Chemical Kinetics

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Chapter 14

• Chemical Kinetics

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Chemical Kinetics

• Study of rxn rates (how fast rxn progresses)
• Measured in ?X/?t
• Also deals with reaction mechanisms
• Steps rxn goes through to move from reactants to
  products

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Factors That Influence Reaction Rate
Under a specific set of conditions, every
reaction has its own characteristic rate, which
depends upon the chemical nature of the reactants.

• Four factors can be controlled during the
  reaction
• Concentration - molecules must collide to react
• Physical state - molecules must mix to collide
• Temperature - molecules must collide with enough
  energy to react
• The use of a catalyst.

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Expressing Rxn Rates

• Rates are expressed in some unit quantity per
  time
• SI units for rates of distance (speed) are in m/s
• Chemical rxn rate units are M/s
• Consider the rxn A?B
• Rxn rates given can be initial, instantaneous,
  or average

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Expressing Rate
The numerical value of the rate depends upon the
substance that serves as the reference. The rest
is relative to the balanced chemical equation.
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Practice
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The Rate Law

• The rate law governs the progress of a given rxn.
• For a general rxn aA bB ? cC dD
• The rate law is given by the equation below
• Rate kAxBy,
• k rate constant x y are rxn orders wrt A B
• All components of a rxns rate law must be
  determined experimentally
• Measure physical quantity that you can relate to
  the concentration of a reactant either _at_ a
  specific instant (initial rate method) or over
  time (integrated rate law)

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Determining Rate Laws

• The Initial rate method
• Used to determine rxn orders experimentally
• Measure initial rate of rxn _at_ different reactant
  concentrations
• Data is listed in a table
• Ratio data, in general rate law form, from 2
  lines in the table to determine order of each
  reactant in rxn
• Choose lines where conc. reactant in question
  changes and conc. of all other reactants stays
  the same

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Practice
Initial Reactant Concentrations (mol/L)
Initial Rate (mol/Ls)
Experiment
O2
NO
1
1.10x10-2
1.30x10-2
3.21x10-3
2
2.20x10-2
1.30x10-2
6.40x10-3
3
1.10x10-2
2.60x10-2
12.8x10-3
4
3.30x10-2
1.30x10-2
9.60x10-3
5
1.10x10-2
3.90x10-2
28.8x10-3

1. Determine the general rate law for the rxn.
2. Calculate the rate constant for experiment 2.

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The Rate Constant

• Specific for a particular rxn at a particular
  temperature, within experimental error
• Units for k tell you the overall rxn order
• Remember units for rate are M/time
• Units for Ax are Mx
• For a rxn with an overall order R, the unit for k
  can be found by

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The Integrated Rate Law

• Can be used for 2 reasons
• Determine reactant concentration after an elapsed
  time--- must know order of reactant, rate
  constant, correct formula
• Determine rxn order for a specific reactant---
  must graph different quantities vs. time and see
  which gives most linear plot
• Can only be used for 0, 1st, and 2nd order rates

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Integrated Rate Law Formulas Plots
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Practice
PROBLEM
Determine the rxn order for N2O5 using the
graphical data given
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Reaction Half-Life

• Time required for reactant concentration to reach
  ½ its initial value

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The Arrhenius Equation

• Describes the relationship between temperature
  and rxn rate
• Higher T ? Larger k ? Increased/faster rate
• Smaller Ea ? Larger k ? Increased/faster rate
• Lower Ea (or T) ? Smaller k ? Decreased/slower
  rate
• A is related to both the collision frequency an
  orientation probability factor (dependent on
  structural complexity)

where k is the kinetic rate constant at T
Ea is the activation energy
R is the energy gas constant
T is the Kelvin temperature
A is the collision frequency factor
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Activation Energy

• Energy that must be overcome for reactants to
  form products
• All rxns regardless of initial and final energies
  have Ea gt 0
• Some bonds must break and new bonds must form
• Reactant molecules gain this energy through
  collisions with one another
• Increasing temperature increases rate as
  collisions and energy of collisions increase

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Practice
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Reaction Energy Diagrams

• Used to depict changes reactant molecules undergo
  to form products

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Reaction Mechanism

• Sequence of single rxn steps that sum to the
  overall rxn
• It is impossible to prove rxn mechanism
  experimentally
• Rxn energy diagrams can elucidate steps in a
  mechanism
• Steps in a mechanism for an overall rxn are
  elementary steps in which the coefficients of
  each reactant denote the reaction rate order wrt
  the reactant
• The sum of all reactant coefficients in an
  elementary step denote the molecularity of the
  step
• The higher the molecularity of an elementary
  step, the slower its rate

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2NO2(g) F2(g) ? 2NO2F(g)

• Experimental rate law determined
• rate kNO2F2
• Accepted mechanism
• NO2(g) F2(g) ? NO2F(g) F(g)
• NO2(g) F(g) ? NO2F(g)

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Correlating Mechanism w/ Rate Law

• For a mechanism to be reasonable, its elementary
  steps must meet 3 criteria
• Elementary steps must add up to overall balanced
  eqtn
• Elementary steps must be physically reasonable
  (usu. bi- or lower molecularity)
• Mechanism must correlate with the rate law
• Overall rate law is usually equivalent to the
  slowest steps (the rate limiting step, RLS) rate
  law
• RLS can be picked out in a rxn energy diagram and
  predicted in a mechanism

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Practice

• The rxn and rate law for the decomposition of
  dinitrogen pentoxide are
• 2N2O5(g)? 4NO2(g) O2(g) rate kN2O52
• and the rxn energy diagram is given above.
  Which of the following
• mechanisms is most likely?
• One-step collision C. 2N2O5(g) ? N4O10(g)
  fast N4O10(g) ? 4NO2(g) O2(g)
  slow
• 2N2O5(g) ? N4O10(g) slow
• N4O10(g) ? 4NO2(g) O2(g) fast

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Catalysis

• Increasing rxn rate by adding a catalyst
• Catalyst function
• Lowers Ea increases k without being consumed or
  changing product amount
• Usually lowers Ea by providing a different
  mechanism