Chemical Kinetics CK1 Chemical kinetics is the study

Chemical Kinetics CK-1 Chemical kinetics is the study of time dependence of the change in the concentration of reactants and products. “The field of chemical kinetics has not yet matured to a point where a set of unifying principles has been identified…There are many different theoretical models for describing how chemical reactions occur. ” (M&S, 1137) Generally, we want to understand the rate of reaction: Reactant Product

Recall from Slide CEq-2… Reactants For each constituent… CK-2 Products

Rate of reaction, v(t) CK-3 v(t), the rate of reaction, is defined as the rate of change in ξ(t) with time per unit volume Note all quantities are positive. Examples: What are units of v(t)? 2 NO(g) + O 2 (g) 2 NO 2 (g) H 2(g) + I 2 (g) 2 HI (g)

The integrated rate law CK-4 The rate can be expressed as a function of the reactant concentrations. Most common function is of form: Rate laws must be determined experimentally and, generally, cannot be deduced from the balanced reaction!! General Example 2 NO(g) + O 2 (g) 2 NO 2 (g) Determined experimentally! The Order: mth order in A nth order in B (m+n)th order overall

Finding rate laws experimentally CK-5 There are two common methods for determining rate laws: Method of isolation Set up reaction so one reactant is in excess. Any change in rate will be due to changes in other reactant. Repeat for other reactant. where Method of initial rates Measure concentration change as a function of time, ~v(t), for a series of experimental conditions. (Conditions must include sets where the reactant A has the same initial concentration but B changes and vice versa). EX-CK 2

Units of k, rate constant concentration time Rate Law (concentration)n (concentration)m Order 0 v=k 1 v =k[A] 2 v = k[A]2 v = [A][B] 1 in [A], [B] v = k[A]1/2 CK-6 2 overall 1/2 Units of k

Rate laws can be complicated CK-7 H 2(g) + I 2 (g) 2 HI (g) H 2(g) + Br 2 (g) 2 HBr (g) These rate laws suggest that these two reactions occur via different mechanisms (sets of individual steps). The first may be a elementary reaction (one step) whereas the latter is certainly a multistep process. We will soon explore how to obtain complicated rate laws from suggested mechanisms. EX-CK 1

Elementary Rxns vs. Complex Reactions CK-8 Complex Reactions Elementary Reactions Reactants Intermediates Products Reactants Products Molecularity of Elementary Reactions: Unimolecular Bimolecular Termolecular Mechanism of a complex reaction is a sequence of elementary reactions.

First order reactions The reaction: has rate law: Let’s integrate… Solution: First order reactions decay exponentially. CK-9

Ozone decays via first order kinetics CK-10 k = 1. 078 × 10 -5 s-1 at 300 K What is slope?

What happens as k increases? k = 0. 0125 s-1 k = 0. 0250 s-1 k = 0. 0500 s-1 k = 0. 1000 s-1 CK-11

Half-life of a first order reaction CK-12 The half-life, t 1/2, is the time it takes to fall to ½ of the starting concentration: At , Figure 28. 3

Other order reactions… Second order reaction: Second order rate: Integrated rate law: Zero order reaction: Zero order rate: Integrated rate law: CK-13

Pseudo-first order reactions CK-14 You can “overload” the other reactants to determine the order with respect to one individual reactant (method of isolation). For Similar to SN 2 Lab , what happens if [B] >> [A]?

Reversible reactions (small Dr. G) A k 1 k-1 B Assume first order, elementary rxn in both directions Rate: Conservation of Mass: Integrate: CK-15

At equilibrium A k 1 k-1 CK-16 B At equilibrium… The forward rate equals the reverse at equilibrium. What is the equilibrium constant for this reaction? In terms of rate constants?

Temperature Dependence of k CK-17 The rate constant can vary in different ways with T. Svante Arrhenius Winner of the 3 rd Nobel Prize in Chemistry Differential form of the Arrhenius Equation:

Arrhenius Parameters CK-18 Integrated forms of Arrhenius equation: Activated (or transition) state Ea is the activation energy. This is the energy required to get over a barrier (at the activated or transition state) between the reactants and products. Ea has units of energy and is T independent. A is the pre-exponential or Arrhenius factor and is T dependent. A is a measure of rate at which collisions occur (and takes lots of things into acct such as orientation, molecular size, number of molecules per volume, molecular velocity, etc). 2 HI(g)→I 2(g) + H 2(g)

Transition-State Theory CK-19 AB‡ is the transition state (or activated complex. ) Transition state theory assumes that the transition state and reactants are in equilibrium with each other, and uses concepts from chemical equilibrium and statistical mechanics to find kinetic info such as rate constants! ‡ Eyring Equation (key to transition-state theory) From CEq: ‡ ‡ Change in Gibbs energy from reactants to TS So… ‡ ‡ ‡ Enthalpy of activation Entropy of activation

Relating Ea to thermodynamics! CK-20 Necessary Pieces… Arrhenius Equation: Differentiate wrt T: or ‡ From Eyring Equation: van’t Hoff Equation (for Kc): Putting it all together… ‡ or ‡

What about A, the pre-exponential? ‡ ‡ and ‡ ‡ ‡ so ‡ Unimolecular Gas Phase Reaction A A‡ Products so ‡ CK-21 ‡ Same for reactions in solution ‡ ‡ Bimolecular Gas Phase Reaction A+B AB‡ Products so ‡ ‡ What is A?

Transition State Theory and NMR Lab CK-22 In the NMR/N, N-DMA Paper, Gasparro et al. found an activation energy of 70. 3 k. J/mol and a pre-factor of 1. 87 × 1010 s-1. Using these values, and a temperature of 298 K, find… ‡ ‡ ‡ Why is TST important? 1. Provides details of a reaction on the molecular scale. 2. Connects quantum mechanics and kinetics. 3. Currently used for many computational studies on reaction rates. EX-CK 3

CK-23 Chapter 29: Reaction Mechanisms

Always remember…. CK-24 • One can never prove a reaction mechanism, although evidence may disprove a mechanism. • Verifying proposed mechanisms requires extensive experimental verification of each proposed step!

Let’s examine a reaction … CK-25 Reaction could progress in multiple ways… How can we distinguish? Case 1: One elementary step EX-CK 4 Case 2: Two step reaction

Now let’s focus on the intermediate… CK-26 How do k 1 and k 2 relate in case a? in case b? (a) I forms quickly but decays slowly… k 1 is fast relative to k 2. (b) I builds up to a constant, nearly negligible, concentration until near end of reaction. … k 1 is slow relative to k 2. Steady state approximation. . . Valid only if k 2 > k 1. EX-CK 5

Rate Laws do not yield unique mechanisms CK-27 An empirically determined rate law does not imply a unique reaction mechanism! Consider reaction: Experimentally, it was determined that the rate is given by: Researchers proposed two possible mechanisms. They need to determine if one of them is correct. So how would researchers distinguish between the mechanisms? EX-CK 6

Remember the Chain Rxn from CK-6? H 2(g) + Br 2 (g) 2 HBr (g) Proposed Mechanism Initiation: Propagation: Inhibition: Termination: EX-CK 7 CK-28

What about the solution kinetics lab? ! CK-29 • Now that we’ve explored reaction mechanisms and rate laws, let’s try to derive the rate laws from the solution kinetics lab… EX-CK 8

Catalysis CK-30 Catalyst: A substance that participates in the chemical reaction but is not consumed. Provides a new mechanism for reaction and can cause reaction to occur faster. In an experiment involving a catalyst, there are two competing reactions: EX-CK 9 If both reactions are elementary, overall rate is given by: