Chemical Kinetics Chapter 12

Reaction Rates Rate = Δ[A]/Δt Rates of reactions are measured in the change of the amount of product or reactant per unit time Usually measured in M/s…[ ] = molarity Rate diminishes as the reaction proceeds

Comparing reactant change and product change 2 NO2 → 2 NO + O2 Rate = Δ[NO2]/Δt = Δ[NO]/Δt = 2 (Δ[O2]/Δt)

Generalizations Reaction rates depend on several factors: Nature of the reactant(s) Temperature Concentration of the reactants Particle size for solid reactants

Rate Laws A rate law (or differential rate law) is a mathematical expression that describes the relationship between the starting concentration of the reactants and the rate of the reaction Rate = k [A]x[B]y k is a temperature dependent rate constant that is unique to a reaction (determined by experiment) X and Y are orders of reaction and are only determined experimentally

Determining a rate law A + B → C + D Trial [A] [B] Initial rate 1 1.35 x 10-7 M/s 2 0.010 M 2.70 x 10-7 M/s 3 0.200 M 5.40 x 10-7 M/s Find the rate law for the reaction, including reaction order with respect to each reactant, the rate constant and the overall order of reaction.

Comparing trials 1 and 2, the concentration of A is unchanged, but the concentration of B was doubled and the rate doubled. Indicating that B has an order of 1. Comparing trials 2 and 3, the same is noted for A… the rate doubles when A is doubled (with B constant). The order with respect to A is also 1. The rate law: rate = k[A][B] k is calculated by entering data into the law from one of the trials and solving for k.

Orders of Reaction 1st order: there is a direct relationship between the initial concentration of the reactant and the rate of reaction 2nd order: a squared relationship exists 3rd order: a cubed relationship exists Zero order: no relationship between the reactant concentration and the rate.

Another example A + B + C → D + E Trial [A] [B] [C] rate 1 0.10 M 8.0 x 10-4 M/s 2 0.20 M 1.6 x 10-3 M/s 3 3.2 x 10-3 M/s 4

Integrated Rate Laws The differential rate law (or rate law) relates the rate of the reaction to the initial reactant concentrations. The integrated rate law relates the concentration of the reactant to elapsed time.

First-Order Laws Rate law: rate = k[A] Integrated rate law: ln[A]t = -kt + ln[A]o y = mx + b Notes: A plot of ln[A]t vs t will give a straight line k is the slope of the line Many reactions and all radioactive decay follow this relationship Half life: t1/2 = ln(2)/k

Second-Order Laws Rate Law: rate = k[A]2 Integrated rate law: 1 [𝐴 ] 𝑡 =𝑘𝑡+ 1 [𝐴 ] 0 Notes: A plot of 1/[A]t vs t gives a straight line k is the slope of the line t 1/2 = 1/k[A]0

Zero-Order Laws Rate Law: rate = k[A]0 = k Integrated Rate Law: [A]t = -kt + [A]0 Notes: [A]t vs t gives a straight line k is the slope of the line Rate is independent of the starting concentration. Often occurs with reactions occurring with a catalyst such as a metal grid or enzyme

Determining the Order of Reaction If concentration and rate data are provided, analyze to find the order(s) of reaction to write the rate law. Solve for k using the rate law. If concentration and time data are provided: Plot the data against time using ln[A], 1/[A], and [A]…the most linear plot will be the order of reaction OR Solve for k at least 2 times for each of the integrated laws…the trials that give the same k give the correct order of reaction

Collision Theory For a reaction to take place: Particles must collide or break apart The rate is dependent on the number of effective collisions Effective collisions require Proper orientation (active site) Sufficient energy (activation energy)

Collision Theory and Rate Anything that increases the number of effective collisions will increase the rate of a reaction Nature of reactants… Concentration of reactants Temperature Particle size Catalysts and Inhibitors

Potential Energy Diagram Negative ∆ H Positive ∆H

Activated Complex and Catalysts

Arrhenius Equation ln 𝑘 1 𝑘 2 = 𝐸 𝑎 𝑅 1 𝑇 2 − 1 𝑇 1 Allows the determination of activation energy for a reaction if the rate constants for two different temperatures are known from data.

Reaction Mechanisms Reactions take place in a series of unimolecular or bimolecular elementary steps Intermediates are chemical species that are not reactants or products, they are produced in one step and consumed in a later step Catalysts and Inhibitors are not reactants or products, they are added at the beginning and reform during the reaction

Rate Determining Step The slowest step in the mechanism The rate determining step will have stoichiometry that correlates with the experimentally determined rate law

Analyzing Mechanisms NO2 + F2  NO2F + F (slow) NO2 + F  NO2F (fast) Net reaction: 2 NO2 + F2  2 NO2F Intermediate: F Rate law: rate = k[NO2][F2]

More… 1: NO2(g) + NO2(g) → NO3(g) + NO(g) (slow) 2: NO3(g) + CO(g) → NO2(g) + CO2(g) (fast) Net reaction: NO2 + CO → NO + CO2 Intermediate: NO3 Catalyst: NO2 Rate law: rate = k[NO2]2

Mechanisms and PE Mechanism: Cl2  2Cl Cl + CO  COCl Cl + COCl  COCl2 Notes: Cl and COCl are intermediates 3rd step is rate-determining due to the high Ea