For the reaction A+2 B ⟶C+D, the rate law is rate of...

For the reaction $\mathrm{A}+2 \mathrm{B} \longrightarrow \mathrm{C}+\mathrm{D}$, the rate law is rate of reaction $=k[\mathrm{A}][\mathrm{B}]$ (a) Show that the following mechanism is consistent with the stoichiometry of the overall reaction and with the rate law. $$ \begin{array}{l} \mathrm{A}+\mathrm{B} \longrightarrow \mathrm{I} \quad \text { (slow) } \\ \mathrm{I}+\mathrm{B} \longrightarrow \mathrm{C}+\mathrm{D} \quad \text { (fast) } \end{array} $$ (b) Show that the following mechanism is consistent with the stoichiometry of the overall reaction, but not with the rate law. $$ \begin{array}{c} 2 \mathrm{B} \frac{k_{1}}{k_{-1}} \mathrm{B}_{2} \text { (fast) } \\ \mathrm{A}+\mathrm{B}_{2} \stackrel{k_{2}}{\longrightarrow} \mathrm{C}+\mathrm{D} \text { (slow) } \end{array} $$

For the reaction $\mathrm{A}+2 \mathrm{B} \longrightarrow \mathrm{C}+\mathrm{D}$, the rate law is rate of reaction $=k[\mathrm{A}][\mathrm{B}]$
(a) Show that the following mechanism is consistent with the stoichiometry of the overall reaction and with the rate law.
$$
\begin{array}{l}
\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{I} \quad \text { (slow) } \\
\mathrm{I}+\mathrm{B} \longrightarrow \mathrm{C}+\mathrm{D} \quad \text { (fast) }
\end{array}
$$
(b) Show that the following mechanism is consistent with the stoichiometry of the overall reaction, but not with the rate law.
$$
\begin{array}{c}
2 \mathrm{B} \frac{k_{1}}{k_{-1}} \mathrm{B}_{2} \text { (fast) } \\
\mathrm{A}+\mathrm{B}_{2} \stackrel{k_{2}}{\longrightarrow} \mathrm{C}+\mathrm{D} \text { (slow) }
\end{array}
$$

Key Concepts

Pre-Equilibrium Assumption

The pre-equilibrium assumption is applied when an initial fast reversible step reaches equilibrium before a slow step occurs. This allows the concentration of intermediates to be expressed in terms of the concentrations of the original reactants, thereby simplifying the derivation of the overall rate law.

Overall Reaction Stoichiometry

This concept involves the balancing of reactants and products in a chemical reaction to ensure that mass is conserved. In any proposed mechanism, the sum of the steps must add up to the overall reaction, ensuring that the number of atoms of each element remains the same on both sides of the equation.

Rate Law Consistency

Rate law consistency refers to the requirement that a reaction mechanism must yield a rate expression that matches the experimentally determined rate law. Any valid mechanism should produce the dependence of the reaction rate on the concentrations of reactants as observed, without relying on the concentrations of intermediates that are typically short-lived.

Rate-Determining Step

The rate-determining step is the slowest step in a reaction mechanism and governs the overall rate of the reaction. The kinetics of the entire process are dominated by this step, and its associated rate constant and reactant concentrations are used in formulating the overall rate law.

Reaction Intermediates

Reaction intermediates are species that are formed in one step of a mechanism and consumed in a subsequent step. They are not present in the overall balanced reaction and do not appear in the final rate law because their concentrations are transient and typically can be expressed in terms of the initial reactants through assumptions like pre-equilibrium or steady state.

Transcript

00:01 So in order to figure out the stoichina, this reaction, we're really just going to add up both sides.

00:06 And so i cancel out anything that's on both the left and right.

00:09 And so we can cancel out this i, this intermediate here.

00:14 And then everything else, you know, we have a on the left.

00:17 We have b and b, so we have 2b.

00:22 And then on the right, we'll have c and d.

00:25 And this is the reaction we're supposed to look at.

00:27 So that's all good.

00:29 Now, in order to figure out the rate law, we need to first decide which is the rate.

00:33 Determining step and that is always the slowest step in this case we're told that that's the first step so this is the rds the rate determining step and so we can figure out the rate law for the overall reaction by using by figuring out the rate law for this first step this elementary reaction so that's going to be rate is equal to the rate constant k that's just some constant we don't know it yet we'd have to do an experiment to figure it out times it's going to be the concentration of a times the concentration of b you know times the concentration of each of the reactness in the rate determining step and this is what we're told is the rate one so this is consistent and that's what we were asked to do our next reaction let's show that this is gonna add up appropriately so the only thing that gets canceled out is this b -2 intermediate and so we get 2b plus a sorry i think i'm blocking it out here 2b plus a is on the left and then c and d are on the right and and so that's exactly what we were asked to find.

01:39 Now, i'm going to get rid of all these red things so we can look at the reaction more clearly.

01:47 We are asked to figure out the rate law.

01:49 So again, we're going to look for the rate determining step, which is the slow step, as always...

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