Chapter 13 Chemical Kinetics Georgia Gwinnett College Chem 1212K Section 10 Fall 2013 Chapter 13 1 Chemical Kinetics The speed of a chemical reaction is called its reaction rate The rate of a reaction is a measure of how fast the reaction makes products or uses reactants Chemical kinetics is the study of the factors that affect reaction rates and the mechanism by which a reaction proceeds 2 Reaction Rates The rate of some event is measured as the change in some quantity that occurs in a given interval of time Reaction rates are defined as the change in concentration of reactant or product over some time interval typically the units are M s or molecules cm 3 s 1 3 Average and Instantaneous Rates Average Rate Change in concentration over some finite interval of time concentration of A at time t 2 concentration of A at time t1 Rate t 2 t1 Instantaneous Rate The rate of change of concentration at a specific instant of time Derivative of the concentration with respect to time The average rate over an infinitesimally small unit of time Use these most frequently If not specified then it is probably an instantaneous rate 4 Reaction Rates 2NO2 g 2NO g O2 g 5 2NO2 g 2NO g O2 g NO2 Concentration mol L Relative Rates NO O2 time s 6 Example Chapter 13 What is the average rate of reaction between 0 and 200 seconds What is the rate of loss of NO2 during this same time period 7 Rate Law The rate law tells us how the rate depends on the concentration of the reactants and possibly products Consider the generic reaction 2A 3B 2C D A typical rate law will have the form n Rate k A B Chapter 13 m 8 Reaction Orders A products Chapter 13 9 Method of Initial Rates Initial rate The instantaneous rate determined just after the reaction begins Initial concentrations of reactants hasn t changed No products to complicate things Perform several experiments with different initial concentrations of reactants Compare the different initial rates to see how they depend on the concentration of each reactant Generally change the initial concentration of one reactant while holding the initial concentrations of the other reactants constant Then repeat the process for the other reactants Once we know the order of each reactant the rate constant can be determined using any of the initial rates 10 Example At elevated temperatures HI reacts according to the chemical equation 2HI H2 I2 at 443 C the rate of reaction increases with concentration of HI as shown in this table Data Point 1 2 3 HI Rate mol L 1 0 005 0 01 0 02 mol L 1 s 1 7 5 x 10 4 3 0 x 10 3 1 2 x 10 2 a Determine the order of the reaction with respect to HI and write the rate expression b Calculate the rate constant and give its units c Calculate the instantaneous rate of reaction for a HI 0 0020M 11 Example Chapter 13 12 Integrated Rate Laws The rate laws we have been considering to this point are more precisely called differential rate laws although we usually just say rate law They tell us how the rate depends on concentration To start our discussion of integrated rate laws we will consider reactions with just one reactant The differential rate law for such a reaction is Integrated rate laws tell us how concentration depends on time The form of the integrated rate law depends on the order of the reaction We will consider 1st order 2nd order and 0th order rate laws 13 1st Order Integrated Rate Law Differential Rate Law Integrated Rate Law ln X t kt ln X 0 X t ln kt X 0 14 2nd Order Integrated Rate Law Differential Rate Law Integrated Rate Law 1 1 kt X t X 0 15 Zeroth Order Integrated Rate Law Differential Rate Law Integrated Rate Law X t kt X 0 16 Half Life The Half Life t1 2 of a reaction is the time required for the concentration of a reactant to fall to one half of its initial value Determine the value of the half life for a 1st order reaction Chapter 13 17 Half Life for 2nd and 0th order reactions 2nd order reaction 0 order reaction th t1 2 1 k X 0 t1 2 X 0 2k Chapter 13 18 Determining the Order of a Reaction Using Integrated Rate Laws What is the reaction order 19 Chapter 13 20 Chapter 13 21 Chapter 13 22 Example The decomposition of SO2Cl2 is first order in SO2Cl2 and has a rate constant of 1 42 x 10 4 s 1 at a certain temperature a What is the half life of this reaction b How long will it take for the concentration of SO2Cl2 to decrease to 25 of its initial concentration c If the initial concentration of SO2Cl2 is 1 00 M how long will it take for the concentration to decrease to 0 78 M d If the initial concentration of SO2Cl2 is 0 150 M what is its concentration after 200 s Chapter 13 23 The Effect of Temperature on Reaction Rate The differential rate law tells us how concentration depends on temperature Rate k X n The temperature dependence is contained in the rate constant A rate constant is only constant if the temp doesn t change Arrhenius Equation Ea RT k Ae Chapter 13 24 Activation Energy Chapter 13 25 Frequency Factor Ea RT k Ae Accounts for how frequently molecules collide Also accounts for the fact that molecules must collide in an orientation that will give rise to a reaction Chapter 13 26 CH4 CO CH3CHO 27 Reactive Collision 28 Unreactive Collision 29 Arrhenius Plots Ea k Ae RT Rearrange the Arrhenius equation to another useful form Chapter 13 30 Example The decomposition of hydrogen iodide 2HI g H2 g I2 g has a rate constant of 9 51 x 10 9 M 1s 1 at 500 K and 1 10 x 10 5 M 1s 1 at 600 K What is the activation energy Chapter 13 31 Rate Laws and Reaction Mechanisms Most chemical reactions do NOT occur in a single step They occur through a series of individual steps known as the reaction mechanism Each of the individual steps is called an elementary step The chemical equation we usually write represents the overall chemical reaction The overall reaction tells us what reactants are present at the beginning and what products are present at the end It is the sum of the individual steps involved in the reaction mechanism The overall reaction does NOT tell us how we get from reactants to products only the mechanism tells us that 32 Reaction mechanism Example Overall reaction H2 g 2 ICl g 2 HCl g I2 g Reaction Mechanism Step 1 H2 g ICl g HI g HCl g Step 2 HI g ICl g HCl g I2 g Reaction Intermediate A species that is formed in one step but then consumed in another Does not appear in overall reaction …