Question

"The rate constant for the reaction: $$ \mathrm{NO}_{2}(g)+\mathrm{CO}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{CO}_{2}(g) $$ is \(1.64 \times 10^{-6} / M \cdot \mathrm{s} . "\) What is incomplete about this statement?

Short answer

The reaction order or rate law is missing in the statement.

Step-by-step solution

Identifying Reaction Type

First, we need to identify the type of reaction given. The reaction is: \( \mathrm{NO}_{2}(g)+\mathrm{CO}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{CO}_{2}(g) \). This is a bimolecular reaction as it involves two reactants.

Understanding Rate Constant Units

The rate constant has units of \( M^{-1} \cdot \mathrm{s}^{-1} \). These units typically correspond to a second-order reaction, where the rate is dependent on the concentration of two reactants.

Determining Missing Information

Since the reaction is bimolecular and the units suggest a second-order reaction, we must check if the statement includes the necessary information for this reaction order. For a complete description, the rate law itself or the reaction order should be explicitly mentioned to ensure clarity.

Conclusion on Incompleteness

The statement is incomplete because it does not specify the reaction order or the rate law directly. For completeness, either the order of reaction (e.g., first order, second order) should be stated, or the rate mechanism should be provided.

Key concepts

Reaction Rate

In chemical kinetics, the term 'reaction rate' refers to how fast a chemical reaction occurs. It is essentially the speed at which reactants are converted into products. The reaction rate can be affected by several factors, such as the concentration of the reactants, temperature, and the presence of catalysts.
In general, understanding reaction rate helps chemists to predict how quickly a reaction reaches completion and to control the process effectively. By controlling variables, researchers can optimize product yields in industrial settings or fine-tune reaction conditions in a laboratory to achieve desired outcomes swiftly.

Rate Constant

The rate constant is a crucial component in understanding the speed of a chemical reaction. It is typically represented by the symbol \( k \). The value of the rate constant is determined experimentally and varies with different reactions. For the given reaction: \( \mathrm{NO}_{2}(g) + \mathrm{CO}(g) \longrightarrow \mathrm{NO}(g) + \mathrm{CO}_{2}(g) \), the rate constant is provided as \( 1.64 \times 10^{-6} / M \cdot \mathrm{s} \).
The units of the rate constant help determine the reaction order, which relates to how the concentration of reactants affects the reaction rate. Specifically, the units \( M^{-1} \cdot \mathrm{s}^{-1} \) suggest a second-order reaction, indicating that the rate depends on the concentrations of two reactants involved. This information is vital for understanding how to effectively manipulate reaction conditions to achieve the desired speed and efficiency.

Bimolecular Reaction

A bimolecular reaction involves two reactant molecules that collide and react with each other during the process. In the given exercise, the reaction between \( \mathrm{NO}_2(g) \) and \( \mathrm{CO}(g) \) is classified as a bimolecular reaction.
Such reactions play a prominent role in understanding mechanisms that involve intermediate steps and further transformations. Bimolecular reactions are common in both organic and inorganic chemistry, where molecular interactions are key to transforming substances. The study of these interactions is essential for designing catalysts, understanding reaction pathways, and predicting reaction outcomes.

Reaction Order

Reaction order is a fundamental concept in chemical kinetics that dictates how the concentration of reactants influences the rate of a reaction. It is not directly derived from the stoichiometry of the reaction but is determined experimentally.

• In a first-order reaction, the rate depends on the concentration of one reactant.
• In a second-order reaction, the rate is proportional to the concentration of two reactants or the square of the concentration of a single reactant.

For the reaction given in the exercise, the units of the rate constant indicate it's a second-order reaction.
Understanding the order helps chemists control reaction conditions to optimize industrial processes, ensuring that reactions proceed at desired speeds and producing targeted amounts of products efficiently.