Kinetics Reaction rate (speed) Measure of how [ ] changes over time rate = [ ] = M/s t A  B Write a formula to show rate of reaction with respect to A? to B? If [A]0 = 1 M, and after 20 s the [A] goes to 0.45 M, what is the rate of the reaction?

What happens to rate as reaction proceeds? Does this make sense? Time, s [A], M Rate, M/s 1.0 M In 1st 20 s = 0.28 20 0.45 M In 2nd 20 s = 0.12 40 0.21 M In 3rd 20 s = 0.006 60 0.09 M In 4th 20 s = 0.0025 80 0.041 M What happens to rate as reaction proceeds? Does this make sense? What would graph look like of [A] vs. time? How can you use the graph to find instantaneous rate?

2 NO2  2 NO + O2 What happens to [NO2] over time? [NO] and [O2]? How does the rate of NO2 decrease compare to rate of NO formation? to that of O2 formation? From this, we get Law of Mass Action a A + b B  c C + d D rate = - 1 [A] = - 1 [B] = + 1 [C] = + 1 [D] a t b t c [t] d t

Concentration Affects Rate Study how [ ] affects rate using Method of Initial Rates: Measure [R] decreasing over time or [P] increasing over time NH4+ + NO2-  N2 + 2 H2O Expt [NH4+]0, M [NO2-]0, M rate0, M/s 1 0.01 0.2 5.4x10-7 2 0.02 10.8x10-7 3 0.04 21.5x10-7 4 0.0202 5 0.0404 21.6x10-7 6 0.0808 43.4x10-7

We found that r0  [NH4+] and [NO2-] Can express the relationships with rate law expressions. rate law expressions show how rate depends on [ ] with something called order We will discuss 0, 1st and 2nd order 1st order: rate is directly prop to [ ] if double [ ], rate doubles. If triple [ ], rate triples, etc. 0 order: rate is independent of [ ] If double [ ], rate same. If triple [ ], rate same. 2nd order If double [ ], rate increases by factor of 4. If triple [ ] , rate increases by factor of 9.

Rate Law Expressions rate = k [R1]order[R2]order = k [A]x[B]y… k = rate constant. units depend on rxn order (next slide) Write the rate law expression for our example. Order of the reaction is  individual orders What is the reaction order for our example?

NH4+ + NO2-  N2 + 2 H2O Determine the value of k NH4+ + NO2-  N2 + 2 H2O Determine the value of k. What are the units of k? If [NH4+] = 0.10 M and [NO2-] = 0.10 M, what is the rate of the reaction with units? Expt [NH4+]0, M [NO2-]0, M rate0, M/s 1 0.01 0.2 5.4x10-7 2 0.02 10.8x10-7 3 0.04 21.5x10-7 4 0.0202 5 0.0404 21.6x10-7 6 0.0808 43.4x10-7

rate constant, k Units tell order Units? 0 order: r = k [A]0 1st order: r = k [A]1 2nd order: r = k [A]2 3rd order: r = k[A]3 99th order? Magnitude tells about rate Large k (109 or higher) means… Small k (10 or lower) means… k affected by temp and catalyst only (to be continued)

A + B  C Write the rate law expression. [A], M [B], M r0, M/s 0.1 4x10-5 0.2 16x10-5 Write the rate law expression. What is the overall order of the reaction? What is value of k with units? What is the rate when [A] = 0.05 M and [B] = 0.10 M?

We have looked at how [ ] affects rate. We can also write expressions that are a function of time = Integrated Rate Laws We will study integrated rate law expressions for 0, 1st, and 2nd order. We will also look at the graphs associated with these expressions.

0 order Integrated Rate Law

1st order Integrated Rate Law

2nd order Integrated Rate Law

Problem to Try Decomposition of an insecticide at 12oC follows 1st order kinetics. The rate constant for this reaction is k = 1.45 yr-1. A lake has had the insecticide dumped into it and the [insecticide] = 5.0x10-7 g/cm3. What is [insecticide] after 1 year? How long to decrease [ ] to 3.0x10-7 g/cm3?

Problem #2 What is the order of this reaction? How to find k? What units for k?

