Atkins’ Physical Chemistry Eighth Edition Chapter 22 – Lecture 3 The Rates of Chemical Reactions Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio de Paula

Rate Law: An experimentally determined law of nature Mechanism: A theory of the sequence of events that may be occurring at the molecular level The mechanism must agree with the rate law!!

Example of a mechanism once believed to be correct H 2 (g) + I 2 (g) ⇌ 2 HI (g) Rate law proposed in 1894: rate f = k f [H 2 ] [I 2 ] rate r = k r [HI] 2 Mechanism:Step (1)H 2 + I 2 ⇌ H 2 I 2 Step (2) H 2 I 2 → 2 HI Rate law proposed in 1967: appears to be a simple bimolecular mechanism

Reaction Mechanisms The overall progress of a chemical reaction can be represented at the molecular level by a series of simple elementary steps or elementary reactions The sequence of elementary steps that leads to product formation is the reaction mechanism. 2NO (g) + O 2 (g) 2NO 2 (g) N 2 O 2 is detected during the reaction! Elementary step:NO + NO N 2 O 2 Elementary step:N 2 O 2 + O 2 2NO 2 Overall reaction:2NO + O 2 2NO 2 +

Elementary step:NO + NO N 2 O 2 Elementary step:N 2 O 2 + O 2 2NO 2 Overall reaction:2NO + O 2 2NO 2 + Intermediates - species that appear in a reaction mechanism but not in the overall balanced equation An intermediate is always formed in an early elementary step and consumed in a later elementary step. Molecularity of a reaction - the number of molecules reacting in an elementary step. Unimolecular reaction – elementary step with 1 molecule Bimolecular reaction – elementary step with 2 molecules Termolecular reaction – elementary step with 3 molecules

Unimolecular reactionA productsrate = k [A] Bimolecular reactionA + B productsrate = k [A][B] Bimolecular reactionA + A productsrate = k [A] 2 Rate Laws and Elementary Steps Writing plausible reaction mechanisms: The sum of the elementary steps must give the overall balanced equation for the reaction. The rate-determining step should predict the same rate law that is determined experimentally. Rate-determining step - the slowest step in the sequence of steps leading to product formation.

Fig Diagrams of possible reaction schemes

Fig Reaction profile when 1 st step is RDS

The experimental rate law for the reaction between NO 2 and CO to produce NO and CO 2 is rate = k[NO 2 ] 2. The reaction is believed to occur via two steps: Step 1:NO 2 + NO 2 NO + NO 3 Step 2:NO 3 + CO NO 2 + CO 2 What is the equation for the overall reaction? NO 2 + CO NO + CO 2 What is the intermediate? NO 3 What can you say about the relative rates of steps 1 and 2? rate = k[NO 2 ] 2 is the rate law for step 1 so step 1 must be slower than step 2

Fig Approach of concentrations to their equilibrium values For the reaction: A ⇌ B In practice, most kinetic studies are on reactions far from equilibrium ∴ Reverse reactions are unimportant

Fig Concentrations of A, I and P with time A → I → P Consumption of A is ordinary 1 st -order decay: Note that the concentration of I rises to a maximum then falls to zero...

Fig Basis of steady-state approximation [I] remains negligibly small A → I → P Assumption :

Fig Comparison of the exact result for the concentrations of a reaction and concentrations from steady-state approximation

How do we postulate a plausible mechanism? Common approach is to use the kinetic isotope effect Process facilitates identification of bond-breaking events Decrease in reaction rate is observed when an atom is replaced with a heavier isotope Primary kinetic isotope effect – the RDS requires scission of a bond involving that isotope Secondary kinetic isotope effect – bond scission occurs in a bond NOT involving that isotope

How do we postulate a plausible mechanism? Effect arises from change in activation energy when atom is replaced with a heavier isotope Change is in zero-point vibrational energy of bond

Fig Changes in reaction profile when a C−H bond is replaced with C−D

Fig Protons can tunnel through the activation barrier Effective barrier height is reduced Important only at low temperatures when most of the reactant molecules are left of the barrier More important in electron transfer reactions even at room temperature

Fig Difference in zero-point vibrational energies to describe the secondary kinetic isotope effect where λ is an experimentally determined parameter If λ > 1 then the deuterated form reacts more slowly If λ < 1 then the undeuterated form reacts more slowly