Problem 4 - A Complete Resource Book in Chemistry for JEE Main

Question

\(3 \mathrm{~A} \longrightarrow \mathrm{B}+\mathrm{C}\) It would be a zero order reaction when (a) the rate of reaction is proportional to square of concentration of \(\mathrm{A}\) (b) the rate of reaction remains same at any concentration of \(\mathrm{A}\) (c) the rate remains unchanged at any concentration of \(\mathrm{B}\) and \(\mathrm{C}\) (d) the rate of reaction doubles if concentration of is increased to double

Step-by-Step Solution

Answer

The correct option is (b), as it describes a zero-order reaction where the rate remains the same at any concentration of \(\mathrm{A}\).

Step 1: Understand zero order reaction

In a zero order reaction, the rate of reaction is independent of the concentration of the reactants. This means that changing the concentration of reactant will not affect the reaction rate.

Step 2: Analyze option (a)

Option (a) suggests that the rate of the reaction is proportional to the square of the concentration of \(\mathrm{A}\). This indicates a second-order dependency on \(\mathrm{A}\), which is inconsistent with zero-order reactions since the rate should be independent of concentration.

Step 3: Analyze option (b)

Option (b) suggests that the rate of reaction remains the same at any concentration of \(\mathrm{A}\). This aligns with the definition of a zero-order reaction, where changes in concentration do not affect the rate of reaction.

Step 4: Analyze option (c)

Option (c) states the rate remains unchanged at any concentration of \(\mathrm{B}\) and \(\mathrm{C}\). While this is true in general since these are reaction products, it doesn't specifically relate to the zero-order dependency on reactant \(\mathrm{A}\).

Step 5: Analyze option (d)

Option (d) indicates that the rate of reaction doubles if the concentration is doubled, suggesting a first-order dependence. In a zero-order reaction, rate should not be affected by changes in concentration.

Step 6: Select the correct option

Based on the definition and analysis, the correct option is (b), as it is the only one describing a consistent zero-order reaction behavior where the rate is constant, not dependent on the concentration.

Key Concepts

Reaction Rate

In chemical reactions, the rate refers to how quickly reactants are converted into products. The reaction rate can be influenced by various factors including temperature, presence of a catalyst, and importantly, the concentration of the reactants. For many reactions, an increase in the concentration of reactants leads to an increase in the reaction rate. However, not all reactions follow this pattern. Particularly, in zero order reactions, the rate is constant and is independent of the concentration of reactants. This unique trait means that even if you add more reactant, the speed at which the reaction occurs doesn’t change. For instance, if the reaction described is zero order, the reaction rate remains constant regardless of any changes in the concentration of reactant A.

Reaction Order

The reaction order indicates the power to which the concentration of a reactant is raised in the rate law equation. It tells us how the rate is affected by the concentration of the reactants.

• Zero Order: For zero order reactions, the rate law is given by: \[ ext{Rate} = k \]Here, the rate constant, \(k\), is the only factor determining the rate, and it remains unaffected by changes in reactant concentration.
• First Order: In first order reactions, the rate changes linearly with concentration, usually described by:\[ ext{Rate} = k[A]^1 \]
• Second Order:These reactions show a quadratic dependency on concentration:\[ ext{Rate} = k[A]^2 \]

The key to zero order kinetics is its independence from concentration, reflecting situations where catalysts or surface reactions limit the process.

Concentration Dependency

Concentration dependency describes how the concentration of reactants affects the rate of a chemical reaction. While most reactions have rates that depend on reactant concentration, zero order reactions are an exception. In a zero order reaction, the concentration has no role in influencing the rate. This can often be observed in enzymatic reactions where, beyond a certain point, substrate concentration exceeds that which the enzyme can process. The concentration becomes irrelevant to the rate, hence exhibiting zero order kinetics. For other reactions, a change in concentration typically changes the reaction rate. For example, doubling the concentration of a reactant in a first-order reaction doubles the rate. Understanding concentration dependency is crucial as it allows chemists to manipulate conditions to control reaction speeds effectively.

Chemical Kinetics

Chemical kinetics is the study of the speed at which chemical reactions occur and the factors that affect this speed. It encompasses concepts like reaction rates, reaction order, and concentration dependency, among others.

• Effect of Temperature: Increasing temperature generally increases reaction rates as particles move faster and collide more frequently.
• Role of Catalysts: Catalysts lower the activation energy of a reaction, allowing it to proceed faster without being consumed.
• Molecularity: Refers to the number of particles involved in an elementary step of the reaction. This is distinct from order, which is determined experimentally.

By studying chemical kinetics, scientists can understand how to control reaction conditions, optimize product yields, and develop new methods for driving reactions efficiently in industrial and laboratory settings. This field's insights are vital for innovations in pharmaceuticals, environmental science, and materials engineering.