Chemical Kinetics

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Chemical Kinetics

• Chapter 16

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Thermodynamics Vs. Kinetics

• Thermodynamics - Will the reaction happen under
  specified Conditions?
• Thermodynamics and Equilibrium - What will be the
  extent of the reaction?
• Kinetics - How quickly will the reaction occur?
• Kinetics - What factors will affect the rate of
  reaction?

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The Rate of Reaction

• Rate of Reaction describes how fast reactants
  are used up and how products are formed
• Chemical Kinetics The study of the rates of
  reactions, what affects them, and the mechanisms
  (steps) in which they occur.

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The Rate of Reactions

• Rates are expressed as (?molarity / ?time)
• Problem you need a way to track the change in
  molarity over time!
• Titration following the acid concentration
• Light absorption over time may change
• Change in pressure over time

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The Rate of Reaction

• One Step Mechanism simplest Case
• A(g) ? B(g) C (g)
• The rate is proportional to the concentration of
  the reactant
• R ? A or R kA
• K specific rate constant
• 2nd equation only valid at given temperature

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The Rate of Reaction

• 2A(g) ? B(g) C(g) (coefficients not one)
• R ? A2 or R kA2
• The reaction is second order with respect to A
• This relationship is found experimentally
• These relationships are only true for simple one
  step mechanisms most are NOT

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The Rate of Reaction

• Rate Law Expressions found only through
  experimentation, not through inspection of
  balanced equations.
• Variation on rate law expression
• aA bB ? cC dD
• (-1/a) ?A / ?t
• (-1/b) ?B / ?t
• ( 1/c) ?C / ?t
• ( 1/d) ?D / ?t

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Factors Affecting the Rate of Reaction

1. The nature of the reactants
2. The state of matter (temperature related)
3. Allotropic Form of matter
4. Diamond vs. graphite, similar ?G values, but
   oxidation of graphite is very rapid

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Factors Affecting the Rate of Reaction

• Chemical Identity
• Mg vs. Na in water (sodium has lower ionization
  energy)
• Particle size of the solid
• Greater surface area in smaller particles can
  speed up the reaction
• Pulverize the solid
• Make an aqueous solution
• Evaporate a liquid

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Factors Affecting Reaction Rate

• Concentration effect is summarized in the rate
  law expression.
• Increasing the concentration of reactants
  increases the frequency of the collisions and
  therefore affects the rate of reactions

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The Rate of Reaction

• 2A(g) B (g) ? 3C(g)
• R k Ax By
• X is the order of reaction with respect to A
• Y is the order of reaction with respect to B
• The overall rate of reaction is x y

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Factors Affecting Reaction Rate

• As slope changes, so does the rate of reaction.
• Concentration affects the rate.
• Rate is considered an instantaneous measurement.
• Generally, we measure the initial rate of
  reaction.

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Example aA bB ? cC
Experiment Initial A Initial B Rate of Formation of C M/s
1 0.10M 0.10M 2.0 x10-4
2 0.20M 0.30M 4.0 x 10-4
3 0.10M 0.20M 2.0 x 10-4
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Example

• What is the order of reaction with respect to
  A?
• What is the order of reaction with respect to
  B?
• If the rate is reported as the rate of formation
  of C, what would be the rate of disappearance of
  A?

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Example 2 aA bB ? cC
Experiment Initial A Initial B Rate of reaction M/s
1 0.20 0.050 4.0 x10-3
2 0.80 0.050 1.6 x10-2
3 0.40 0.200 3.2 x10-2
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Example 2

• What is the order of reaction with respect to
  A?
• What is the order of reaction with respect to
  B?
• If the rate is reported as the rate of formation
  of C, what would be the rate of disappearance of
  A?

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Integrated Rate Law Equation

• First Order Reaction aA ? products
• R kA
• First order in A, 1st order overall
• The Integrated Rate Equation is
• ln(Ao/A) akt
• Rearranged lnAo lnA akt
• lnA -akt lnAo
• Y mx b

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Plot of lnA vs Time
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First Order Reaction
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Integrated Rate Equations

• First Order Reactions
• Useful to approximate the time when half of the
  reactants are used up because the rate slows down
  considerably!
• Rearrange the equation to solve for T
• T(1/ak) (lnAo/A)

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Integrated Rate Equations

• When A ½ Ao
• T1/2 (1/ak) (lnAo/1/2Ao)
• T1/2 (1/ak) ln 2 0.693/ak
• ?for 1st order reactions only, t1/2 depends only
  on the constant and does not change as the
  reaction progresses.
• Practical Example Half-life!

