Problem 68 - Chemistry The Central Science

Question

What is the molecularity of each of the following elementary reactions? Write the rate law for each. \(\begin{array}{l}{\text { (a) } 2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g)} \\ {\mathrm{CH}_{2}} \\ {\text { (b) } \mathrm{H}_{2} \mathrm{C}-\mathrm{CH}_{2}(g) \longrightarrow \mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}_{3}(g)} \\ {\text { (c) } \mathrm{SO}_{3}(g) \longrightarrow \mathrm{SO}_{2}(g)+\mathrm{O}(g)}\end{array}\)

Step-by-Step Solution

Answer

(a) The molecularity of the reaction \(2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g)\) is 2. The rate law is: Rate = k[NO]^2. (b) The molecularity of the reaction \(\mathrm{H}_{2} \mathrm{C}-\mathrm{CH}_{2}(g) \longrightarrow \mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}_{3}(g)\) is 1. The rate law is: Rate = k[H₂C-CH₂]. (c) The molecularity of the reaction \(\mathrm{SO}_{3}(g) \longrightarrow \mathrm{SO}_{2}(g)+\mathrm{O}(g)\) is 1. The rate law is: Rate = k[SO₃].

Step 1: (a) Identify Molecularity and Rate Law for Reaction 1:

In the first elementary reaction, we have: \(2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g)\) The molecularity of this reaction is 2, as there are two molecules of NO reacting. The rate law for this reaction is given by: Rate = k[NO]^2 Where Rate is the reaction rate and k is the rate constant.

Step 2: (b) Identify Molecularity and Rate Law for Reaction 2:

In the second elementary reaction, we have: \(\mathrm{H}_{2} \mathrm{C}-\mathrm{CH}_{2}(g) \longrightarrow \mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}_{3}(g)\) The molecularity of this reaction is 1, as there is only one molecule of H₂C-CH₂ reacting. The rate law for this reaction is given by: Rate = k[H₂C-CH₂] Where Rate is the reaction rate and k is the rate constant.

Step 3: (c) Identify Molecularity and Rate Law for Reaction 3:

In the third elementary reaction, we have: \(\mathrm{SO}_{3}(g) \longrightarrow \mathrm{SO}_{2}(g)+\mathrm{O}(g)\) The molecularity of this reaction is 1, as there is only one molecule of SO₃ reacting. The rate law for this reaction is given by: Rate = k[SO₃] Where Rate is the reaction rate and k is the rate constant.

Key Concepts

Molecularity

Molecularity in chemical kinetics refers to the number of molecules participating as reactants in an elementary reaction. Understanding molecularity helps us analyze simple reactions, which consist of discrete steps, to form a comprehensive picture of complex reactions.
There are three primary types of molecularity:

• Unimolecular: A single molecule undergoes a transformation, as seen in the reaction \(SO_{3}(g) \rightarrow SO_{2}(g) + O(g)\). This is a unimolecular reaction because only one molecule is involved.
• Bimolecular: Two molecules come together to react, such as in \(2 NO(g) \rightarrow N_{2}O_{2}(g)\). Here, two molecules of NO are involved, making it a bimolecular reaction.
• Termolecular: This involves three molecules reacting, although such reactions are rare because the simultaneous collision of three molecules is less probable.

Understanding these classifications helps in predicting the behavior of reactions and facilitates the development of accurate rate laws.

Rate Law

The rate law of a chemical reaction is an equation that relates the rate of reaction to the concentration of reactants. For elementary reactions, the rate law is directly related to the molecularity.
The general form of a rate law is given by: \[\text{Rate} = k[A]^m[B]^n\]where:

• \(k\) is the rate constant, a unique value for each reaction at a given temperature.
• \([A]\) and \([B]\) are the concentrations of the reactants.
• \(m\) and \(n\) are the orders of reaction for each reactant, determined by the stoichiometry of the elementary step.

For example, in the reaction \(2 NO(g) \rightarrow N_{2}O_{2}(g)\), the rate law is \(\text{Rate} = k[NO]^2\), directly reflecting its bimolecular nature. Similarly, \(\text{Rate} = k[SO_{3}]\) represents a unimolecular reaction, showing that only one molecule of \(SO_{3}\) contributes to the rate.

Elementary Reactions

Elementary reactions are fundamental steps in a reaction mechanism. These reactions occur in a single event or step at the molecular level. Understanding these reactions is crucial for developing accurate reaction mechanisms.
Characteristics of elementary reactions include:

• Stoichiometry directly reflects the molecularity: The coefficients in the balanced equation indicate how many molecules of each reactant are involved. For example, \(2 NO(g) \rightarrow N_{2}O_{2}(g)\) shows the involvement of two molecules of NO.
• Elementary reactions are not generalized: Unlike overall reactions, elementary reactions are defined by specific collisions and transformations.
• Rate laws can be directly determined: Because elementary reactions occur as single-step processes, their rate laws are directly linked to their molecularity and stoichiometric coefficients.

Understanding elementary reactions helps chemists build full kinetic models by piecing together how complex reactions might proceed from simpler steps.