Chemical Kinetics including Arrhenius equation

Chemical Kinetics including Arrhenius equation

1. Temperature and Reaction Rates
ForthemajorityofreactionstherateincreaseswithT
k
T
Experimental observation
k= A exp(-B/T)
T
B
-lnA ln
T
B
- lnA - ln :logs taking
T
B
exp
A
:and
=∴
=






−=
k
k
k

2. lnk
1/T
Intercept= lnA
Slope = -B
In practice can only
measure over a limited
Temperature range
B is positive if rate increases with T

3. Van’tHoff Treatment
•JustasequilibriumconstantKvarieswithT,sodoesk
Remember?
•TemperaturedependenceofKisgivenby:
Considerthefollowingreaction:
C+D Y+Z
2
RT
U

dT
dlnK
ο
∆
=
k
1
k
-1

4. 2
1-1-
2
11
2
111-1
11
2
1-1
1-1
1-
1
1-
1
RT
E

dT
dln
RT
E

dT
dln
:equations 2 into splitting
RT

dT
dln
-
dT
dln

U
RT
U

dT
dln
-
dT
dln

ln - ln ln lnK and K
=
=
−
=∴
−=°∆
°∆
=∴
===
−
−
k
k
EEkk
EE
kk
kk
k
k
k
k

5. 





=






=






=
==∴
RT
E
-Aexp :Generally
RT
E
-expA
RT
E
-expA
:gives gintegratin
dT
RT
E
dln and dT
RT
E
dln
1-
1-1-
1
11
2
1-
1-2
1
1
k
k
k
kk
Thus, the experimentally determined term B is
related to an energy term associated with the reaction

6. Arrhenius Treatment
“Normalmoleculesexistinequilibriumwithactivated
molecules:Onlyactivatedmoleculesreact”
Eistheenergyrequiredtoformtheactivatedspeciesfrom
reactants
E=ActivationEnergy=E
A
TheArrheniusEquation






=
RT
E
-Aexp
A
k

7. Activation Energy
•Energylevelsofreactants,productsandactivatedspecies
duringareactionisrepresentedbyaPotentialEnergy
Diagram:
Energy
Reaction Co-ordinate
E
1
E
-1
∆U
o
C + D
Y + Z
Endothermic
Process
E
A≥∆U
o
Activated species

8. E
1=ActivationEnergyforforwardreaction
E
-1==ActivationEnergyforreversereaction
∆U
o
=E
1–E
-1
Remember:∆H=∆U+∆(PV)(≈0forsolidsandliquids)
∴∆Hcanbedetermined
Energy
Reaction Co-ordinate
Activated species
E
1
∆UC + D
Y + Z
E
-1
Exothermic
Process
E
A≤∆U
o

9. Determining E
A
Onlyobtainedbyexperiment
Measurekat2differenttemperatures








=








∴








−=








=
= 21
12A
1
2
12
A
1
2
2
A
22
1
A
11TT
T -T
R
E
ln
T
1

T
1
R
E
- ln and
phigher tem
RT
E
-lnA ln T
lower temp
RT
E
-lnA ln T
k
k
k
k
k
k

10. ConsiderareactionwithE
A=50kJmol
-1
.Whatistheeffectof
increasingTfrom300to310K?
rise ureK temperat 10every for doubled ist coefficien Rate
1.91

310 300
300 310
8.314
10 50
ln
1
2
3
1
2
=






×
−×
=
k
k
k
k

11. In-class Problem 21
The reaction 4A + 3B →2C +3D is first order in A and second order in B. The
measured rate coefficient is found to be 3.5×10
-6
dm
6
mol
-2
s
-2
at 300 K and
8.5×10
-6
dm
6
mol
-2
s
-2
at 310 K.
Calculate the activation energy.
Determine the rate coefficient at 330 K.

12. In-class Problem 22
The rate coefficient for a reaction at 30°C is measured to be exactly three times
that of the value at 20° C. Calculate the activation energy.

13. Graphical Method for Determination of Activation Energy
The following table shows the rate coefficients for the
rearrangement of methyl isonitrileat various temperatures
(a)From these data, calculate the activation energy for the
reaction.
(b)What is the value of the rate coefficient at 430.0 K?

14. Analyze and Plan:We are given the rate coefficients, k ,
measured at several temperatures. We can obtain E
Afrom the
slope of a graph of lnkversus1/T .Once we know E
Awe can use
the Arrhenius equation together with the given rate data to
calculate the rate coefficient at 430.0 K.
Solve:(a)Wemustfirstconvertthetemperaturesfromdegrees
CelsiustoKelvin.Wethentaketheinverseofeachtemperature,
1/Tandthenaturallogofeachratecoefficient,lnk.Thisgives
usthefollowingtable:

15. A graph of ln kversus 1/T results in a straight line

16. Theslopeofthelineisobtainedbychoosingtwowell-separated
points,asshown,andusingthecoordinatesofeach:
Becauselogarithmshavenounits,thenumeratorinthisequationis
dimensionless.Thedenominatorhastheunitsof1/Tnamely,K
-1
.Thus,the
overallunitsfortheslopeareK.Theslopeequals–E
A/R.Weusethevalue
forthemolargasconstantR=8.314J/molKandobtain
Divide by 1000 to convert to kJ

17. (b)Todeterminetheratecoefficient,k
1,atT
1=430Kwecanusethe
ArrheniusequationwithE
A=160kJ/mol,andoneoftherate
coefficientsandtemperaturesfromthegivendata,suchask
2=2.52×
10
-5
s
-1
andT
2=462.9K
Thus,
Notethattheunitsofk
1arethesameasthoseofk
2

18. In-class Problem 23
The thermal decomposition of ethanol (CH
3CHO) is a second order reaction.
Write down an expression for the rate of loss of ethanol in terms or reactant
concentration. The rate coefficients for the reaction at various temperatures were
measured as follows
Use a graphical method to determine the activation energy (in kJ mol
-1
)
and the pre-exponential factor (in dm
3
mol
-1
s
-1
)
T (°C) 427 487 537 637 727
k(dm
3
mol
-1
s
-1
)0.011 0.105 0.178 20.0 145.0

19. In-class Problem 24
The rate coefficients for the gas phase decomposition of ethane at various
temperatures were measured as follows
From the data determine the activation energy for the decomposition
and calculate the pre- exponential factor, A
k(s
-1
) 2.5×10
-5
8.2×10
-5
23.1×10
-5
57.6×10
-5
141.5× 10
-5
T (K) 823 843 863 883 903

20. The rate coefficient for the association of an inhibitor with carbonic anhydrase
was studied as a function of temperature.
Extra Problem 25
What is the activation energy for the reaction?
k(mol
-1
dm
3
s
-1
)1.04×10
-6
1.34×10
-6
1.53×10
-6
1.89×10
-6
2.29×10
-6
2.84×10
-6
T (K) 289.0 293.5 298.1 303.2 308.0 313.5