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Example 3

• Cyclopentane decomposes to propene in a 1st order
  reaction. K 9.2 s-1 at 1000oC.
• A) calculate the half life at this temperature.
• B) How much of a 3.0g sample is left after 0.50
  seconds? (assume grams are in the same
  proportionality as molarity)

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Second Order Reactions

• R kA2
• If a reaction is second order to a particular
  reactant and second order overall, the Integrated
  Rate Equation is
• 1/A 1/Ao akt
• At t1/2 A 1/2Ao
• 1/(1/2)Ao 1/Ao akt(1/2)
• 2/Ao 1/Ao akt(1/2)
• 1/Ao akt(1/2) and t1/2 1/akAo
• Concentration varies with each passing time
  periodconcentration dependant!

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Second Order Reaction

• The Half life of a second order reaction depends
  on the initial concentration at the beginning of
  THAT time period.

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Example 4

• CH3CHO (g) ? CH4 (g) CO (g)
• R CH3CHO2 and k 2.0 x 10-2 L/mole hr at
  527oC
• a) What is the half life if 0.10 mol is injected
  into a 1.0L vessel?
• b) How many moles of CH3CHO remain after 200
  hours?

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Second Order Reaction
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Zero Order Reactions

• Zero Order Reaction aA ? products
• R k
• Integtrated Rate Law
• A Ao akt
• At t1/21/2Ao Ao akt
• T1/2 Ao / 2ak

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Zero Order Reaction
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Zero Order Reactions
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Graphical Review

• Can you pick out which is Zero, First, and Second
  Order?

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Rate Law R k R kA R kA2
Units of k M/t 1/time 1/Mt
Reg. IRE A Ao akt ln(Ao/A) akt 1/A 1/Ao akt
IRE ymxb
S.L.Graph A vs. t lnA vs.t 1/A vs. t
Slope -ak -ak ak
T1/2 Ao/2ak .693/ak 1/akAo
y int. Ao lnAo 1/Ao
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Investigating Factors Affecting Reaction Rate

• Collision Theory, Transition State Theory,
  Temperature, Catalysts and Activation Energy

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Collision Theory

• Generally, any factor which increases the number
  of molecular or ionic collisions in solution will
  increase the rate of reaction
• Stirring
• Temperature
• Concentration
• Not Every Collision will guarantee a reaction!
  Orientation of the collision often affects the
  outcome!

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Transition State Theory

• Transition State short lived high energy
  complex between reactant and product.

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Exothermic Reaction
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Endothermic Reaction
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Transition State

• Ea forward Ea reverse ?E rxn
• Activation energy is generally kinetic energy,
  when equal or greater to the Ea, the reaction
  will proceed, if not, the reaction will not
  proceed.

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Effect of Temperature

• k increases with kelvin
• Theoretical Explanation
• Best model to explain is collision theory
• Kinetic molecular theory says the faster the
  particles move, the more they will collide

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Effect of Temperature

• Observed reaction doesnt increase with
  temperature as fast as the expected number of
  collisions

• Solution
• Arrhenius 1880
• Not all collisions are effective, there must be a
  minimum amount of energy which must be present
  (Ea)

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Effect of Temperature

• effective collisions total collisions
  (e(-Ea/RT))
• Total collisions Z
• -Ea/RT fraction of collisions with Ea or
  greater at a given temperature

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PROBLEM!

• Number of observed collisions were less than
  calculated
• ? many of the collisions were ineffective due to
  orientation.
• Fudge Factor P
• P steric factor (lt1) fraction of collisions
  with correct orientation

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Arrhenius Equation

• k Z p (e(-Ea/RT))
• Z and p combined into ultimate fudge factor A
  (frequency factor)
• k A (e(-Ea/RT))
• Alternate form
• lnk -Ea/RT lnA
• Y m x b

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Alternate Form 2

• Ln(k1/k2) -Ea/R (1/T1 1/T2)
• Use to directly calculate the effect of
  temperature on the rate constant!

