4//004 Chapter 4 Chemical Kinetics 4- Rates of Chemical Reactions 4- Reaction Rates and Concentrations 4-3 The Dependence of Concentrations on Time 4-4 Reaction Mechanisms 4-5 Reaction Mechanism and Rate Laws 4-6 Effect of Temperature on Reaction Rates 4-7 Kinetics of Catalysis FB Chapter 4
Chapter 4 Chemical Kinetics Thus far in the course, we have been using and taling about chemical reactions Reactants, products, and how much is involved Chemical Kinetics deals with how fast a reaction proceeds Kinetics Rates of Chemical Reactions And how to deduce reaction mechanisms from observed rates of reactions Activation Energy Catalysts 4//004 FB Chapter 4
4//004 Chapter 4 Reaction Mechanisms Most reactions proceed not thru a single step but through a series of steps Each Step is called an elementary reaction Types of elementary Reactions. Unimolecular (a single reactant) E.g., A B + C (a decomposition). Bimolecular (most common type) E.g., A + B products 3. Termolecular (less liely event) E.g., A + B + C products FB Chapter 4 3
Chapter 4 Chemical Kinetics Reaction Mechanism is a detailed series of elementary steps and rates which are combined to yield the overall reaction ne goal of chemical inetics is to use the observed rate to chose between several possible reaction mechanisms. 4//004 FB Chapter 4 4
average reaction rate units are mol/l s average rate [X] t mol mol L s [X] f [X] i t t f i L [X] t s To measure rates we could monitor the disappearance of reactants or appearance of products e.g., N + C N + C 4//004 FB Chapter 4 5
To measure rates we could monitor the disappearance of reactants or appearance of products e.g., N + F N F 4//004 FB Chapter 4 6
FB Chapter 4 7 4//004 Generalized Reaction aa + bb cc + dd t D d t C c t B b t A a rate ] [ ] [ ] [ ] [ +
rder of a Reaction N + decomposition 5 N e.g., rate aa [A] n products 4//004 FB Chapter 4 8
e.g., aa rate [ A] products n n does not have to be an integer n 3/ three halves order reaction Note that n does not equal the coefficient of the reactant. It is related to the reaction mechanism and determined experimentally. 4//004 FB Chapter 4 9
aa + rate bb [A] m products [B] verall reaction order m + n as before rate a n m th order in [A] n th order in [B] [A] m [B] n [ A] [ B] t b t 4//004 FB Chapter 4 0
Example 4- At elevated temperatures, HI reacts according to the chemical equation HI H + I at 443 C, the rate of reaction increases with concentration of HI, as shown in this table. Data [HI] Rate Point (mol L - ) (mol L - s - ) 0.005 7.5 x 0-4 0.0 3.0 x 0-3 3 0.0. x 0 - 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] 0.000M 4//004 FB Chapter 4
4//004 ( ) 3 4 n rate rate ( ) ( ) ([ HI] ) ([ HI] ) n 0.005 7.5 x 0-4 0.0 3.0 x 0-3 3 0.0. x 0 - a) Determine the order of the reaction with respect to HI and write tae the rate theexpression ratio of any two data points rate rate 3.0x0 7.5x0 4 n HI H + rate second I Data [HI] Rate Point (mol L - ) (mol L - s - ) [HI] [HI] [HI] order FB Chapter 4 n n 0.00 0.0050 in answer HI to n and part A n
Example 4- b) Calculate the rate constant and give its units rate [HI] answer to part A rate [HI] 30 L mol 7.5x0 - s - 4 mol (0.0050 mol answer to B L L Example 4- c) Calculate the instantaneous rate of reaction for a [HI] 0.000M rate ( - -)( - 30 L mol s 0.000 mol L ). x 0 [HI] -4 mol L - s - - - answer to C s ) - 4//004 FB Chapter 4 3
Similarly for two or more concentrations aa rate + bb products [ A] m [ B] n order is p m + n units of are mol ( p ) ( L p ) s Example A + B C tae rate rate the ratio of any two n ([X] ) ([X] ) n data points initial Rate [A] [B] mol L - s -.0x0-4.0x0-4.8x0-6.0x0-4 3.0x0-4 8.4x0-6.0x0-4 3.0x0-4 3.4x0-5 4//004 FB Chapter 4 4
