Chemical Kinetics

1
Chapter 14
Chemical Kinetics
2
Overview

• Reaction Rates
• Stoichiometry, Conditions, Concentration
• Rate Equations
• Order
• Initial Rate
• Concentration vs. Time
• First Order Rxns.
• Second Order Rxns.
• Graphical Methods

3
Contd

• Molecular Theory
• Activation Energy
• Concentration
• Molecular Orientation
• Temperature
• Arrhenius Equation
• Reaction Mechanisms
• Elementary Steps, Reaction Order, Intermediates
• Catalysts

4
Reaction Rates

• What Affects Rates of Reactions?
• Concentration of the Reactants
• Temperature of Reaction
• Presence of a Catalyst
• Surface Area of Solid or Liquid Reactants

5
Reaction Rates (graphical)

• Average Rate DM Dt

M
for reaction A ? B
DM
time
Dt
6
Rates

• for A ? B- DA DB Dt
  DtRate of the disappearance of A is equal in
  magnitude but opposite in sign to the rate of the
  appearance of B

7

• Average Rate--D mol (or concentration) over a
  period of time, Dt
• Instantaneous Rate-- slope of the tangent at a
  specific time, t
• Initial Rate-- instantaneous rate at t 0

M
tangent at time, t
t
time
8
Average Rate
Afinal time - Ainitial time
Dtfinal - Dtinitial
for A ? B
9
Instantaneous Ratetime, t slope of the
tangent at time t
M
tangent at time, t
t
time
10
Stoichiometry

• 4PH3 gt P4 6H2
• - 1DPH3 1 DP4 1 DH2
  4 Dt 1 Dt 6 Dt
• - DPH3 4 DP4 2 DH2
  Dt Dt 3 Dt

11
General Relationship

• Rate - 1 DA - 1 DB 1 DC
  1 DD a D t b D t c D t d D
  t aA bB ? cC dD

12
Conditions which affect rates

• Concentration
• concentration ? rate
• Temperature
• temperature ? rate
• Catalyst
• substance which increases rate but itself remains
  unchanged

13
Rate Equations

• aA bB ? xX rate law
  rate kAmBn
• m, n are orders of the reactants
• extent to which rate depends on concentration
• m n overall rxn order
• k is the rate constant for the reaction

14
Examples

• 2N2O5 gt 4NO2 O2 rate
  kN2O5 1st order
• 2NO Cl2 gt 2NOCl rate
  kNO2Cl2 3rd order
• 2NH3 gt N2 3H2 rate kNH30
  k 0th order

15
Determination of Rate Equations

• Data for A B gt C
• Expt. A B initial rate
• 1 0.10 0.10 4.02 0.10 0.20
  4.03 0.20 0.10 16.0
• rate kA2B0 kA2 k 4.0 Ms-1
  400 M-1s-1 (0.10)2 M2

16
Exponent Values Relative to DRate

• Exponent Value conc rate
• 0 double same 1 double double 2
  double x 4 3 double x
  8 4 double x 16

17
Problem

• Data for 2NO H2 gt N2O H2O
• Expt. NO H2 rate
• 1 6.4x10-3 2.2x10-3 2.6x10-5
  2 12.8x10-3 2.2x10-3 1.0x10-4
  3 6.4x10-3 4.5x10-3 5.0x10-5 rate
  kNO2H2

18
Units of Rate Constants

• units of rates M/s
• units of rate constants will vary depending on
  order of rxn M 1 (M)2 (M)
  for s sM2 rate
  k A2 B
• rate constants are independent of the
  concentration

19
Concentration vs. Time 1st and 2nd order
integrated rate equations

• First Order rate - DA k A
  D t
• ln At - kt A reactant A0
• or ln At - ln A0 - kt

20
Conversion to base-10 logarithms

• ln At - kt A0
• tolog At - kt A0
  2.303

21
Problem

• The rate equation for the reaction of sucrose in
  water is, rate kC12H22O11. After 2.57 h at
  27C, 5.00 g/L of sucrose has decreased to 4.50
  g/L. Find k. C12H22O11(aq)
  H2O(l) gt 2C6H12O6
• ln 4.50g/L - k (2.57 h) 5.00g/L
• k 0.0410 h-1