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Catalysts

• Catalysts substances added to a reaction which
  provide an alternative pathway to the reaction,
  thus lowering the activation energy for the
  reaction.
• Heterogeneous catalysts exist in the different
  state as the reactants.
• Homogeneous catalysts exists in the same state
  as the reactants.

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• Lowers Ea by facilitating the breaking of bonds
• Increases the rate of reaction

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Catalysts

• Heterogeneous works by contact (contact
  catalyst)
• Adsorbtion reactant comes in contact with the
  catalyst
• Desorbtion newly formed product separates from
  the catalyst.
• Page 692 graphic!

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Catalysts

• Enzymes natural protein based catalysts
• Work on same principles
• Enzyme-substrate complex provides the alternative
  pathway to high energy biological processes.

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Reaction Mechanisms

• Writing Rate Laws for Multi-Step Reactions

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Reaction Mechanisms Vocabulary

• Reaction Mechanisms series of elementary steps
  by which a reaction occurs.
• Elementary Step a reaction whose rate law can
  be written from its molecularity (the number of
  species that must collide to produce the reaction
  of the elementary step)
• Reaction Intermediate a product that is
  immediately consumed in a subsequent reaction.

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PROBLEM!!!

• Sometimes problems are given where the overall
  reaction does not seem to match the rate law
• NO2 (g) CO (g) ? NO (g) CO2 (g)
• Rate law given as R kNO22
• There must be an explanation!

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Multi Step Reactions

• NO2 (g) CO (g) ? NO (g) CO2 (g)
• Rate law given as R kNO22
• Step 1 - NO2(g) NO2(g) ? NO3(g) NO(g)
• Step 2 - NO3(g) CO (g) ? NO2(g) CO2 (g)
• Step 1 and 2 are elementary steps and each has
  their own rate constant
• The elementary steps (when summed) must give the
  overall balanced reaction equation
• The rate law for the slow step must agree with
  the experimentally determined rate law

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Summary
Elementary Step Molecularity Rate Law
A ? prod Unimolecular R kA
AA ? prod Bimolecular R kA2
A B ? prod Bimolecular R kAB
2A B ? prod Trimolecular R kA2B
A B C ? prod Trimolecular R kABC
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Rate Determining Step

• Slow step rate determining step
• Most reactions are multiple step reactions
• Reactions can never occur faster than its slowest
  step
• If Step 1 is the slow step, then CO2 can only be
  produced as fast as NO3 is produced
• The overall rate k1NO22

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Reaction Mechanisms

• Deduction of Rate Mechanism
• Experimentally determine the rate law
• Propose mechanisms using two rules
• Devise experiment to eliminate less likely
  possibilities.

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Example

• 2NO2(g) F2(g) ? 2NO2F(g)
• Rate kNO2F2
• Possible Mechanisms
• Step 1 NO2 F2 ? NO2F F Slow?
• Step 2 F NO2 ? NO2F Fast?
• Is this an acceptable mechanism?
• Steps add up.
• Does the rate law agree with the rate law of the
  slow step? (R k1NO2F2)

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Exceptions

• See Page 683 yellow box.
• Particularly true of reactions ? third order
  because the tri molecular collisions arent
  likely to occur frequently!
• These reactions are generally explained with
  mechanisms where tri molecular collisions do not
  occur.

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Example

• 2NO (g) Br2 (g) ? 2NOBr (g) R kNO2Br
• NO Br2 ? NOBr2 (Fast Equ. Step)
• NOBr2 NO ? 2NOBr (Slow)
• Slow Step R2 k2NOBr2NO
• R1f R2f as it is at equilibrium

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Example Continued

• k1f NOBr2 k1RNOBr2 rearrange
• NOBr2 (k1f /k1R) NOBr2
• R2 k2NOBr2NO substitute NOBr2
• Overall R k2 (k1f /k1R) NO Br2 NO

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Example Continued

• k2 (k1f /k1R) overall rate constant k
• ?R k2 (k1f /k1R) NO Br2 NO
• R k NO2 Br2
• Consistent with the overall rate law