Problem 90 - A Complete Resource Book in Chemistry for JEE Main

Question

In which of the following reactions, the concentration of reactant is equal to concentration of product at equilibrium \((\mathrm{K}=\) equilibrium constant \()\) ? (a) \(\mathrm{A} \rightleftharpoons \mathrm{B} ; \mathrm{K}=0.01\) (b) \(\mathrm{R} \rightleftharpoons \mathrm{P} ; \mathrm{K}=1\) (c) \(\mathrm{X} \rightleftharpoons \mathrm{Y} ; \mathrm{K}=10\) (d) \(\mathrm{L} \rightleftharpoons \mathrm{J} ;=0.025\)

Step-by-Step Solution

Answer

In reaction (b) \( \mathrm{R} \rightleftharpoons \mathrm{P} ; \mathrm{K}=1 \), reactant and product concentrations are equal at equilibrium.

Step 1: Understanding Equilibrium Constant

At equilibrium, the equilibrium constant (K) is defined as the ratio of the concentration of products to the concentration of reactants. When K=1, it implies that the concentration of products is equal to the concentration of reactants.

Step 2: Apply Equilibrium Constant Definition

Review the given reactions to identify the value of K. In reaction (b), \( \mathrm{R} \rightleftharpoons \mathrm{P} ; \mathrm{K}=1 \), hence the concentrations of \( \mathrm{R} \) and \( \mathrm{P} \) will be equal at equilibrium.

Step 3: Evaluate All Options

Check all the options to confirm that only reaction (b) has an equilibrium constant of 1. Recognize that the other values of K indicate unequal concentrations of reactants and products.

Key Concepts

Equilibrium Constant

The equilibrium constant, denoted as \( K \), is a fundamental concept in chemistry that determines the ratio of the concentrations of products to reactants when a chemical reaction is at equilibrium. At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction. The formula for the equilibrium constant varies depending on the type of chemical equilibrium, but at its core, it can be expressed as:\[K = \frac{[\text{Products}]}{[\text{Reactants}]}\]Here, the concentrations of the products and reactants are measured in moles per liter. A larger \( K \) value signifies a reaction where the products are favored, meaning a higher concentration of products compared to reactants at equilibrium. Conversely, a smaller \( K \) indicates that the reactants are favored.

• When \( K = 1 \): The concentrations of reactants and products are equal.
• When \( K > 1 \): Products are more favored at equilibrium.
• When \( K < 1 \): Reactants are more favored.

Understanding the equilibrium constant helps in predicting the position of equilibrium in a given reaction, thus providing insight into the behavior of chemical reactions.

Concentration of Reactants and Products

The concentration of reactants and products at equilibrium varies according to the value of the equilibrium constant, \( K \). This concentration tells us how much of each species is present when the reaction is at equilibrium.
In reactions where \( K = 1 \), the concentration of reactants is equal to the concentration of products. This indicates a balanced equilibrium position where neither the reactants nor the products are favored.
In practice, the concentration of each species is critical in determining the direction and extent of the reaction. For instance:

• If initially, the concentration of reactants is much higher than that of products, the reaction will likely shift towards the products to reach equilibrium.
• If products are initially more concentrated, it will shift towards forming reactants.

The ability to calculate and understand these concentrations allows chemists to manipulate reaction conditions to obtain the desired outcome, such as increasing the yield of a product or purifying a particular reactant.

Chemical Reactions at Equilibrium

Chemical reactions reach a state of equilibrium when the rate of the forward reaction equals the rate of the reverse reaction. Once equilibrium is achieved, the concentrations of reactants and products remain constant, although the reactions continue to occur.
This dynamic balance allows for both the backward and forward processes to occur simultaneously yet steadily, creating what is known as a dynamic equilibrium.
Key characteristics of chemical reactions at equilibrium include:

• The reaction has no net change in the concentration of reactants and products.
• It can be achieved from either direction of the reaction.
• The equilibrium position is determined by the initial concentrations of reactants and products and can be predicted by the value of \( K \).

Understanding how reactions behave at equilibrium is critical for various scientific and industrial applications. It allows prediction and control of reactions to optimize processes such as synthesis, purification, and even in pharmaceutical manufacturing. Adjusting conditions such as temperature, pressure, and concentration helps shift the equilibrium towards the desired direction, enabling chemists and engineers to tailor the outcomes of chemical processes effectively.