Problem 89 - A Complete Resource Book in Chemistry for JEE Main

Question

The rate equation for a chemical reaction is Rate of reaction \(=[\mathrm{X}][\mathrm{Y}]\) Consider the following statements in this regard (1) The order of reaction is one (2) The molecularity of reaction is two (3) The rate constant depends upon temperature Of these statements (a) 1 and 3 are correct (b) 1 and 2 are correct (c) 2 and 3 are correct (d) 1,2 and 3 are correct

Step-by-Step Solution

Answer

The correct statement combination is (c) 2 and 3 are correct.

Step 1: Understanding the Rate Equation

The given rate equation is \( \text{Rate} = [\text{X}][\text{Y}] \). This indicates that the rate of reaction is directly proportional to the concentration of X and Y individually.

Step 2: Identifying the Order of the Reaction

The order of a reaction is the sum of the exponents of the concentration terms in the rate law. Here, both X and Y have an exponent of 1, so the order of the reaction is \(1 + 1 = 2\), not one. Thus, statement (1) is incorrect.

Step 3: Understanding Molecularity

Molecularity refers to the number of molecules coming together to react in a single step, which in this case are two: X and Y. Therefore, statement (2) regarding molecularity being two is correct.

Step 4: Rate Constant and Temperature Dependency

The rate constant is known to vary with temperature changes. Therefore, statement (3) is correct as the rate constant is indeed temperature-dependent.

Step 5: Final Decision

Based on our analysis: statement (1) is incorrect, statement (2) is correct, and statement (3) is correct. Therefore, the correct answer is the option where statements 2 and 3 are true, which is (c).

Key Concepts

Reaction Order

In chemistry, the order of a reaction is a crucial concept that describes how the rate of reaction depends on the concentration of reactants. It's not simply related to the number of molecules reacting, but rather the sum of the powers of the concentration terms in the rate equation. For example, if the rate law is given as \( \text{Rate} = [\text{A}]^m[\text{B}]^n \), the reaction order is \( m+n \).
For the given exercise, the rate equation \( \text{Rate} = [\text{X}][\text{Y}] \) suggests that both terms have an exponent of one. Hence, the reaction order is \( 1 + 1 = 2 \), indicating a second-order reaction.
Understanding the order is important because it helps predict how changes in concentration affect the reaction rate. A higher-order reaction is generally more sensitive to changes in concentrations compared to a lower-order one.

• Zero-order: rate is independent of concentration changes.
• First-order: rate changes proportionately with concentration changes.
• Second-order: rate is even more sensitive to concentration changes, typically squared impact.

Molecularity of Reaction

Molecularity is another fundamental concept in understanding reactions. It describes the number of molecules or atoms colliding in a single step during a reaction. This concept is distinct from reaction order because it pertains to the mechanism of the reaction rather than the mathematical expression for rate.
In the given problem, the reaction involves two molecules: X and Y, colliding together in a single step. Therefore, the molecularity of this reaction is two, and such reactions are called bimolecular reactions.
Molecularity can be:

• Unimolecular: involving one molecule.
• Bimolecular: involving two molecules, as in our given example.
• Termolecular: involving three molecules, which is less common due to the low likelihood of three particles colliding simultaneously.

Molecularity is always a whole number, contrasting with reaction order, which may be fractional.

Temperature Dependency of Rate Constant

The rate constant \( k \) in a chemical reaction is not actually a constant, as it varies with temperature. This dependency is captured by the Arrhenius equation, \( k = Ae^{-E_a/RT} \), where \( A \) is the frequency factor, \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.
As temperature increases, particles move faster and collide more often, often overcoming the activation energy barrier, thereby increasing the rate constant. This is why the rate of reaction generally speeds up with an increase in temperature.
Understanding this concept is vital because:

• It helps in controlling reaction rates in industrial and laboratory settings.
• Enables prediction of how reactions will proceed under changing environmental conditions.
• Shows the temperature effect on both exothermic and endothermic reactions.

Remember, while the reaction rate is sensitive to temperature changes, as highlighted by the temperature dependency of the rate constant, concentration changes affect the rate depending on the reaction order.