Question

The rate law for the reaction: $$ 2 \mathrm{H}_{2}(g)+2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) $$ is rate \(=k\left[\mathrm{H}_{2}\right][\mathrm{NO}]^{2}\). Which of the following mechanism can be ruled out on the basis of the observed rate expression? Mechanism I $$ \begin{array}{cc} \mathrm{H}_{2}+\mathrm{NO} \longrightarrow & \mathrm{H}_{2} \mathrm{O}+\mathrm{N} & (\text { slow }) \\ \mathrm{N}+\mathrm{NO} \longrightarrow & \mathrm{N}_{2}+\mathrm{O} & \text { (fast) } \\ \mathrm{O}+\mathrm{H}_{2} \longrightarrow & \mathrm{H}_{2} \mathrm{O} & \text { (fast) } \end{array} $$ Mechanism II $$ \begin{array}{ll} \mathrm{H}_{2}+2 \mathrm{NO} \longrightarrow \mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O} & \text { (slow) } \\ \mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \longrightarrow \mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O} & \text { (fast) } \end{array} $$ Mechanism III $$ 2 \mathrm{NO} \rightleftarrows \mathrm{N}_{2} \mathrm{O}_{2} $$ (fast equilibrium) $$ \begin{array}{c} \mathrm{N}_{2} \mathrm{O}_{2}+\mathrm{H}_{2} \longrightarrow \mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O} & \text { (slow) } \\ \mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \longrightarrow \mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O} & \text { (fast) } \end{array} $$

Short answer

Mechanism I can be ruled out.

Step-by-step solution

Identify the observed rate law

The given rate law for the reaction is \( \text{rate} = k[\text{H}_2][\text{NO}]^2 \). This means that the reaction rate is first order with respect to hydrogen \( \text{H}_2 \) and second order with respect to nitric oxide \( \text{NO} \).

Analyze Mechanism I

The slow step in Mechanism I is \( \text{H}_2 + \text{NO} \rightarrow \text{H}_2\text{O} + \text{N} \) which suggests the rate expression \( \text{rate} = k'[\text{H}_2][\text{NO}] \). This is inconsistent with the observed rate law as it is first order in \( \text{NO} \), while the observed rate law needs second order in \( \text{NO} \).

Analyze Mechanism II

The slow step in Mechanism II is \( \text{H}_2 + 2\text{NO} \rightarrow \text{N}_2\text{O} + \text{H}_2\text{O} \) which gives the rate expression \( \text{rate} = k''[\text{H}_2][\text{NO}]^2 \). This matches the observed rate law exactly, with respect to both orders of \( \text{H}_2 \) and \( \text{NO} \).

Analyze Mechanism III

In Mechanism III, the slow step is \( \text{N}_2\text{O}_2 + \text{H}_2 \rightarrow \text{N}_2\text{O} + \text{H}_2\text{O} \). The equilibrium of \( 2\text{NO} \rightleftarrows \text{N}_2\text{O}_2 \) leads to \( [\text{N}_2\text{O}_2] = K[\text{NO}]^2 \). Combining both gives the rate \( \text{rate} = k'''[\text{H}_2][\text{NO}]^2 \), which also matches the observed rate law.

Key concepts

Reaction Mechanisms

In chemistry, a reaction mechanism is a series of elementary steps that describe how a chemical reaction occurs at the molecular level. Each step involves a unique interaction between molecules, leading to the transformation of reactants into products. Understanding reaction mechanisms is essential because it provides insight into the speed (or rate) at which a reaction occurs and helps us deduce the reaction's rate law.
One of the crucial aspects of determining a reaction mechanism is identifying the **rate-determining step**. This is the slowest step in the sequence and dictates the overall reaction rate. When analyzing a proposed mechanism, one must identify this step and relate it to the experimental rate law. This is precisely what we did with the provided reaction mechanisms to verify which matched the given rate law of the reaction.
Each potential mechanism is evaluated based on how the concentration of reactants in the rate-determining step affects the rate, using the rate expression. If the predicted rate law from a mechanism's slow step doesn't match the observed rate law, then that mechanism can be ruled out as incorrect.

Order of Reaction

The order of reaction refers to the sum of the powers to which all reactant concentrations appear in the rate law. It provides information about how the concentration of reactants affects the rate of reaction. In the given problem, the rate law is expressed as \( ext{rate} = k[ ext{H}_2][ ext{NO}]^2 \). This indicates that the reaction is first order with respect to \( ext{H}_2 \) and second order with respect to \( ext{NO} \).
Overall, the reaction is third-order because the sum of the exponents, 1 for \( ext{H}_2 \) and 2 for \( ext{NO} \), equals 3. This means that the rate of reaction increases with the concentration of \( ext{H}_2 \) and increases significantly more with the concentration of \( ext{NO} \).
Understanding the order of reaction helps chemists predict the behavior of reactions under different conditions and is vital in industrial processes where controlling reaction rates is crucial.

Chemical Kinetics

Chemical kinetics is the branch of chemistry that studies the speed or rate of chemical reactions and the factors that affect these rates. It involves analyzing how different conditions such as temperature, pressure, concentration, and catalysts influence reaction speeds.
In relation to the exercise, the study of kinetics helps us understand why a particular rate law is observed. It involves developing mathematical models to describe reaction speeds, which we compare to experimental data. Kinetic studies lead to the formulation of rate laws that predict how changes in conditions will affect reaction rates.
The concept of **activation energy** is also central in kinetics. It is the minimum energy required for a reaction to occur. Reaction mechanisms can provide insights into the activation energy by revealing the energy barrier of the slowest step. By comparing the calculated rate laws from proposed mechanisms to the observed rate laws, we can elucidate this energy landscape.

Chemical Reactions

Chemical reactions are processes where reactants are transformed into products. These transformations involve breaking old chemical bonds and forming new ones. Recognizing the pattern of these changes is essential for predicting the behavior of chemical systems.
Chemical reactions can be classified into different types such as synthesis, decomposition, single replacement, and double replacement. In analyzing any reaction, noting the type gives insight into the mechanism. For example, the exercise focuses on a multi-step reaction where the method of breaking and forming bonds across different steps influences the overall reaction rate.
Catalysts can profoundly impact chemical reactions by lowering the activation energy, speeding up the reaction without being consumed. They work by providing an alternative pathway or mechanism. In this case, the mechanisms provided are composed of intermediate steps that show possible pathways of product formation, influencing which mechanism would occur."}]}]} กัสแ>Description Written in a simplified manner, this article is intended to assist students in comprehending essential concepts related to chemical reactions, focusing on reaction mechanisms, reaction order, chemical kinetics, and the nature of chemical reactions. Each section breaks down complex ideas into digestible facts, offering an in-depth understanding tailored towards mastering the foundational elements of chemical reaction studies. This approach enables learners to better internalize how and why reactions proceed the way they do, emphasizing the importance of these laws and processes, while linking theoretical aspects to real-world applications. Efficiently providing students with knowledge that they can apply practically in various contexts. มาส<|vq_4034|>```jsonschema _SIMPLE_EXTENSION_schema``halo to python short simple bibberockunu```jsonschema solicitor_simple_response``generator_marker_SIMPLE_EXTENSION_response_band``# Test Output Red-SHOOT`NO benchmark<|vq_13913|>{