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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
t
A
t
B
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
1. Graph [ ] vs. time2. Take slope at various pts3. Evaluate rate for various concentrations
[N2O5]
(M)
Rate (M/s)
1.0 2
0.5 1.0
0.25 0.5
Graphical Analysis
When concentration is halved… Rate is halved Order = 1 Rate = k[N2O5]1
[NO2]
(M)
Rate (M/s)
1.0 2
2.0 8
4.0 32
Graphical Analysis
When concentration is doubled… Rate is quadrupled Order = 2 Rate = k[N2O5]2
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 0.1 2
0.1 0.2 4
0.2 0.2 6
[NH4] [NO2-] Rate
0.1 0.1 2
0.1 0.2 4
0.2 0.2 8
[NH4] [NO2-] Rate
0.1 0.1 2
0.1 0.2 4
0.2 0.2 6When [NO2] doubles, rate doubles,
First order with respect to (wrt) NO2
m = 1
When [NO2] doubles, rate doubles,
First order with respect to (wrt) NO2
n = 1
Rate = k[NH4+] [NO2-]
Try this one:
Rate = k [NO2-]2
[NH4+] [NO2
-] Rate (M/s)
0.1 0.1 2
0.1 0.2 8
0.2 0.2 8
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:
][][
Akt
A
0]ln[]ln[ AktA 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:
2][][
Akt
A
0][
1
][
1
Akt
A
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:
kt
A
][
0][][ AktA 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
kk
A
A
693.0ln(2)t
ktln(2) )][
][2ln(
)y
xln(ln(y)-ln(x) :Remember
0
0
,)2
][ln(]ln[
]ln[)2
][ln(
]ln[)2
][ln(
]ln[]ln[
00
00
00
0
ktA
A
ktAA
AktA
AktA
Half-Life
First order
Second order
Zero Order
kt
693.02/1
02/1 ][
1
Akt
k
At
2
][ 02/1
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