Consider this overall reaction, which is experimentally...

Consider this overall reaction, which is experimentally observed to be second order in $X$ and first order in $Y$ : $$ \mathrm{X}+\mathrm{Y} \longrightarrow \mathrm{XY} $$ a. Does the reaction occur in a single step in which $X$ and $Y$ collide? b. Is this two-step mechanism valid? $$ \begin{array}{ll} 2 \mathrm{X} \underset{k_{2}}{\stackrel{k_{1}}{\rightleftharpoons}} \mathrm{X}_{2} & \text { Fast } \\ \mathrm{X}_{2}+\mathrm{Y} \underset{k_{3}}{\longrightarrow} \mathrm{XY}+\mathrm{X} & \text { Slow } \end{array} $$

Consider this overall reaction, which is experimentally observed to be second order in $X$ and first order in $Y$ :
$$
\mathrm{X}+\mathrm{Y} \longrightarrow \mathrm{XY}
$$
a. Does the reaction occur in a single step in which $X$ and $Y$ collide?
b. Is this two-step mechanism valid?
$$
\begin{array}{ll}
2 \mathrm{X} \underset{k_{2}}{\stackrel{k_{1}}{\rightleftharpoons}} \mathrm{X}_{2} & \text { Fast } \\
\mathrm{X}_{2}+\mathrm{Y} \underset{k_{3}}{\longrightarrow} \mathrm{XY}+\mathrm{X} & \text { Slow }
\end{array}
$$

Key Concepts

Molecularity

Molecularity is a concept that describes the number of molecules colliding in an elementary reaction step. It helps in understanding the nature of elementary steps, in contrast to the overall stoichiometry which may involve multiple collisions or steps. Recognizing the difference between molecularity and the experimentally observed reaction order is important in mechanistic studies.

Pre-Equilibrium Approximation

In some mechanisms, a fast reversible step reaches equilibrium before a slower, subsequent step occurs. The pre-equilibrium approximation allows one to express the concentration of an intermediate in terms of the reactants’ concentrations, thereby linking the kinetics of the slow step to the overall rate law. This is especially useful when an intermediate is difficult to measure directly.

Rate-Determining Step

The rate-determining step is the slowest step in a reaction mechanism and controls the overall reaction rate. Since the rate law is typically governed by this step, identifying it is key to understanding the kinetics and for deriving the overall rate law through the contribution of intermediates generated in preceding fast steps.

Chemical Reaction Mechanisms

This concept deals with the sequence of elementary steps that make up an overall chemical reaction. It emphasizes that the observable rate law of a reaction may not directly correspond to the stoichiometry of the overall reaction equation, but rather depends on the detailed steps and intermediates involved. Understanding the mechanism is crucial for correlating experimental rate data with the pathway by which reactants convert to products.

Elementary Reactions

Elementary reactions are the individual steps in a reaction mechanism that occur in a single event or collision between molecules. The rate law for an elementary reaction can be directly written from the molecularity of the colliding species, and these steps serve as the building blocks in understanding the overall kinetics of a complex reaction.

Reaction Order and Rate Law

Reaction order refers to the exponents of the concentration terms in the rate law and indicates how the rate depends on the concentration of each reactant. It is an experimentally determined quantity that can provide insight into the number of species involved in the rate?determining step, allowing chemists to propose or rule out potential reaction mechanisms.

Transcript

00:01 In this question we've been asked to determine the validity of the proposed mechanisms.

00:06 So for us to answer this question we have to appreciate that for a mechanism to pass validation, it has to meet or satisfy two conditions.

00:15 The first condition is that the steps, the steps, if we look at the steps, the sum of these steps should be equal to the overall reaction.

00:29 And the second condition is the rate law predict by the mechanism should be consistent with the experimentally derived rate law.

00:40 That is the experimental rate law should be equal to the rate low predicted by the mechanism, prediction by the mechanism.

00:54 So if these two conditions are met, it means that mechanism, the proposed mechanism is valid.

01:01 Now applying this, let's look at the first condition.

01:03 We've been given two steps in which we have two moles of x reacting to form x2 where we have k1 and k this is k2 and k1 so we also have another step in which we have our x2 reacting with y to form xy and x and if we combine these two what we are going to have is this scores and one of these goals so we are left with only one so this is plus this course cancels out and we are left with y forming xy so this indeed is the reaction that we've been given this is the overall reaction so indeed the first two the sum of these two steps in the mechanism they indeed form the overall reaction that we've been given so in terms of the first condition this mechanism is valid now going on to look at the right expression let's check if the rate law proposed by the reaction mechanism reflects what is observed by experiments...

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