Problem 68 - Chemistry The Central Science In Si Units

Question

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

Step-by-Step Solution

Answer

(a) Bimolecular, rate law: \(k[\mathrm{NO}]^2\). (b) Unimolecular, rate law: \(k[\mathrm{H}_{2} \mathrm{C}-\mathrm{CH}_{2}]\). (c) Unimolecular, rate law: \(k[\mathrm{SO}_{3}]\).

Step 1: Understanding Molecularity

Determine the number of reactant molecules involved in each elementary reaction. Molecularity refers to this count and is a direct observation from the balanced equation. It describes how many entities participate in an elementary step.

Step 2: Analyzing Reaction (a)

For the elementary reaction \(2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g)\), two molecules of \(\mathrm{NO}\) are involved. This makes the reaction bimolecular, as two molecules are required for the reaction to occur.

Step 3: Analyzing Reaction (b)

In the reaction \(\mathrm{H}_{2} \mathrm{C}-\mathrm{CH}_{2}(g) \longrightarrow \mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}_{3}(g)\), there is only one molecule involved in the reaction. Thus, the reaction is unimolecular.

Step 4: Analyzing Reaction (c)

The reaction \(\mathrm{SO}_{3}(g) \longrightarrow \mathrm{SO}_{2}(g)+\mathrm{O}(g)\) involves a single \(\mathrm{SO}_{3}\) molecule decomposing, which means it is also unimolecular.

Step 5: Writing Rate Laws

Rate laws for elementary reactions are based on molecularity. For bimolecular reactions, rate = \(k[A]^n [B]^m\), where \(A, B\) are reactants. For unimolecular, rate = \(k[A]\).

Step 6: Rate Law for Reaction (a)

Reaction (a) is bimolecular: \(\text{Rate} = k[\mathrm{NO}]^2\).

Step 7: Rate Law for Reaction (b)

Reaction (b) is unimolecular: \(\text{Rate} = k[\mathrm{H}_{2} \mathrm{C}-\mathrm{CH}_{2}]\).

Step 8: Rate Law for Reaction (c)

Reaction (c) is unimolecular: \(\text{Rate} = k[\mathrm{SO}_{3}]\).

Key Concepts

Molecularity

Molecularity refers to the number of molecules or atoms involved in an elementary reaction. It gives us an insight into how many reactant particles collide or interact in a single elementary step. This concept helps determine whether a reaction is unimolecular, bimolecular, or even termolecular. It is simply an observation directly from examining the balanced reaction equation.

• Unimolecular: Involves a single reactant molecule that undergoes a reaction, e.g., decomposition reactions.
• Bimolecular: Involves two reactant molecules or atoms coming together to react.
• Termolecular: Rarely involves three molecules simultaneously colliding to react.

Understanding molecularity allows us to predict how the reaction might proceed and aids in formulating the rate law of the reaction.

Rate Laws

Rate laws describe how the concentration of reactants influences the rate of a chemical reaction. For elementary reactions, the rate law can be directly derived from their molecularity. This makes understanding the concept of molecularity very helpful.

• Unimolecular Reaction Rate: For reactions where only one molecule participates, the rate is directly proportional to the concentration of that reactant. Given by a simple expression: \( \text{Rate} = k[A] \).
• Bimolecular Reaction Rate: In these reactions, the rate depends on both reactant concentrations: \( \text{Rate} = k[A][B] \) or \( \text{Rate} = k[A]^2 \) if the two reactant molecules are identical.
• Order of Reaction: It's important to note that the order of reaction can often match the molecularity in these simple elementary reactions.

By knowing the rate laws, chemists can predict how changes in concentration affect the speed of a reaction.

Unimolecular Reactions

Unimolecular reactions are a class of chemical reactions that involve the transformation of a single reactant molecule into one or more products. These reactions typically happen when sufficient energy within a molecule allows it to rearrange or disintegrate.

• In the case of a decomposition reaction, a molecule breaks down into simpler products.
• Unimolecular reactions often correspond to processes such as radioactive decay or certain decomposition reactions.
• The rate law for a unimolecular reaction is given by \( \text{Rate} = k[A] \), where \( A \) is the concentration of the single reactant.

Understanding unimolecular reactions is crucial for analyzing systems where a single molecule demonstrates spontaneous reaction behavior.

Bimolecular Reactions

Bimolecular reactions feature two reactant molecules that collide and react with each other to create a product or several products. This is a common type of elementary reaction seen in many chemical processes.

• These reactions often involve collisions between two different molecules (or two molecules of the same kind), such as two gases reacting in the atmosphere.
• For a bimolecular reaction with two different reactants, the rate law is \( \text{Rate} = k[A][B] \), indicating dependence on both reactant concentrations.
• If it's the same molecule colliding (such as \(2 \text{NO} \)), the rate law becomes \( \text{Rate} = k[A]^2 \).

Recognizing bimolecular reactions aids in predicting reaction dynamics, as well as their rate laws for effective chemical analysis.

Chemical Kinetics

Chemical kinetics is the branch of chemistry that studies the speed at which chemical reactions occur and the factors that affect these rates. It dives deep into the nature of reaction mechanisms and pathways.

• Focus: Kinetics focuses on the rate of reactions and the steps (mechanism) by which they occur.
• Reaction Mechanisms: Kinetics examines sequences of elementary reactions, or steps, that lead to the overall reaction from reactants to products.
• Kinetics also investigates factors like temperature, pressure, and catalysts that influence reaction rates.

Understanding chemical kinetics is essential for controlling reaction speed, optimizing processes, and predicting product yields in both industrial and research settings.