22
Concentration vs. Time

• Second Order rate - DA kA2
  Dt
• 1 - 1 kt At A0
• second order rxn with one reactant rate k
  A2

23
Problem

• Ammonium cyanate, NH4NCO, rearranges in water to
  give urea, (NH2)2CO. If the original
  concentration of NH4NCO is 0.458 mol/L and k
  0.0113 L/mol min, how much time elapses before
  the concentration is reduced to 0.300
  mol/L? NH4NCO(aq) gt (NH2)2CO(aq) rate
  kNH4NCO
• 1 - 1 (0.0113)
  t
• (0.300) (0.458)
• t 102 min

24
Graphical Methods

• Equation for a Straight Line
• y bx a
• lnAt - kt lnA0 1st
  order
• 1 kt 1 2nd
  order At A0

b slopea y interceptx time
25
First Order 2H2O2(aq) 2H2O(l)
O2(g)
H2O2
time
26
First Order 2H2O2(aq) 2H2O(l)
O2(g)
slope, b -1.06 x 10-3 min-1 - k
ln H2O2
time
27
Second Order 2NO2 2NO O2
1/NO2
slope, b k
time
28
Half-Life of a 1st order process
0.020 M
t1/2 0.693 k
M
0.010 M
0.005 M
t1/2
t1/2
time
29
Problem

• The decomposition of SO2Cl2 is first order in
  SO2Cl2 and has a half-life of 4.1 hr. If you
  begin with 1.6 x 10-3 mol of SO2Cl2 in a flask,
  how many hours elapse before the quantity of
  SO2Cl2 has decreased to 2.00 x 10-4 mol?
• SO2Cl2(g) gt SO2(g) Cl2(g)
  

30
Temperature Effects

• Rates typically increase with T increase
• Collisions between molecules increase
• Energy of collisions increase
• Even though only a small fraction ofcollisions
  lead to reaction
• Minimum Energy necessary for reactionis the
  Activation Energy

31
Molecular Theory (Collision Theory)
Activation Energy, Ea
DH reactionEa forward rxn.Ea reverse rxn.
Energy
Reactant
Product
Reaction Progress
32
Activation Energy

• Activation Energy varies greatly
• almost zero to hundreds of kJ
• size of Ea affects reaction rates
• Concentration
• more molecules, more collisions
• Molecular Orientation
• collisions must occur sterically

33
The Arrhenius Equation

• increase temperature, inc. reaction rates
• rxn rates are a to energy, collisions, temp.
  orient
• k Ae-Ea/RT
• k rxn rate constant
• A frequency of collisions
• -Ea/RT fraction of molecules with energy
  necessary for reaction

34
Graphical Determination of Ea

• rearrange eqtn to give straight-line eqtn
• y bx a
• ln k -Ea 1 ln A
  R T

slope -Ea/R
ln k
1/T
35
Problem

• Data for the following rxn are listed in the
  table. Calculate Ea graphically, calculate A and
  find k at 311 K.
• Mn(CO)5(CH3CN) NC5H5 gt Mn(CO)5(NC5H5)
  CH3CN
• ln k k, min-1 T (K) 1/T x 10-3
• -3.20 0.0409 298 3.35
• -2.50 0.0818 308 3.25
• -1.85 0.157 318 3.14

36
slope -6373 -Ea/REa (-6373)(-8.31 x 10-3
kJ/K mol) 53.0 kJ
y intercept 18.19 ln A
A 8.0 x 10 7
-3.20 -2.50 -1.85
ln k
k 0.0985 min-1
3.14 3.25 3.35 x 10-3
1/T
37
Problem

