Problem 103 - Chemistry The Science in Context

Question

NO and \(\mathrm{Cl}_{2}\) is proportional to the product of the concentrations of the two gases: \([\mathrm{NO}]\left[\mathrm{Cl}_{2}\right] .\) The following two-step mechanism was proposed for the reaction: (1) \(\quad \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightarrow \mathrm{NOCl}_{2}(g)\) (2) \(\quad \mathrm{NOCl}_{2}(g)+\mathrm{NO}(g) \rightarrow 2 \mathrm{NOCl}(g)\) Overall \(\quad 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{NOCl}(g)\) Which step must be the rate-determining step if this mechanism is correct?

Step-by-Step Solution

Answer

Answer: The rate-determining step is Step 1: NO(g) + Cl2(g) → NOCl2(g).

Step 1: Identify the given overall rate law

The given overall rate law states that the rate of the reaction between NO and Cl2 is proportional to the product of their concentrations: \([\mathrm{NO}]\left[\mathrm{Cl}_{2}\right]\).

Step 2: Write rate laws for individual steps

Now, we need to write rate laws for each step in the proposed mechanism: Step 1: \(\mathrm{NO}(g)+\mathrm{Cl}_{2}(g)\rightarrow\mathrm{NOCl}_{2}(g)\) Rate law for step 1: \(rate_1=k_1[\mathrm{NO}][\mathrm{Cl}_{2}]\) Step 2: \(\mathrm{NOCl}_{2}(g)+\mathrm{NO}(g)\rightarrow 2\mathrm{NOCl}(g)\) Rate law for step 2: \(rate_2=k_2[\mathrm{NOCl}_2][\mathrm{NO}]\)

Step 3: Compare rate laws

We need to determine which step has a rate law that matches the overall rate law given, \([\mathrm{NO}]\left[\mathrm{Cl}_{2}\right]\). For step 1, the rate law is \(rate_1=k_1[\mathrm{NO}][\mathrm{Cl}_{2}]\), which matches the given overall rate law. For step 2, the rate law is \(rate_2=k_2[\mathrm{NOCl}_2][\mathrm{NO}]\), which does not match the given overall rate law.

Step 4: Identify the rate-determining step

Since the rate law for step 1 matches the overall rate law, we can conclude that step 1 is the rate-determining step for this mechanism. Thus, the rate-determining step is the reaction \(\mathrm{NO}(g)+\mathrm{Cl}_{2}(g)\rightarrow\mathrm{NOCl}_{2}(g)\).

Key Concepts

Reaction Mechanisms

A reaction mechanism is a step-by-step sequence of elementary reactions by which a chemical change occurs. It provides insight into the pathway from reactants to products, describing each individual step in detail. This allows us to understand not only the starting materials and the final products but also what happens in between.

In the case of the reaction between \( ext{NO}\) and \( ext{Cl}_2\), the proposed mechanism is a two-step process:

• Step 1: \( ext{NO}(g) + ext{Cl}_2(g) ightarrow ext{NOCl}_2(g)\)
• Step 2: \( ext{NOCl}_2(g) + ext{NO}(g) ightarrow 2 ext{NOCl}(g)\)

Each step in a reaction mechanism represents an elementary reaction and is characterized by a unique molecularity, which denotes the number of molecules participating in that specific step. These steps, though discrete, together lead to the formation of the final products.

Understanding reaction mechanisms can help predict the behavior of reactions under different conditions and determine the rate laws governing each step.

Rate Law

The rate law is an expression that relates the rate of a chemical reaction to the concentration of its reactants. It is crucial in understanding how different variables affect the speed of a reaction. The general form of the rate law is:

• \[ ext{Rate} = k[ ext{A}]^m[ ext{B}]^n \]

where \(k\) is the rate constant, \(m\) and \(n\) are the orders of the reaction with respect to reactants A and B, respectively.

For the given reaction mechanism, the overall rate law is derived from the rate-determining step, which is the slowest step in the mechanism:

• Overall Rate Law: \[ ext{Rate} = k_1[ ext{NO}][ ext{Cl}_2] \]

This matches the rate law for Step 1 in the mechanism, indicating that this step controls the speed of the overall reaction. Identifying the correct step that aligns with the experimental rate law is essential for predicting how changes in conditions might alter the reaction rate.

Chemical Kinetics

Chemical kinetics is the study of the rates of chemical processes. It helps us understand how fast reactions occur and what factors influence these rates. Various factors, such as temperature, concentration, and catalysts, significantly impact the rate at which reactions proceed.

In the context of our reaction involving \( ext{NO}\) and \( ext{Cl}_2\), chemical kinetics plays a vital role in identifying the rate-determining step. This step has the highest activation energy barrier and thus progresses slower than the other steps, effectively regulating the speed of the entire reaction.

• Temperature changes can affect reaction rates by altering the energy of molecules, thereby influencing how often effective collisions occur.
• The presence of a catalyst can lower the activation energy, speeding up the slow step and hence the overall reaction.

By studying chemical kinetics, chemists can design experiments to probe reaction mechanisms, adjust reaction conditions to optimize rates, and engineer reactions to achieve desired outcomes more efficiently.