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) \(L \rightleftharpoons \quad J ;=0.025\)

Step-by-Step Solution

Answer

Reaction (b) is where reactant concentration equals product concentration at equilibrium because K = 1.

Step 1: Understanding Equilibrium Constant

The equilibrium constant (K) is a ratio of the concentration of products to reactants at equilibrium. It is expressed as K = [products]/[reactants].

Step 2: Identifying Reaction Where Reactant Equals Product

For the equilibrium concentration of reactants to equal that of products, the equilibrium constant K must be 1. This is because K = [products]/[reactants], and if [products] = [reactants], then K = 1/1 = 1.

Step 3: Examining Provided Reactions

Looking at the reactions given: (a) K = 0.01 (b) K = 1 (c) K = 10 (d) K = 0.025. Here, option (b) "\(\mathrm{R} \rightleftharpoons \mathrm{P} ; \mathrm{K}=1\)" satisfies the condition K = 1.

Key Concepts

Equilibrium Reactions

Equilibrium reactions refer to reversible chemical reactions where the conversion of reactants to products and the conversion of products back to reactants occur at the same rate. This delicate balance results over time in a state where the concentrations of reactants and products remain constant. However, it is important to note that this does not necessarily mean they are equal in concentration.

Instead, equilibrium is characterized by a constant ratio of product to reactant concentrations, defined by the equilibrium constant, known as K. This is a special state because it signals that the reaction has reached a point at which there is no longer a net change in concentration for both reactants and products over time.

• Equilibrium reactions can appear static, but they are dynamic processes occurring continuously.
• The rates of the forward and reverse reactions are equal, hence no macroscopic change is observed.
• At equilibrium, a mixture of reactants and products exists, varying in quantity depending on the particular reaction quote.

By understanding how equilibrium functions in reversible reactions, we gain valuable insights into how chemical reactions occur naturally, and how they can be manipulated to favor either products or reactants depending on desired outcomes.

Concentration of Reactants and Products

In a chemical equilibrium, the concentration of reactants and products is crucial as it helps define the equilibrium constant, K, of the reaction. Concentration, often measured in moles per liter, indicates how many moles of a substance are present in a given volume.

The equilibrium constant equation is given by:\[K = \frac{[\text{products}]}{[\text{reactants}]}\]The values of K indicate which side of the reaction is favored at equilibrium. When K is equal to 1, it implies that the concentrations of reactants and products are equal at equilibrium.

• If K > 1, the products are favored, indicating a higher concentration of products compared to reactants at equilibrium.
• If K < 1, the reactants are favored, meaning there is a higher concentration of reactants compared to products.

Concentration plays a pivotal role in the reversibility of reactions, and measuring these concentrations helps predict reaction behaviors and alterations in an equilibrium reaction.

Chemical Equilibrium

Chemical equilibrium is the point in a reversible reaction where the rate of the forward reaction equals the rate of the reverse reaction. This results in stable concentrations of both reactants and products. At this state, the system is said to be at equilibrium, and no net change in concentration occurs despite the reaction continuing at the molecular level.

An important aspect of chemical equilibrium is Le Chatelier’s Principle, which states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium shifts to counteract the change and establish a new equilibrium. Conditions that affect chemical equilibrium include concentration changes, temperature shifts, and pressure adjustments.

• Temperature: Raising the temperature favors the endothermic direction, while lowering it favors the exothermic reaction.
• Pressure: Changes affect equilibria that involve gases; increasing pressure will favor the side with fewer gas molecules.
• Concentration: Increasing the concentration of either reactants or products will shift the equilibrium to consume the excess substance.

Understanding chemical equilibrium is essential for industrial applications and laboratory settings, where controlling the outcome of reactions is crucial for achieving desired results.