Problem 74 - Chemistry The Central Science

Question

What is the molecularity of each of the following elementary reactions? Write the rate law for each. (a) \(2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g)\)

Step-by-Step Solution

Answer

The molecularity of the elementary reaction \(2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g)\) is 2. The rate law for this reaction is \(Rate = k[\mathrm{NO}]^{2}\).

Step 1: Determine the molecularity of the elementary reaction

We can determine the molecularity of the elementary reaction by looking at the reactants. The given reaction is: \[2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g)\] There are 2 molecules of NO(g) required for the reaction, we can see it from the coefficient "2" in front of NO(g). Thus, the molecularity of the reaction is 2.

Step 2: Write the rate law for the elementary reaction

To write the rate law for the elementary reaction, we can use the formula: \[Rate = k[\mathrm{Reactant}]^{m}\] Where Rate is the rate of the reaction, k is the rate constant, [Reactant] is the concentration of the reactant, and m is the order of the reaction with respect to the reactant. Since this is an elementary reaction with molecularity 2, the order of the reaction with respect to NO(g) is the same as its stoichiometric coefficient, which is 2. Therefore, the rate law for this reaction is: \[Rate = k[\mathrm{NO}]^{2}\]

Key Concepts

Molecularity

When discussing molecularity, we refer to the minimum number of molecules, atoms, or ions required to collide for an elementary reaction to occur. In simple terms, it counts how many reactant particles are involved in a single step of a reaction.
For example, if two molecules of a reactant are needed, like in the case of the reaction provided in the exercise \[2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g)\], the molecularity is two.

• Unimolecular: Involves one molecule. For instance, the isomerization of cyclopropane to propene is a unimolecular reaction.
• Bimolecular: Involves two molecules. Most reactions, like the one given (where 2 NO molecules react), are bimolecular.
• Termolecular: Involves three molecules. This is quite rare, as it's unlikely for three molecules to collide simultaneously.

Molecularity is always a whole number and cannot be zero or fractional since it must represent actual physical particles colliding in a single step. Unlike reaction order, it is derived directly from the reaction equation of an elementary step.

Elementary Reaction

Elementary reactions are fundamental processes where reactants are directly converted to products in a single step. These are the simplest types of reactions and serve as the building blocks of more complex reactions. The provided example \[2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g)\] is an elementary reaction.

• Direct Process: The reaction occurs in a single event. Unlike complex reactions, there are no intermediates or multiple steps involved.
• Rate Law Derivation: The rate law for an elementary reaction can be written directly using the stoichiometry of the reaction. This makes predicting the rate law straightforward.

Understanding elementary reactions helps in the study of complex mechanisms by providing insight into how molecules interact and lead to the formation of products. Each step in a mechanism, when broken down to its simplest form, is described as an elementary reaction.

Reaction Order

Reaction order indicates how the rate of a reaction depends on the concentration of its reactants. For elementary reactions, reaction order can be determined from the stoichiometry provided in the balanced reaction equation.
In the reaction \[2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g)\], the reaction order with respect to NO is 2 because the coefficient of NO in the balanced equation is 2.

• Order of Reaction: It's the sum of the powers of the concentration terms in the rate law equation. For the example given, the rate law is \[Rate = k[\mathrm{NO}]^{2}\] and thus it is a second-order reaction overall.
• Determination from Mechanisms: In complex reactions, the overall order may not align with the stoichiometric coefficients, as it depends on the rate-determining step, which is often an elementary reaction like those discussed here.

The concept of reaction order is critical in the field of chemical kinetics, as it helps chemists understand and predict how changes in concentration impact the speed of a reaction. It also aids in the design of industrial processes where controlling reaction rates is crucial.