Problem 68 - Chemistry: The Central Science in SI Units, Global Edition

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) (c) \(\mathrm{SO}_{3}(g) \longrightarrow \mathrm{SO}_{2}(g)+\mathrm{O}(g)\)

Step-by-Step Solution

Answer

The molecularity and rate laws for the given elementary reactions are: (a) The reaction is bimolecular (molecularity = 2) with two molecules of NO reacting. The rate law is: Rate = k[NO]^2. (b) No reaction provided. (c) The reaction is unimolecular (molecularity = 1) with one molecule of SO3 reacting. The rate law is: Rate = k[SO3].

Step 1: a) Determining the molecularity of the reaction

The given reaction is: \( 2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g) \) There are 2 molecules of NO reacting in this elementary reaction. Therefore, the molecularity of the reaction is 2 (bimolecular).

Step 2: a) Writing the rate law for the reaction

Since this is a bimolecular reaction with two molecules of NO reacting, the rate law is written as: Rate = k[NO]^2

Step 3: b) Not provided

There's no reaction provided for part (b). Please provide the reaction to solve the problem.

Step 4: c) Determining the molecularity of the reaction

The given reaction is: \( \mathrm{SO}_{3}(g) \longrightarrow \mathrm{SO}_{2}(g) + \mathrm{O}(g) \) There is 1 molecule of SO3 reacting in this elementary reaction. Therefore, the molecularity of the reaction is 1 (unimolecular).

Step 5: c) Writing the rate law for the reaction

Since this is a unimolecular reaction with one molecule of SO3 reacting, the rate law is written as: Rate = k[SO3]

Key Concepts

Elementary Reactions

Elementary reactions are the simplest form of chemical reactions. These are singular steps that occur at the molecular level involving the actual collision and transformation of reactant molecules. In an elementary reaction, all reactants transform directly into products in a single event, or step. This makes them different from complex reactions, which involve multiple elementary steps.
For example, in the given exercise, the reaction \(2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g)\) is an elementary reaction. This means that two molecules of NO collide and immediately form one molecule of \(\mathrm{N}_{2} \mathrm{O}_{2}\).
Understanding elementary reactions is crucial, as they allow us to establish a direct relationship between reaction mechanisms and rate laws. Furthermore, since these reactions occur in one step, their reaction orders are derived directly from their stoichiometry.

Rate Law

The rate law provides an equation that relates the rate of a chemical reaction to the concentration of its reactants. Specifically, it describes how the concentration of each reactant affects the reaction rate.
For elementary reactions, the rate law is particularly straightforward since it directly follows the stoichiometry of the reaction. This means that the coefficients in the balanced chemical equation directly become the exponents in the rate law's expression.
Taking one of our examples, for the reaction \(2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g)\), the rate law is expressed as:

• Rate = \(k[\mathrm{NO}]^2\)

This indicates a second-order reaction with respect to NO because it involves two molecules of NO reacting. Similarly, for the reaction \(\mathrm{SO}_{3}(g) \longrightarrow \mathrm{SO}_{2}(g)+\mathrm{O}(g)\), the rate law is:

• Rate = \(k[\mathrm{SO}_{3}]\)

This represents a first-order reaction since it involves just one molecule of \(\mathrm{SO}_{3}\) reacting.

Unimolecular and Bimolecular Reactions

Molecularity refers to the number of reactant molecules involved in an elementary step. It helps categorize reactions based on the number of molecules required to initiate the reaction. Molecularity is always a whole number, and here are some common types:

• Unimolecular reactions: In these reactions, only one molecule is needed to proceed. It usually involves a single compound breaking down into two or more products. An example is \(\mathrm{SO}_{3}(g) \longrightarrow \mathrm{SO}_{2}(g) + \mathrm{O}(g)\), where the molecularity is 1, thus termed unimolecular.
• Bimolecular reactions: These involve two reacting molecules. This might include two identical or two different molecules colliding to form products. For instance, \(2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g)\), is a bimolecular reaction because it involves two NO molecules.

Understanding molecularity aids in predicting the mechanisms of reactions as well as their likely rates under varying conditions.