Half Life Expressions, t1/2 From integrated rate laws can find half life of reaction t1/2 is the time it takes for ½ [A]0 to decrease [A] = [A]0/2 0 order 1st order 2nd order

What Influences Rate? Rate is dependent on Nature of Reactants (s, l, g) (powder vs. chunk) As increase surface area, increase rate b/c … [R]: as determined by order In general, as ↑[R], ↑rate b/c… Temperature In general, as ↑T, ↑rate b/c… Catalyst Add catalyst, ↑rate b/c…

Further info for Temp/Catalyst Collision Theory: for a reaction to occur Molecules/R’s must collide Need enough energy to get effective collision (similar to threshold E for promoting e-) = EA Need proper orientation (alignment of orbitals) Example with chalk and desk Which of these would temp influence? What about catalyst?

Collision Theory AB + C → A + BC Must break AB bond and make BC bond At some point, get activated complex/transition state (*) ABC EA is the energy to reach the activated complex (next slide) Rate depends on EA (if increase EA, rate will likely decrease)

Reaction Profiles

Add Catalyst How would reaction profile change if add catalyst?

Catalyst and Rxn Mechanisms Increase rate by lowering EA and/or aligning things better and/or provide a new pathway of lower energy. Note: cat both a R and P (A + cat  B + cat) Reaction pathway = Rxn Mechanism Shows all steps involved to convert R to P Some reactions are simple, 1 step mechanisms; others are not

Reaction Mechanisms If rxn occurs in 1 step = elementary rxn If rxn requires more than 1 step = non elementary Molecularity is determined by #R’s A  B unimolecular A + B  C bimolecular A + B + C  D termolecular 2 A  B bimolecular Reactions that are termolecular and higher are not elementary (involve multistep mechanisms)

Rxn Mechanisms A + B  C + D Molecularity? This reaction occurs in two steps: A + A  E + C E + B  A + D Does NIE match? Note: E formed in one step and consumed in a subsequent step = intermediate (not transition complex) The A that you crossed off could be an example of _________________

EP Diagram Why two peaks? How many EA? Label them. Where are reactants? Where are products? Any transition states? How many? Label them. Intermediates?

Problem 2 O3 (g)  3 O2 (g) Might occur in 2 steps: O3  O2 + O O3 + O  2 O2 What is molecularity for each step? Confirm NIE. Identify intermediates if there are any. Evidence of a catalyst?

Can determine rate law expression from rxn mechanism If rxn is elementary, rate law is based on molecularity A  B uni, so 1st order: rate = k [A]1 A + B  C rate = ? 2A + B  C rate = ? If rxn is not elementary, uglier (next slides)

Not Elementary Two scenarios Slow step is first step Slow step is not first step Note: slow step is rate determining step

Slow Step is First Step Treat mechanism as elementary since slow step is rate determining step, the other steps don’t matter for determining the overall rate of rxn If we treat this step as elementary, molecularity becomes order Ex. Decomp of N2O is a 2 step process as follows: N2O  N2 + O (slow) N2O + O  N2 + O2 (fast) Write NIE. Identify intermediates. Identify any catalyst. What is the rate law expression?

Slow Step is Not 1st Step 2 NO + Br2  2 NOBr Experimental rate law is r = k [NO]2[Br2] Could this be an elementary (one step) rxn? Why or why not?

Alternate mechanism is NO + Br2 NOBr2 (fast) NOBr2 + NO  2 NOBr (slow) Any intermediates? Write a rate law expression from slow step. Notice: intermed in the rate expression (not allowed). Remove using the fast equil.

H2 + 2 ICl  I2 + 2 HCl Proposed Mech H2 + ICl  HI + HCl HI + ICl  I2 + HCl Write NIE. Identify intermediates. If step 1 is slow and step 2 fast, write rate law. If step 1 is fast equil and step 2 is slow, write rate law.

2 NO + Cl2 2 NOCl A graph of 1/[NO] vs time is linear with a positive slope. Can the following mechanism work? If so, is the first step slow or a fast equil? NO + Cl2  NOCl2 NOCl2 + NO  2 NOCl