Question

Write the rate laws for the following elementary reactions. a. ${\mathrm{CH}}_3\mathrm{NC}(g)\to {\mathrm{CH}}_3\mathrm{CN}(g)$ b. ${\mathrm{O}}_3(g)+\mathrm{NO}(g)\to {\mathrm{O}}_2(g)+{\mathrm{NO}}_2(g)$ c. ${\mathrm{O}}_3(g)\to {\mathrm{O}}_2(g)+\mathrm{O}(g)$ d. ${\mathrm{O}}_3(g)+\mathrm{O}(g)\to 2{\mathrm{O}}_2(g)$

Short answer

For the given elementary reactions, the rate laws are as follows: a. Rate = k$[{\mathrm{CH}}_3\mathrm{NC}]$ b. Rate = k$[{\mathrm{O}}_3][\mathrm{NO}]$ c. Rate = k$[{\mathrm{O}}_3]$ d. Rate = k$[{\mathrm{O}}_3][\mathrm{O}]$

Step-by-step solution

Reaction a: Convert reactants to products

For reaction a, we are given the elementary reaction: ${\mathrm{CH}}_3\mathrm{NC}(g)\to {\mathrm{CH}}_3\mathrm{CN}(g)$ Since this is an elementary reaction and there is only one reactant, it is a first-order reaction. Therefore, the rate law for this reaction can be written as: Rate = k$[{\mathrm{CH}}_3\mathrm{NC}]$

Reaction b: Convert reactants to products

For reaction b, we are given the elementary reaction: ${\mathrm{O}}_3(g)+\mathrm{NO}(g)\to {\mathrm{O}}_2(g)+{\mathrm{NO}}_2(g)$ Since this is an elementary reaction with two reactants, it is a second-order reaction (first-order with respect to each reactant). Therefore, the rate law for this reaction can be written as: Rate = k$[{\mathrm{O}}_3][\mathrm{NO}]$

Reaction c: Convert reactants to products

For reaction c, we are given the elementary reaction: ${\mathrm{O}}_3(g)\to {\mathrm{O}}_2(g)+\mathrm{O}(g)$ Since this is an elementary reaction with only one reactant, it is a first-order reaction. Therefore, the rate law for this reaction can be written as: Rate = k$[{\mathrm{O}}_3]$

Reaction d: Convert reactants to products

For reaction d, we are given the elementary reaction: ${\mathrm{O}}_3(g)+\mathrm{O}(g)\to 2{\mathrm{O}}_2(g)$ Since this is an elementary reaction with two reactants, it is a second-order reaction (first-order with respect to each reactant). Therefore, the rate law for this reaction can be written as: Rate = k$[{\mathrm{O}}_3][\mathrm{O}]$

Key concepts

Elementary Reactions

Elementary reactions are the most straightforward chemical reactions. They involve a single step where reactants are directly converted to products without any intermediate stages. These reactions provide a clear basis for understanding reaction mechanisms. Elementary reactions are characterized by:

• Simplicity: They occur in one step without any hidden or complex pathways.
• Definitive stoichiometry: The number of molecules reacting and the rate law can be directly derived from the reaction equation.
• Rate laws that match the stoichiometry of the reactants.

For example, in the reaction ${\mathrm{CH}}_3\mathrm{NC}(g)\to {\mathrm{CH}}_3\mathrm{CN}(g)$, the rate law is directly related to the concentration of the reactant $[{\mathrm{CH}}_3\mathrm{NC}]$. Understanding these types of reactions is crucial because they build the foundation for more complex multistep reactions.

First-Order Reactions

First-order reactions are a type of elementary reaction where the rate is directly proportional to the concentration of a single reactant. This means that as the concentration of the reactant changes, the reaction rate changes at the same rate.The rate law for a first-order reaction is given by:$$\text{Rate}=k[A]$$Where $k$ is the rate constant and $[A]$ is the concentration of the reactant. Examples include reaction (a) ${\mathrm{CH}}_3\mathrm{NC}(g)\to {\mathrm{CH}}_3\mathrm{CN}(g)$ and reaction (c) ${\mathrm{O}}_3(g)\to {\mathrm{O}}_2(g)+\mathrm{O}(g)$. These reactions proceed at a rate determined solely by the concentration of ${\mathrm{CH}}_3\mathrm{NC}$ or ${\mathrm{O}}_3$.
First-order reactions are common in processes like radioactive decay and certain biological reactions. Knowing a reaction is first-order helps predict how quickly a reaction will occur given initial concentrations.

Second-Order Reactions

Second-order reactions involve either two molecules of the same reactant or one molecule each of two different reactants coming together to form products. The rate of a second-order reaction is proportional to the product of the concentrations of the two reactants (either the same or different).The general rate law for a second-order reaction is:$$\text{Rate}=k[A][B]$$or, if the reaction is of one reactant type:$$\text{Rate}=k[A{]}^2$$For instance, in reactions (b) ${\mathrm{O}}_3(g)+\mathrm{NO}(g)\to {\mathrm{O}}_2(g)+{\mathrm{NO}}_2(g)$ and (d) ${\mathrm{O}}_3(g)+\mathrm{O}(g)\to 2{\mathrm{O}}_2(g)$, the rate is influenced by the concentrations of two different reactants.
Second-order reactions are important in scenarios where collisions between molecules drive the reaction, such as certain combustion processes and some enzymatic actions.

Reaction Kinetics

Reaction kinetics is the study of the rates at which chemical reactions occur and the factors affecting these rates. It connects the fundamental theory behind the reactions to experimental data, allowing prediction and control of reaction processes. Reaction kinetics involves several key considerations:

• Rate Laws: Derived from experimental data, they quantify the relationship between reactant concentrations and reaction rate.
• Reaction Order: Indicates how the rate depends on reactant concentrations, such as first or second order.
• Temperature: Often, increasing temperature speeds up reactions due to more energetic collisions between molecules.
• Catalysts: Substances that increase reaction rates without being consumed, by lowering the activation energy.

Understanding kinetics is crucial for industries that rely on chemical reactions, as it helps optimize conditions for desired outcomes. For students, mastering reaction kinetics provides insights into why reactions occur at varying speeds and under different conditions, supporting an in-depth grasp of chemical reactivity.