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Reaction Rates: How fast reactions occur Kinetics Reaction Rates: How fast reactions occur

How do we measure rxn rates? Rates must be measured by experiment Indicators that a reaction is happening Color change Gas evolution Precipitate formation Heat and light Many ways to measure the rate Volume / time Concentration / time Mass / time Pressure / time

How do we measure rxn rate? A  B How fast product appears How fast reactant disappears

Forward vs Reverse Rxn Some rxns are reversible After a sufficient amount of product is made, the products begin to collide and form the reactants We will deal only w/ rxns for which reverse rxn is insignificant 2 N2O5(aq)  4 NO2(aq) + O2 (g) Why is reverse rxn not important here?

Rate Law Math equation that tells how reaction rate depends on concentration of reactants and products Rates = k[A]n K = rate constant / proportionality constant n = order of reaction Tells how reaction depends on concentration Does rate double when concentration doubles? Does rate quadruple when concentration doubles?

2 kinds of rate laws Both determined by experiment Differential Rate Law How rate depends on [ ] Integrated Rate Law How rate depends on time

Differential Rate Law 2 methods Graphical analysis Method of initial rates

Graphical Analysis Graph [ ] vs. time Take slope at various pts Evaluate rate for various concentrations

Graphical Analysis When concentration is halved… [N2O5] (M) Rate (M/s) Rate is halved Order = 1 Rate = k[N2O5]1 [N2O5] (M) Rate (M/s) 1.0 2 0.5 0.25

Graphical Analysis When concentration is doubled… [NO2] (M) Rate (M/s) Rate is quadrupled Order = 2 Rate = k[N2O5]2 [NO2] (M) Rate (M/s) 1.0 2 2.0 8 4.0 32

Method of Initial Rates Initial rate calculated right after rxn begins for various initial concentrations NH4+(aq) + NO2-(aq)  N2(g) + 2H2O(l) Rate = k [NH4+]n[NO2-]m [NH4+] [NO2-] Rate (M/s) 0.1 2 0.2 4 8

Rate = k[NH4+] [NO2-] [NH4] [NO2-] Rate 0.1 2 0.2 4 8 [NH4] [NO2-] When [NO2] doubles, rate doubles, First order with respect to (wrt) NO2 n = 1 When [NO2] doubles, rate doubles, First order with respect to (wrt) NO2 m = 1 Rate = k[NH4+] [NO2-]

Calculate k, using any of the trials, you should get the same value Try this one: [NH4+] [NO2-] Rate (M/s) 0.1 2 0.2 8 Rate = k [NO2-]2 Calculate k, using any of the trials, you should get the same value

Integrated Rate Law Tells how rate changes with time Laws are different depending on order Overall reaction order is sum of exponents Rate = k  zero order Rate = k[A]  first order Rate = k[A]2  second order Rate= k[A][B]  second order

First order integrated rate law Rearrange and use some calculus to get: This is y = mx + b form A plot of ln[A] vs time will give a straight line If k and [A]0 (initial concentration) known, then you know the concentration at any time

Second order integrated rate law Rearrange and use some calculus to get: This is y = mx + b form A plot of 1/[A] vs time will give a straight line If k and [A]0 (initial concentration) known, then you can now the concentration at any time

Zero order integrated rate law Rearrange and use some calculus to get: This is y = mx + b form A plot of [A] vs time will give a straight line If k and [A]0 (initial concentration) known, then you can now the concentration at any time

Graphs give order of rxn Use graphs to determine order If [A] vs time = zero order If ln [A] vs time = first order If 1/ [A] vs time = second order

Half-life Def’n: time it takes for concentration to halve Depends on order of rxn At t1/2 [A]=[A]0/2

Half-life: First order

Half-Life First order Second order Zero Order