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 ti i di t d ( ) i i l t W ill 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 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 Understanding the nature of the elementary reactions and the role of elementary reactions in complex processes will occupy us until spring break.
Transcript
Rate LawsWe have seen how to obtain the differential form of rate lawsbased upon experimental observation. As they involve derivatives,we must integrate the rate equations to obtain the timew mu g qu mdependence 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 ti i di t d ( ) i i l t W ill 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 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 Understanding the nature of the elementary reactions and the role of elementary reactions in complex processes will occupy us untilspring break.
Rate Lawsn C H polyethylenen C2H4 polyethylene
Definitely a composite reaction, telling essentially nothingabout the reaction mechanism!about the reaction mechanism!Definitions:
A cti n m ch nism is s i s f l m nt st ps th tA reaction mechanism is a series of elementary steps thatfully describe the overall composite reaction.
Elementary steps are very “simple” single step reactionsElementary steps are very simple single step reactionswhere the underlying physics of is well understood. Wellunderstood is a concept that depends on your point of view.
The composite reaction gives the overall stoichiometry, butmight well not show the actual processes. We need the elementary steps for that!elementary steps for that!
First, what is a reaction mechanism in more detail?
Reaction Mechanism
A detailed sequence of elementary steps for a reaction
Reasonable mechanism:
1 Elementary steps sum to the overall reaction1. 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.
Types of Elementary ReactionsClassified 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) COMMONx mpl di cti d cexample – radioactive decay
2. Molecularity = 2 (two molecules) COMMON
3 Molecularity = 0 (catalyzed rxn large excess of catalyst) HAPPENS3. Molecularity = 0 (catalyzed rxn, large excess of catalyst) HAPPENS
4. Molecularity = 3 (three molecules collide and react) VERY RARE
5. Molecularity > 3 ESSENTIALLY NEVER OBSERVED5. Molecularity 3 ESSENTIALLY NEVER OBSERVED
These reactions occur at rates that relate to the molecularity,and thus share rate laws with composite reactions. BUT, thep ,composite reactions have empirically determined rates,not necessarily related to molecularity.
Composite Reactionsp
Composite reactions involve two or more Composite reactions involve two or more elementary steps
reaction is constant, independent of reactant concentration
Half-lives of higher reactions
The rate of a zeroth order reaction is c nst nt ind p nd nt f is constant, independent of
reactant concentration
The half-life of a first order reaction is constant, independent p
of reactant concentration
The half-life of a second order reaction A+A scales as 1/k[A]
Elementary ReactionsElementary Reactions
Elementary reactions occur in a single encounter
Unimolecular: A Rate = k[A]
Elementary reactions occur in a single encounter
Bimolecular: A + B Rate = k[A][B]
Termolecular: A + B + C Rate = k[A][B][C]Termolecular: A B C Rate k[A][B][C]
Termolecular reactions are rare;higher molecularities are unknown.
For elementary reactionsFor elementary reactions,“reaction order” is replaced by “molecularity”
Back to integrated rate laws
Now that we know about elementary reactions, we can lookat how the integrated rate laws might apply to elementaryprocesses First we would write the three 2nd order rxns asprocesses. First, we would write the three 2 order rxns as
A + A P
A B PThe first two are 2nd order from thisperspective while the third is a three-A + B P
A + B + B P
perspective, while the third is a threebody (3rd order) process, and much lesscommon.
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