Rate Laws. many elementary reactions. The overall stoichiometry of a composite reaction tells us little about the mechanism!
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1 Rate Laws We have seen how to obtain the differential form of rate laws based upon experimental observation. As they involve derivatives, we must integrate the rate equations to obtain the time dependence of concentrations. We will do this for a few cases, all involving these empirical rate laws. Here the rate law need not bear any relationship to the stoichiometry of the reaction. Our next step will be to understand the origin of the empirical laws. This leads to the concept of elementary reactions where the reaction is direct and occurs (or nor) in a single encounter. We will see how the more complex rate laws arise from multiple elementary processes. These more complex reactions are composite reactions, made up of many elementary reactions. The overall stoichiometry of a composite reaction tells us little about the mechanism! Understanding the nature of the elementary reactions and the role of elementary reactions in complex processes will occupy us until spring break.
2 Rate Laws n C 2 H 4 polyethylene Definitely a composite reaction, telling essentially nothing about the reaction mechanism! Definitions: A reaction mechanism is a series s of elementary steps thatt fully describe the overall composite reaction. Elementary steps are very simple single step reactions where the underlying physics of is well understood. Well understood is a concept that depends on your point of view. The composite reaction gives the overall stoichiometry, but might well not show the actual processes. We need the elementary steps for that! First, what is a reaction mechanism in more detail?
3 Reaction Mechanism A detailed sequence of elementary steps for a reaction Reasonable mechanism: 1. Elementary steps sum to the overall reaction 2. Elementary steps are physically reasonable 3. Mechanism is consistent with rate law and other experimental observations (generally found from rate limiting (slow) step(s) A mechanism can be supported but never proven Next, a little more about elementary reactions.
4 Types of Elementary Reactions Classified by molecularity, this is, the order of the elementary reaction This is the number of molecules that are involved in the reaction. Molecularity of elementary reactions: 1. Molecularity = 1 (one molecule involved) COMMON example radioactive decay 2. Molecularity = 2 (two molecules) COMMON 3. Molecularity = (catalyzed rxn, large excess of catalyst) HAPPENS 4. Molecularity = 3 (three molecules collide and react) VERY RARE 5. Molecularity > 3 ESSENTIALLY NEVER OBSERVED These reactions occur at rates that relate to the molecularity, and thus share rate laws with composite reactions. BUT,, the composite reactions have empirically determined rates, not necessarily related to molecularity.
5 Composite Reactions Composite reactions involve two or more elementary steps Composite reactions are likely when: 1. Complex rearrangements occur 2. More than two molecules of reactants are involved 3. The rate equation does not correspond to the stoichiometric equation 4. Reaction intermediates are detected
6 ConcepTest 1 Which of the following reactions is almost certainly not an elementary reaction? A. H 2 S + O 2 H 2 O + SO B. CH 4 + F HF + CH 3 C. NO + NO 3 2NO 2 D. He + + N 2 N + + N + He Next, we investigate the integrated rate laws.
7 First Order Reactions, n=1 A X = -k[a] 1 Differential form: Integrated form: d [A] dtd k[a] d[a] d[a] k[a] or dt d [A] kdt Integrating, g, [ A] t d [A] [A] k dt or ln [A] [A] A which says that A A e [ ] kt kt
8 First Order Reactions, n=1 A X Units of k: s 1 Half-life (t 1/2 ): ln 2 k A A e kt
9 Second Order Reactions, n=2 Differential form: A X d [A] d t Integrated form: 2 Integrating, A A d A kt A d A A 2 k A t k dt = -k[a] 2 2 A kt A A A A
10 Second Order Reactions, n=2 A X Rearranging, A A 1 kt A Units of k: dm 3 mol 1 s 1 Half-life life (t 1/2 ): 1 ka
11 Second Order Reactions, n=2 Rates vary enormously
12 Zero Order Reactions, n= Differential form: Integrated form: A X d A k d t A A d A k dt t = -k[a] A A kt or A t A kt for t A k Units of k: mol dm 3 s 1 Half-life (t 1/2 ): A 2k A A t
13 Messy for higher order reactions
14 [A] X X X X X X X X X X ConcepTest X X X X 2 X X X X X X X X X X X X X X XXXXXXX X X X X X X What is the X X X order X X of this reaction? X X X X X X X X X X X A. X X Zero X XXXXXXX X order X X X X X X X X X B. X X First X X X order X X X X X X X X X C. X X Second X X X X order X X X X XXXXXXX X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X XXXXXX X X X X X X X X X X X
15 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx The half-life of a first order reaction is constant, independent d of reactant concentration
16 Half-lives of higher reactions The rate of a zero th order reaction is constant, nt independent nt of reactant concentration The half-life of a first order reaction is constant, independent of reactant concentration The half-life of a second order reaction A+A scales as 1/k[A]
17 Elementary Reactions Elementary reactions occur in a single encounter Unimolecular: A Rate = k[a] Bimolecular: A + B Rate = k[a][b] Termolecular: A + B + C Rate = k[a][b][c] Termolecular reactions are rare; higher molecularities are unknown. For elementary reactions For elementary reactions, reaction order is replaced by molecularity
18 Back to integrated rate laws Now that we know about elementary reactions, we can look at how the integrated rate laws might apply to elementary processes. First, we would write the three 2 nd order rxns as A + A P A + B P A + B + B P The first two are 2 nd order from this perspective, while the third is a threebody (3 rd order) process, and much less common.
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