Rate Laws. We have seen how to obtain the differential form of rate laws

Transcription

1 Rate Laws We have seen how to obtain the differential form of rate laws based upon experimental observation. s 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 observed 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 fails to take place) in a single encounter. We will see how the more complex rate laws arise from multiple elementary processes.

2 Zero Order Reactions, n= X d Differential form: Integrated form: Units of k: mol dm 3 s 1 Half-life (t 1/2 ): 2k d d t k k dt t kt or t kt for t 2k k X k

3 First Order Reactions, n=1 Differential form: Integrated form: Integrating, [ ] X d[] dt k[] d [] d [] k[] or kdt dt [] t d[] [] kdt or ln kt [] [] [ ] which says that e kt t If X, then X t 1 1 e kt

4 First Order Reactions (Figure 9.2) t e kt

5 First Order Reactions, n=1 Units of k: s 1 X ln2 kt e Half-life (t 1/2 ): (indep of []) k

6 Second Order Reactions, n=2 X d[] d t Differential form: 2 Integrated form: d 2 kt Integrating, t d kdt kt

7 Second Order Reactions, n=2 Rearranging, X 1 kt Units of k: dm 3 mol 1 s 1 Half-life (t 1/2 ): 1 k t 1/2 lengthens as is consumed

8 Compare 1 st and 2 nd order reactions with the same initial rates 2 nd Why is 2 nd order faster?

9 Second Order Reactions, n=2 nother form is + B X d k B dt We will encounter this form often in the case where [B] >> [] In this case, [B] cons t, so we can define k P = k[b], nd the result is a pseudo first-order reaction: d dt k B k p

10 Second Order Reactions, n=2 Rates vary enormously

11 Messy for higher order reactions

12 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 + scales as 1/k[]

13 [] X X X X X X X X X X ConcepTest X X X X 1 X X X X X X X X X X X X X X XXXXXXX X X X X X X What is X X the X X order X of this reaction? X X X X X X X X X X X. 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

14 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx The half-life of a first order reaction is constant, independent d of reactant concentration

15 Elementary Reactions Elementary reactions occur in a single encounter Unimolecular: Rate = k[] Bimolecular: + B Rate = k[][b] Termolecular: + B + C Rate = k[][b][c] Termolecular reactions are rare; higher molecularities are unknown. For elementary reactions For elementary reactions, reaction order is replaced by molecularity

16 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

17 ConcepTest 2 Which of the following reactions is almost certainly not an elementary reaction?. H 2 S + O 2 H 2 O + SO B. CH 4 + F HF + CH 3 C NO NO 2NO C. NO + NO 3 2NO 2 D. He + + N 2 N + + N + He

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 + P + B P + 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.

19 Rate laws + P + B P + B + B P d dt d dt d k k 2 B k B 2 dt Generally not an elementary Rx Case 1: 1 1 kt Case 2: if [B] >> [], then [B] is essentially constant, and [B] e k t Pseudo first order reaction

20 Reaction Mechanism 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 im is consistent it t with rate law and other experimental observations (generally found from rate limiting (slow) step(s) mechanism can be supported but never proven