Question

If the reaction $$\mathrm{NO}_{2}+\mathrm{CO} \longrightarrow \mathrm{NO}+\mathrm{CO}_{2}$$ occured by a one-step collision process, what would be the expected rate law for the reaction? The actual rate law is rate \(=k\left[\mathrm{NO}_{2}\right]^{2}\). Could the reaction actually occur by a one-step collision between \(\mathrm{NO}_{2}\) and CO? Explain.

Short answer

The expected rate law for a one-step reaction would be rate = k[NO2][CO]. However, the actual rate law is rate = k[NO2]^2, indicating the reaction likely involves more than a simple one-step collision process between NO2 and CO.

Step-by-step solution

Analyze the Balanced Chemical Equation

The balanced chemical equation is given as NO2 + CO → NO + CO2. If the reaction occurs through a one-step collision process, then the rate law is determined by the stoichiometry of the reactants in the balanced equation.

Write the Expected Rate Law

Given it is a one-step process and following the law of mass action, the expected rate would depend on the concentrations of both reactants. Hence, the expected rate law should be rate = k[NO2][CO], where k is the rate constant.

Compare the Expected Rate Law With the Actual Rate Law

The actual rate law is given as rate = k[NO2]^2. This suggests that the reaction rate is second order with respect to NO2 and does not depend on the concentration of CO.

Determine the Mechanism Consistency

Because the actual rate law does not match the expected one-step collision based on reactants stoichiometry, we can conclude that the reaction likely does not occur through a one-step process, as it would otherwise depend on the concentrations of both NO2 and CO.

Key concepts

Reaction Mechanism

Understanding the reaction mechanism is crucial when we discuss the intricacies of chemical reactions. It stands for the step-by-step sequence of elementary reactions by which overall chemical change occurs. A mechanism describes the actual pathway, including the various intermediates and transition states, taken from reactants to products.

An elementary reaction refers to a reaction in which the reactants convert to products in a single step and involves a specific molecular collision. The complexity of these mechanisms can vary; some reactions proceed through a single step, while others take multiple successive steps, involving various intermediates.

In the discussed exercise, the actual rate law indicates a discrepancy from the expected single-step mechanism, hinting that a more complex path is involved. It is evident that simply colliding NO2 and CO does not explain the observed reaction kinetics; thus, we can infer that a single-step reaction mechanism is not at play here. This highlights the importance of deducing the correct mechanism to accurately predict the reaction rates.

Stoichiometry

The concept of stoichiometry is central to the study of chemical reactions. Stoichiometry refers to the quantitative relationship between the amounts of reactants and products in a chemical reaction. These relationships are based on the balanced chemical equation and the conservation of mass and atoms.

In the context of the rate law, stoichiometry is often assumed to dictate reaction orders when thinking about simple, one-step reactions. In an ideal scenario, the coefficients in the balanced chemical equation might give us direct insights into the order of the reaction with respect to each reactant. However, in real-world chemistry, the observed reaction orders can deviate from stoichiometric predictions because real mechanisms may involve elementary steps that do not directly reflect the overall stoichiometry of the reaction. As a result, despite the simplicity of the balanced chemical equation in the given exercise, the actual rate law tells us that the stoichiometry alone doesn’t provide enough information to determine the mechanism or the order of the reaction.

Law of Mass Action

The law of mass action is an essential principle in chemical kinetics that relates the rate of a reaction to the concentrations of reactants. In its simple form, it states that the rate of a chemical reaction at a constant temperature is proportional to the product of the molar concentrations of the reactants, each raised to a power equal to their respective coefficients as derived from the balanced equation.

The law of mass action underpins the concept of the reaction quotient and equilibrium constants. However, it is important to clarify that the powers, or reaction orders, used in an empirical rate law are not always equal to the stoichiometric coefficients. They must be determined experimentally and often reveal the reaction's mechanism. In our exercise's case, the actual rate law (rate = k[NO2]^2) suggests that the law of mass action does not support a simple one-to-one interaction between NO2 and CO, as would be suggested by a straightforward interpretation of the stoichiometric equation.

Rate Constant

The rate constant, denoted by k, is a proportionality factor that relates the rate of a reaction to the concentrations of reactants in the rate law equation. It is a unique value for each chemical reaction at a given temperature and indicates the speed at which a reaction proceeds. The magnitude of the rate constant gives insights into the likelihood of a reaction; a large value of k implies a fast reaction, while a small k value indicates a slower process.

From the exercise, we observe that the actual rate law mentions k in association with [NO2]^2, which means the reaction rate increases by the square of the concentration of NO2. This underlines that for every unit increase in the concentration of NO2, the rate of reaction increases by a factor of the square of that unit. Additionally, the absence of CO in the rate law equation suggests that the rate constant here is independent of the concentration of CO, which deviates from the expected outcome based on a simple collision theory and elucidates the fact that reaction kinetics can be much more complex than initially hypothesized.