Two mechanisms are proposed for the reaction 2 NO(g)+O2( g) ⟶2 NO2( g) Mecbanism 1 : NO + O

step 1 In this problem, we're going to look at the slow step in each mechanism. Then we write the rate

Two mechanisms are proposed for the reaction 2 NO(g)+O2( g)...

Two mechanisms are proposed for the reaction $$ 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{~g}) $$ \mathrm{Mecbanism } 1 : \mathrm { NO } + \mathrm { O } _ { 2 } $\rightleftharpoons \mathrm{NO}_{3}$ $$ \begin{aligned} &\mathrm{NO}_{3}+\mathrm{NO} \longrightarrow 2 \mathrm{NO}_{2} \\ &\text { Mecbanism } 2: \mathrm{NO}+\mathrm{NO} \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{2} \end{aligned} $$ slow $$ \mathrm{N}_{2} \mathrm{O}_{2}+\mathrm{O}_{2} \longrightarrow 2 \mathrm{NO}_{2} $$ slow Show that each mechanism is consistent with the observed rate law: rate $=k[\mathrm{NO}]^{2} \times\left[\mathrm{O}_{2}\right]$

Two mechanisms are proposed for the reaction
$$
2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{~g})
$$
\mathrm{Mecbanism } 1 : \mathrm { NO } + \mathrm { O } _ { 2 } $\rightleftharpoons \mathrm{NO}_{3}$
$$
\begin{aligned}
&\mathrm{NO}_{3}+\mathrm{NO} \longrightarrow 2 \mathrm{NO}_{2} \\
&\text { Mecbanism } 2: \mathrm{NO}+\mathrm{NO} \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{2}
\end{aligned}
$$
slow
$$
\mathrm{N}_{2} \mathrm{O}_{2}+\mathrm{O}_{2} \longrightarrow 2 \mathrm{NO}_{2}
$$
slow
Show that each mechanism is consistent with the observed rate law: rate $=k[\mathrm{NO}]^{2} \times\left[\mathrm{O}_{2}\right]$

Key Concepts

Consistency of Mechanisms with Observed Rate Law

For a proposed mechanism to be considered valid, it must yield a rate law that is consistent with experimental observations. By applying approximations such as the rate-determining step and pre-equilibrium conditions, one can derive a theoretical rate law from the mechanism that should match the empirically determined rate law. This consistency check is essential in mechanistic validation.

Pre-Equilibrium (or Equilibrium Approximation)

In cases where a fast step precedes the slow, rate-determining step, the reactants and intermediates can rapidly reach equilibrium. The pre-equilibrium approximation allows us to express the concentration of intermediates in terms of the reactants by assuming equilibrium is achieved before the slow step occurs. This is critical in linking the mechanistic steps to the overall rate law.

Rate-Determining Step

The rate-determining step is the slowest step in a reaction mechanism, acting as a bottleneck that controls the overall reaction rate. Since it limits how fast the entire process can proceed, the rate law for the overall reaction is often directly influenced by the kinetics of this particular step.

Elementary Steps and Molecularity

Elementary steps are the individual processes that occur during a reaction, each characterized by its molecularity – the number of species involved in the step. The rate law for an elementary reaction is directly determined by its molecularity, making these steps fundamental to deriving the overall rate law from the mechanism.

Reaction Mechanism

A reaction mechanism is a detailed sequence of elementary steps by which a chemical reaction occurs. It breaks down the overall process into individual stages, each representing a simple collision or transformation event. Understanding the mechanism helps relate the microscopic steps to the macroscopic rate law observed in experiments.

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