Reaction Mechanisms and their relationship to Rate Laws Prashansa Agrawal, PhD Case Western Reserve University

What is reaction mechanism? Why is it important to study the reaction mechanism? How is it going to be useful?

What is Reaction mechanisms? The reaction mechanism is the series of elementary reactions that must occur to go from reactants to products. Each step occur at different rate. One step usually affects the rate the most—slowest step--Rate Determining step

Requirement for Reaction Mechanism

Reaction Mechanism Things to Remember: Most reactions do NOT occur completely in one step. Most of a chemical reaction use a series of several simple reactions (elementary steps)---- Reaction Mechanism. Sometimes only certain reactants affect rate.

For example, decomposition of ozone: 2O3 (g) ⟶ 3O2 (g) Actual mechanism is two steps: O3 (g) ⟶ O2 (g) + O (Intermediate) O + O3 (g) ⟶ 2O2 (g) _____________________________ 2O3 (g) + O ⟶ 3O2 (g) + O

Molecularity- no. of molecules on the reactant side

Rate Law for Elementary Reactions

Rate Law for Elementary Reactions follows directly from its molecularity because an elementary reaction is an individual molecular event termolecular reaction: 2NO + O2 ⟶ 2NO2 rate = k[NO]2 [O2 ]

An elementary reaction can also be an overall reaction e. g An elementary reaction can also be an overall reaction e.g., the gas-phase decomposition of cyclobutane, C4H8, to ethylene, C2H4, occurs via a unimolecular, single-step mechanism: C4H8 ⟶ Activated complex ⟶ 2C2H4 Rate = k[C4 H8 ] The rate of decomposition of C4H8 is directly proportional to its concentration and the reaction exhibits first-order behavior.

This should always be true! Mechanism example and reaction intermediates 2NO2(g) Slow→ NO(g)+NO3(g) Elementary step 1 NO3(g) + CO(g) fast→ NO2(g) )+CO2(g)  Elementary step 2 _________________________________________________ NO2(g)+CO(g) → NO(g)+CO2(g)   Overall reaction Note: 1. The elementary steps should add up to the overall reaction. 2. Reaction intermediate do NOT appear in the overall reaction equation or overall rate law This should always be true!

The rate determining step A B C

The rate determining step The rates of each elementary step is very important to determine rate law of overall reaction. The slowest step in a reaction mechanism is called the rate determining or rate limiting step. In general, the rate law for the overall reaction is the same as the rate law for the rate-determining (slower) step.

A Reaction Profile

Key points in Reaction mechanisms The reaction mechanism describes the sequence of elementary reactions that must occur to go from reactants to products. Reaction intermediates are formed in one step and then consumed in a later step of the reaction mechanism and NOT the part of overall reaction. The slowest step in the mechanism is called the rate determining or rate-limiting step. The overall reaction rate is determined by the rates of the steps up to (and including) the rate-determining step.

Why it is important to learn? Differentiate overall reaction from elementary reactions (steps) Write a balanced chemical equation for a process given its reaction mechanism Identify the molecularity of elementary reactions Derive the rate law consistent with a given reaction mechanism

The rate limiting step is the first elementary step The rate limiting step is the first elementary step. Therefore, we would expect the overall rate to be similar to the rate of the rate of the NO2 reacting in Elementary step 1. 2NO2(g) Slow→ NO(g)+NO3(g) Elementary step 1 NO3(g) + CO(g) fast→ NO2(g) )+CO2(g)  Elementary step 2 ____________________________________________________ NO2(g)+CO(g) → NO(g)+CO2(g)   Overall reaction 1. What would happen to the reaction rate if we added a catalyst that increased the rate of Elementary step 2 by 10x? Rate increases. Rate decreases. No change in rate.

2. Which elementary process is bimolecular 2. Which elementary process is bimolecular?     (a) A⟶⟶ products     (b) A + B⟶⟶ products     (c) A + A + B⟶⟶ products     (d) Both (b) and (c) 3. Which elementary process is termolecular?     (a) A⟶⟶ products     (b) A + B⟶⟶ products     (c) A + A + B⟶⟶ products     (d) Both (b) and (c)  

Rate Law: Equation that relates rate and concentrations of reactants in the rate determining step Things to remember: The rate and rate law do NOT necessarily depend on the overall reaction. They DO depend on the SLOWEST STEP. The rate law for the overall reaction is consistent with the rate of each elementary step.

Relating Reaction Mechanisms to Rate Laws NO2 (g) + CO(g) ⟶ CO2 (g) + NO(g) For temperatures above 225 °C, the rate law has been found to be: rate = k[NO2][CO] The reaction is first order with respect to NO2 and first-order with respect to CO. This is consistent with a single-step bimolecular mechanism and it is possible that this is the mechanism for this reaction at high temperatures.

At temperatures below 225 °C, the reaction is described by a rate law that is second order with respect to NO2: rate = k [NO2] 2 This is consistent with a mechanism that involves the following two elementary reactions, the first of which is slower and is therefore the rate-determining step: NO2 (g) + NO2 (g) ⟶ NO3 (g) + NO(g) (slow) NO3 (g) + CO(g) ⟶ NO2 (g) + CO2 (g) (fast) __________________________________________ NO2 (g) + CO(g) ⟶ CO2 (g) + NO(g)

If rate-determining step is preceded by a step involving an equilibrium (fast and reversible) reaction, the rate law for the overall reaction: Formation of NO2 from NO and O2 NO(g) + O2(g) ⇌ NO3(g) (fast and reversible) Rate=k1[NO] [O2] NO3(g) + NO(g)⟶ 2NO2(g) (slow) Rate=k2[NO3] [NO] rateforward = ratereverse kf [NO][O2] = kr [NO3] kf [NO][O2]/ kr = [NO3] Rate=k2[NO3] [NO] and Rate=k2 kf [NO][O2]/ kr [NO] koverall = k2 kf /kr Rate= koverall[NO]2[O2]

Rate Laws for Overall Reactions

Practice: Analyzing a mechanism Let's consider the proposed reaction mechanism below: 1. What is the balanced chemical equation for this overall reaction? A. 2NO+H2→N2O+H2O B. N2O2+2H2→N2+2H2O C. 2NO+2H2→N2+2H2O

2. What is the rate determining step? A Step 1 B Step 2 C Step 3 D There is no rate determining step.

3. What are the intermediates in this reaction? NO N2O2 N2O H2O N2