For Example A + B C initial Rate [A] [B] mol L - s -.0x0-4.0x0-4.8x0-6.0x0-4 3.0x0-4 8.4x0-6.0x0-4 3.0x0-4 3.4x0-5 A m B n n rate ([X] ) rate ([X] ) n rate [ ] [ ] tae the ratio of any two data points st When A is constant (.0x 0-4 ), B increases X 3 and rate increases X 3 [ B] n rate [ B] [ A] n [ B] 4//004 FB Chapter 4 5
For Example A + B C initial Rate [A] [B] mol L - s -.0x0-4.0x0-4.8x0-6.0E0-4 3.0x0-4 8.4x0-6.0x0-4 3.0x0-4 3.4x0-5 rate nd When B is constant (3.0x 0-4 ), A increases X and rate increases X 4 [ A] m [] m rate [ A] [ B 4 4 m [ A] ] [ B] tae rate rate the ratio of any m ([X] ) ([X] ) m two data points 4//004 FB Chapter 4 6
Can now solve for rate [A] [B] [A] rate [B] [x0.8x0 4 ] 6 [x0 4 ].8x0 6 L mol - s - 4//004 FB Chapter 4 7
A 4-3 The Dependence of Concentrations on Time First rder Reactions in general, for first order products [ A] rate t [ A] For now, just accept this important formula 4//004 FB Chapter 4 8
Integrated Rate Law for a st rder Reaction [A] [A] 0 e t If we tae the ln of both sides Recall y mx + b or y b + mx A plot of ln [A] vs t will be a straight line with the Intercept ln[a] 0 Slope - 4//004 FB Chapter 4 9
ln[ A] ln[ A] 0 t First rder Reaction ln [A} (in mol / L 0.0E+00.0E+04 4.0E+04 6.0E+04 0 - - -3-4 -5-6 Slope - Time (in seconds) 4//004 FB Chapter 4 0
Second rder Reactions In General, for second order A From calculus products A [ ] rate - t [ A] for a Integrated Rate Law nd rder Reaction [A] t + This is also the equation for a straight line Y mx +b [A] o 4//004 FB Chapter 4
4//004 FB Chapter 4
[A] t + [ A] o Second rder Reaction /[A] (L /mol) 50 00 50 00 50 0 Slope 0 500 000 Time (in seconds) 4//004 FB Chapter 4 3
Summary Integrated Rate Laws First rder Reactions ln[ A] ln[ A] 0 t Second rder Reactions t + [A] [ A] o 4//004 FB Chapter 4 4
In the real world, if we don t now the order of the reaction [A] n plot both ln [A} (in mol / L First rder Reaction 0.0E+00.0E+04 4.0E+04 6.0E+04 0 - - -3-4 -5-6 Time (in seconds) /[A] (L /mol) Second rder Reaction 50 00 50 00 50 0 0 500 000 Time (in seconds) 4//004 FB Chapter 4 5
4//004 Chapter 4-4 Reaction Mechanisms Most reactions proceed not thru a single step but through a series of steps Each Step is called an elementary reaction Types of elementary Reactions. Unimolecular (a single reactant) E.g., A B + C (a decomposition). Bimolecular (most common type) E.g., A + B products 3. Termolecular (less liely event) E.g., A + B + C products FB Chapter 4 6
Chapter 4 Chemical Kinetics Reaction Mechanism is a detailed series of elementary steps and rates which are combined to yield the overall reaction ne goal of chemical inetics is to use the observed rate to chose between several possible reaction mechanisms. 4//004 FB Chapter 4 7
.).) N N 3 + + N C N N 3 + + N (slow) C (fast) Notice that N 3 is formed and consumed. This is called a reactive intermediate Notice also that Step is bimolecular Step is bimolecular Reactive intermediate is N 3 sum N + N N 3 3 + C + N + N + C overall 4//004 N + C N + C FB Chapter 4 8
4//004 Chemical Equilibrium A direct connection exists between the equilibrium constant of a reaction that taes place in a sequence of steps and the rate constants in each step. a.) at equil: forward rate reverse rate b.) K eq f / r aa.) f.) f & r + bb cc + dd Forward reaction rate Reverse reaction rate f r [A] a [B] [C] [A] c a b [D] [B] d b r [C] K c eq r [D] d f [A] [C] FB Chapter 4 9 c a [B] [D] d b
A direct connection exists between the equilibrium constant of a reaction that taes place in a sequence of steps and the rate constants in each step. a.) at equil: forward rate reverse rate b.) K eq f / r (sometimes n / -n ) The boo uses a general reaction to illustrate this principle. A (g) + B (g) C (g) + D (g) Suppose the reaction proceeds by the following two step mechanism K K 4//004.) A (g) + A (g) A (g) Rate [A] - Rate - - [A ].) A (g) + B (g) C (g) + D (g) Rate [A ][B] - Rate - - [C][D] KK [ A ][ C][ D] [ C][ D] [ A] [ A ][ B] [ A] [ B] FB Chapter 4 30