• The energy of activation for
• C4H8(g) gt 2C2H4(g)
• is 260 kJ/mol at 800 K and k 0.0315 sec
• Find k at 850 K.
• ln k2 - Ea (1/T2 - 1/T1) k1
  R
• k at 850 K 0.314 sec-1

38
Reaction Mechanisms

• Elementary Step
• equation describing a single molecular event
• Molecularity
• unimolecular
• bimolecular
• termolecular
• 2O3 gt 3O2
• (1) O3 gt O2
  O unimolecular(2) O3 O gt 2 O2
  bimolecular

39
Rate Equations

• Molecularity Rate Law
• unimolecular rate kA bimolecular rate
  kAB bimolecular rate kA2
  termolecular rate kA2B
• notice that molecularity for an elementary step
  is the same as the order

40
2O3 gt 3O2

• O3 gt O2 O rate kO3
• O3 O gt 2O2 rate kO3O
• 2O3 O gt 3O2 O
• O is an intermediate

41
Problem

• Write the rate equation and give the molecularity
  of the following elementary steps
• NO(g) NO3(g) gt 2NO2(g)
• rate kNONO3 bimolecular
• (CH3)3CBr(aq) gt (CH3)3C(aq) Br-(aq)
  
• rate k(CH3)3CBr unimolecular

42
Mechanisms and Rate Equations

• rate determining step is the slow step --the
  overall rate is limited by the ratedetermining
  step
• step 1 NO2 F2 gt FNO2 F rate
  k1NO2F2 k1 slow
• step 2 NO2 F gt FNO2 rate
  k2NO2F k2 fast
• overall 2NO2 F2 gt 2FNO2 rate
  k1NO2F2

43
Problem

• Given the following reaction and rate law
  NO2(g) CO(g) gt CO2(g) NO(g) rate
  kNO22
• Does the reaction occur in a single step?
• Given the two mechanisms, which is most
  likelyNO2 NO2 gtNO3 NO NO2 gt
  NO ONO3 CO gt NO2 CO2 CO
  O gt CO2

44
Reaction Mechanisms Equilibria

• 2O3(g) 3O2(g) overall rxn
• 1 O3(g) O2(g) O(g) fast
  equil. rate1 k1O3 rate2
  k2O2O
• 2 O(g) O3(g) 2O2(g)
  slow rate3 k3OO3
• rate 3 includes the conc. of an intermediate and
  the exptl. rate law will include only species
  that are present in measurable quantities

k3
45
Substitution Method

• at equilibrium k1O3 k2O2O
• rate3 k3OO3 O k1 O3
  k2 O2
• rate3 k3k1 O32 or k2 O2
• overall rate k O32 O2

substitute
46
Problem

• Derive the rate law for the following reaction
  given the mechanism step below
• OCl - (aq) I -(aq) OI -(aq)
  Cl -(aq)
• OCl - H2O HOCl OH -
  fast
• I - HOCl HOI Cl - slow
• HOI OH - H2O OI - fast

k3
k4
47
Contd

• rate1 k1 OCl -H2O
• rate 2 k2 HOClOH -
• HOCl k1OCl -H2O k2OH
  -
• rate 3 k3 HOClI -
• rate 3 k3k1OCl -H2OI - k2 OH
  -
• overall rate k OCl -I - OH -

solvent
48
Catalyst

• Facilitates the progress of a reaction
  bylowering the overall activation energy
• homogeneous
• heterogeneous

49
Ea
Ea
DHrxn
Energy
Reaction Progress
catalysts are used in an early rxn step but
regenerated in a later rxn step
50
Uncatalyzed Reaction
O3(g) ltgt O2(g) O(g)
O(g) O3(g) gt 2O2(g)
Catalyzed Reaction
Step 1 Cl(g) O3(g) O(g) gt ClO(g) O2(g)
O(g)
Step 2 ClO(g) O2(g) O(g) gt Cl(g)
2O2(g)
Overall rxn O3(g) O(g) gt 2O2(g)
51
Ea uncatalyzed rxn
Ea catalyzed rxn
Cl O3 O
ClO O2 O
Cl O2 O2