1\)) indicates that the reactants are favored at equilibrium. When \(K = 1\), the reaction has comparable amounts of reactants and products at equilibrium.

Step 2: Comparing Given Values of K

We have four cases with different \(K\) values: \(K = 1\), \(K = 10\), \(K = 10^{-2}\), and \(K = 10^{2}\). The larger the \(K\) value, the more the reaction has progressed towards forming products.

Step 3: Identifying the Largest K

Among the given values, \(K = 10^{2}\) has the largest value. This means that in option (d), the reaction proceeds the farthest towards completion, favoring product formation.

Key Concepts

Reaction Completion

When we talk about reaction completion, we're essentially looking at how far a reaction proceeds towards forming products. This concept is closely related to the equilibrium constant, often denoted by the symbol \( K \). The value of \( K \) gives us an idea of the reaction's extent:

• If \( K > 1 \), it suggests that the reaction favors products, meaning it progresses significantly towards completion.
• If \( K < 1 \), the reaction favors the reactants, indicating it doesn't go far toward making products.
• When \( K = 1 \), it implies an equilibrium state where products and reactants are present in similar amounts.

The larger the value of \( K \), the more the reaction moves forward to completion.In a set of given options, like those in our exercise, the reaction that goes farthest to completion will always correspond to the option with the largest \( K \) value. This is because a larger \( K \) implies a greater tendency for product formation at equilibrium.

Product Formation

Product formation is intimately connected with the equilibrium constant \( K \). In a chemical reaction, the substances that result from the reaction are known as products. To understand product formation, looking at the \( K \) value provides crucial insight:

• Higher \( K \) values indicate a greater formation of products. This means that at equilibrium, there's a higher concentration of products compared to reactants.
• When comparing scenarios with different \( K \) values, the one with the greatest \( K \) value signals the most product formation, which directly reflects the reaction's completion status.

This can be clearly seen when comparing the reaction scenarios in our exercise. For the case with \( K = 10^{2} \), the value reveals significant preferential formation of products, showing that the reaction goes the farthest toward completion as compared to smaller values like \( K = 1 \), \( K = 10 \), or \( K = 10^{-2} \). Thus, when predicting product formation, always consider the size of \( K \) as a reliable indicator.

K Value Comparison

\( K \) value comparison is a practical tool in predicting the direction and extent of a chemical reaction's progress. A quick comparison of \( K \) values can tell us how far a reaction has gone towards completion when given different options:

• In a series of reactions with varying \( K \) values, identify the largest \( K \). This value pinpoints the reaction that has progressed furthest towards making products.
• For example, among \( K = 1 \), \( K = 10 \), \( K = 10^{-2} \), and \( K = 10^{2} \), the comparison shows \( K = 10^{2} \) as the largest. This suggests that reaction proceeds further to completion in this case.

K value comparison helps simplify understanding and predicting chemical equilibria by saying a lot about the favorability and dominance of product formation in a reaction equilibrium. While it's easy to get lost in the formulas and numbers, remember that bigger \( K \) means more products, leading to a better grasp of the concept behind chemical equilibria.