4-5 Reaction Mechanism & Rate Laws Typically with a reaction one of several elementary step reaction is the slowest step. This is called the Rate Determining Step (RDS) Case #: When the RDS occurs first, the first step is slow and determines the rate of the overall reaction..).) N N + F + F N Step is the RDS rate N F [N F + F ][F ] (slow) (fast) 4//004 FB Chapter 4 3
.).) N N + F + F rate N N F Step is the RDS [N F + F ][F ] (slow) (fast) E n e r g y F + N N + F N F Reaction Progress 4//004 FB Chapter 4 3
Case #: When the RDS occurs after one or more Fast steps, mechanisms are often signaled by a reaction order greater than two. The slow step determines the overall rate of the reaction..).) N N verall N + N N + reaction + N 3 molecule reaction. Is it A Termolecular or Bimolecular reactions? Three way collisions are rare. Try a two step mechanism. - N (fast) (slow) rate [N ][ But N is a reactive intermediate ] 4//004 FB Chapter 4 33
.) N +.) N N N + - N (fast) (slow) rate [N ][ ] E n e r g y N + N + N Reaction Progress 4//004 FB Chapter 4 34
.) N +.) N N N + - N (fast) (slow) 4//004 rate [N forward rate reverse rate ][ Need to express [intermediates] in terms of other reactants at equilibrium K [N] - [N - [N [N FB Chapter 4 35 ] [N] ] ] - [N] ] K [N] [N ]
.) N +.) N N N + - N (fast) (slow) rate [N ][ ] ] K [N] [N Substituting for [N ] in the rate expression above rate K [N] [ ] 4//004 FB Chapter 4 36
.) N +.) N N N + - N (fast) (slow) rate [N ][ ] rate K [N] [ ] E slow n e fast r g y N + N + N Reaction Progress 4//004 FB Chapter 4 37
4-6 The Effect of Temperature on Reaction Rates Arrenhius Equation where E a is the Activation energy units are energy per mole and A is the "pre - exponential factor" is a constant and has the units of 4//004 FB Chapter 4 38
Arrenhius Equation Ae Ea RT y mx + b 8.5 An Arrenhius Plot Slope -Ea/R 8 ln 7.5 7 6.5 6 0.005 0.007 0.009 0.003 0.0033 0.0035 /T (K - ) 4//004 FB Chapter 4 39
Transition State E E af -E a r The Activation Energy (E a ) is the minimum collision energy that reactants must have in order to form products 4//004 FB Chapter 4 40
Transition State E n e r g y E a f E a r Reaction Progress E E af -E a r The Activation Energy (E a ) is the minimum collision energy that reactants must have in order to form products 4//004 FB Chapter 4 4
Catalyst Chapter 4 Chemical Kinetics provides a lower energy path, but it does not alter the energy of the starting material and product rather it changes the energy of the transition (s), in the reaction A catalyst has no effect on the thermodynamics of the overall reaction Inhibitor is a negative catalyst. It slows the rate of a reaction frequently by barring access to path of low Ea and thereby forcing the reaction to process by a path of higher Ea. 4//004 FB Chapter 4 4
4//004 FB Chapter 4 43
Kinetics of Catalysis A catalyst has no effect on the thermodynamics of the overall reaction It only provides a lower energy path Examples Pt and Pd are typical catalysts for hydrogenation reactions (e.g., ethylene to ethane conversion) Enzymes act as catalysts Phases Homogenous catalysis the reactants and catalyst are in the same catalyst (gas or liquid phase) Heterogeneous catalysis reaction occurs at the boundary of two different phases (a gas or liquid at the surface of a solid) 4//004 FB Chapter 4 44
Chapter 4 Chemical Kinetics Example / exercise 4-, 4-, 4-3, 4-4, 4-5, 4-6, 4-7, 4-8, 4-9 Problems 7, 9,, 5, 9,, 3, 5, 37, 4, 43, 45, 5, 53 4//004 FB Chapter 4 45