Problem 104 - Chemistry: An Atoms-Focused Approach

Question

A proposed mechanism for the reaction of \(\mathrm{NO}_{2}(g)\) and \(\mathrm{CO}(g)\) is $$\begin{array}{ll}\text { Step 1 } & 2 \mathrm{NO}_{2}(g) \rightarrow \mathrm{NO}(g)+\mathrm{NO}_{3}(g) \quad \text { slow } \\ \text { Step 2 } & \mathrm{NO}_{3}(g)+\mathrm{CO}(g) \rightarrow \mathrm{NO}_{2}(g)+\mathrm{CO}_{2}(g)\end{array}$$ a. Write the equation for the overall reaction. b. Write the rate law predicted by the mechanism for the overall reaction. c. Identify the reactants and products of the reaction. d. Identify any intermediates in the reaction.

Step-by-Step Solution

Answer

The overall reaction equation is: \(\mathrm{NO}_2(g) + \mathrm{CO}(g) \rightarrow \mathrm{NO}(g) + \mathrm{CO}_2(g)\) b. What is the rate law predicted by this mechanism? The rate law for the reaction is: \(\text{Rate} = k[\mathrm{NO}_2]^2\) c. What are the reactants and products of this reaction? Reactants: \(\mathrm{NO}_2(g)\) and \(\mathrm{CO}(g)\) Products: \(\mathrm{NO}(g)\) and \(\mathrm{CO}_2(g)\) d. What is the intermediate in this reaction mechanism? The intermediate in this mechanism is \(\mathrm{NO}_3(g)\).

Step 1: a. Overall Reaction

To find the overall reaction, we need to add the steps 1 and 2 together, while eliminating any common species that exist on both the reactant and product side of the equations: Step 1: \(2 \mathrm{NO}_2(g) \rightarrow \mathrm{NO}(g) + \mathrm{NO}_3(g)\) (slow) Step 2: \(\mathrm{NO}_3(g) + \mathrm{CO}(g) \rightarrow \mathrm{NO}_2(g) + \mathrm{CO}_2(g)\) Adding both steps and simplifying: \(2\mathrm{NO}_2(g) + \mathrm{CO}(g) \rightarrow \mathrm{NO}(g) + 2\mathrm{NO}_2(g) + \mathrm{CO}_2(g)\) Notice that one of the product species (\(\mathrm{NO}_2(g)\)) is also a reactant. Therefore, we can eliminate one \(\mathrm{NO}_2(g)\) from both sides: \(\mathrm{NO}_2(g) + \mathrm{CO}(g) \rightarrow \mathrm{NO}(g) + \mathrm{CO}_2(g)\) This is the overall reaction equation.

Step 2: b. Rate Law

The rate law for the reaction can be determined by the slow step in the mechanism, which is step 1. For this step, \(\text{Rate} = k[\mathrm{NO}_2]^2\) Thus, the rate law for the reaction is \(\text{Rate} = k[\mathrm{NO}_2]^2\).

Step 3: c. Reactants and Products

For the overall reaction, we can identify the reactants and products as follows: Reactants: \(\mathrm{NO}_2(g)\) and \(\mathrm{CO}(g)\) Products: \(\mathrm{NO}(g)\) and \(\mathrm{CO}_2(g)\)

Step 4: d. Intermediates

Intermediates are species that are produced in one step of the reaction and consumed in another step. In this mechanism, the intermediate is \(\mathrm{NO}_3(g)\) since it is produced in step 1 but consumed in step 2.

Key Concepts

Reaction Mechanism

In chemical kinetics, understanding the reaction mechanism is crucial. A reaction mechanism is essentially a series of steps that illustrate how the reactants transform into products. Each step represents an elementary reaction, which is a simple molecular event. In the case of the given exercise, the reaction mechanism consists of two main steps:

• Step 1: Two \(\mathrm{NO}_{2}(g)\) molecules react to form \(\mathrm{NO}(g)\) and \(\mathrm{NO}_{3}(g)\). This step is slow.
• Step 2: \(\mathrm{NO}_{3}(g)\) reacts with \(\mathrm{CO}(g)\) to produce \(\mathrm{NO}_{2}(g)\) and \(\mathrm{CO}_{2}(g)\).

This mechanism provides a detailed pathway of molecular interactions, breaking down complex reactions into simpler, comprehensible steps. Understanding the reaction mechanism allows chemists to predict the rate at which a reaction proceeds and how it can be controlled or optimized.

Rate Law

The rate law is an equation that describes the rate of a chemical reaction. It relates the concentration of reactants to the rate of reaction using specific exponents. The rate law for a reaction provides insights into the reaction mechanism. In the given mechanism, the rate law is derived from the slowest step—often called the "rate-determining step." For the reaction involving \(\mathrm{NO}_{2}(g)\) and \(\mathrm{CO}(g)\), this step is step 1: \(2 \mathrm{NO}_{2}(g) \rightarrow \mathrm{NO}(g) + \mathrm{NO}_{3}(g)\). Therefore, the rate law can be expressed as:\[\text{Rate} = k[\mathrm{NO}_{2}]^2\]This equation indicates that the rate of reaction is directly proportional to the square of the concentration of \(\mathrm{NO}_{2}\). Such information is critical in predicting how changes in concentration will affect the speed of the reaction. It's important to remember that rate laws are determined experimentally and are influenced by the reaction's mechanism.

Chemical Intermediates

Intermediates play a unique role in reaction mechanisms. They are species that are created in one step and consumed in another, and do not appear in the final overall reaction. In our reaction mechanism, \(\mathrm{NO}_{3}(g)\) acts as an intermediate. Here's how it works:

• In Step 1, \(\mathrm{NO}_{3}(g)\) is produced when \(2 \mathrm{NO}_{2}(g)\) reacts.
• In Step 2, this intermediate then reacts with \(\mathrm{CO}(g)\) to eventually form \(\mathrm{NO}_{2}(g)\) and \(\mathrm{CO}_{2}(g)\).

The presence of intermediates is indicative of a reaction mechanism, and recognizing them is essential for understanding the detailed flow of the reaction, allowing chemists to map out each transition state from reactants to products.

Overall Reaction Equation

The overall reaction equation gives a simplified representation of a chemical reaction, showing only the initial reactants and final products without any intermediates. To derive the overall reaction, you sum all the steps of the mechanism, ensuring that any species appearing on both sides are canceled out.For the proposed mechanism of \(\mathrm{NO}_{2}(g)\) reacting with \(\mathrm{CO}(g)\), the steps combine and simplify to:\[\mathrm{NO}_{2}(g) + \mathrm{CO}(g) \rightarrow \mathrm{NO}(g) + \mathrm{CO}_{2}(g)\]This equation summarizes the transformation process, illustrating the direct relationship between reactants and products. It is essential for providing an overview of the chemical reaction without the complexity of intermediates or multiple steps, delivering a straightforward picture of what happens in the reaction.