Ch 15 Kinetics: The Study of Reaction Rates

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Ch 15 Kinetics The Study of Reaction Rates

• Brady Senese, 4th Ed.

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15.1 Introduction

• Rate of Reaction is the relationship between
  changes in concentration and time. The speed
  of a reaction
• Because reactions often occur in a series of
  steps, we study the mechanism- that is to say
  the series of reactions that leads to the overall
  change

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Collision Theory of Reactions

• In order for a reaction to occur, three
  conditions must be met
• The particles must collide
• The energy of the collision must be sufficient to
  break necessary bonds and initiate the reaction
  Fig 15.12 p. 672
• The particles must be oriented properly so that
  the new bonds can be established. Fig 15.9 p.670

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15.2 Factors affecting reaction rate

• Chemical nature
• Bond strengths
• General reactivity
• Ability to establish contact with one another
• Physical state
• Surface area for liquids, solids, and
  heterogeneous mixtures (fig 15.3)
• Amount of Mixing
• Particle shape/size

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Factors (continued)

• Concentration of reactants
• Molarity for solutions
• Pressure effects for gases
• Volume effects for gases
• Temperature- the 10 rule (fig 15.10)
• Catalysts (fig 15.16)

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15.3 Measuring Rates

• Units of M/s
• Can be measured using the change in concentration
  of any substance in the reaction
• Rates based on each substance related by the
  stoichiometric coefficients of the reaction.
• May be measured in three ways
• instantaneous rate
• average rate
• initial rate

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Rates and Coefficients

• Examine the reaction aA bB ?dD
• The stoichiometric relationship between
  substances A and B is given as ab
• This means that for every a mol A consumed, so
  also must b moles B be consumed.
• Since the units of concentration are M/s, the
  mole ratio allows us the relate the rate as it
  applies to any other compound in the reaction.
• RateA(b/a)RateB

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In the reaction 2A 3B ?5D

• We measured the rate of disappearance of
  substance A to be 3.5(10-5)M/s. What is the rate
  of appearance of D?
• .

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Initial Rate

• Initial RateThe slope of the line connecting the
  start to the reaction end coordinates

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Average Reaction Rates

• Average rate of reaction
• The slope of the line connecting the starting and
  ending coordinates for a specified time frame

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Instantaneous Reaction Rates

• Instantaneous Rate the slope of the tangent to
  the curve
• The slope of the line tangent to the curve at a
  specific time.

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Fig 15.2
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Reaction Rate

• Since the rates differ according to
  stoichiometry, the Reaction rate is often used.
• The Rrxn matches that of the substance with the
  lowest coefficient.
• Convert the measured rate to the Rrxn

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15.4 Reaction Rate Law Rate (M/s)kRxtntorder

• k is a reaction rate constant, a measure of
  time efficiency. (high values of k mean high
  efficiency). k varies with temperature and
  stoichiometry.
• Determined by running the reaction under the same
  conditions, varying only the concentrations of
  reactants. Each experiment has its own rate
  law.
• Ratio of rate laws for each experiment allows us
  to determine the orders of each reactant.

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Rates the factors controlling them. 2NO(g)
O2(g) ? 2NO2(g)

• Every set of conditions for a reaction can be
  recorded using a rate law RatekReactantsorder
  
• The rate law is unique to temperature and
  concentration conditions. For each set of data
  shown, a rate law can be written.

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Find order for first reactant (con)

• To solve such a problem, we ratio the rate laws.
  Select 2 rate laws that vary in concentration for
  only one of the substances. If we choose 1 2.
  ks are constant if the temperature is
  constant.

Ex. 2NO(g) O2(g) ? 2NO2(g) Rate Law 1
.024M/sk.015NO.015O2 Rate Law 2
.096M/sk.030NO.015O2 Rate Law 3
.048M/sk.015NO.030O2 Rate Law 4
.192M/sk.030NO.030O2
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Find order for O2 (con p.2)
Ex. 2NO(g) O2(g) ? 2NO2(g) Rate Law 1
.024M/sk.0152.015O2 Rate Law 2
.096M/sk.0302.015O2 Rate Law 3
.048M/sk.0152.030O2 Rate Law 4
.192M/sk.0302.030O2

• Now choose 2 rate laws whose O2 is changing,
  and, preferably whose NO is not. Since we know
  the exponent on NO, at this stage it doesnt
  matter. If we choose 1 3

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Orders

• Orders are indicated for each reactant
• They indicate the degree of resistance to
  reaction.
• The overall reaction order is the sum of
  individual reactant orders
• Orders may be negative, fractional or integers.
  In this course we will usually encounter positive
  integers.
• They must be determined from experimental data!

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Determine the value of k

• At this stage, we can solve for k. Use any rate
  law and substitute the now known orders.

Ex. 2NO(g) O2(g) ? 2NO2(g) Rate Law 1
.024M/sk.0152.0151 Rate Law 2
.096M/sk.0302.0151 Rate Law 3
.048M/sk.0152.0301 Rate Law 4
.192M/sk.0302.0301
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Rate law overview

• Rate laws relate the rate of the reaction to the
  reactant concentrations used for a given set of
  conditions.
• Because the value of k varies with temperature,
  so will the rate law.

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Integrated Rate Laws

• Integrated rate laws tell us how the reactant
  concentration varies with time during the course
  of a reaction.
• Derived from one-reactant systems and a plot of
  the relationships of reactant and time.
• Plot vs time
• Plot ln vs time
• Plot 1/ vs time

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Graphical Determination of Order
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Zero Order Reactions relate rxtnt to time

• A plot of vs time will be linear.
• The equation of the line will be as shown.
• Diffusion controlled.
• Rate is independent of concentrations of
  reactants
• Still require reactants!!!!!
• Usually fast reactions in viscous media

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First Order Graph-relates ln A to time.
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First Order Reactions aA -gt Product

• Rate(M/s)kA1
• Typically these reactions are decomposition type,
  or radioactive decay.
• If the rate law is specified as dA/dtkA or
  Integrating the equation gives us

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Plot of 1/ vs time describes 2nd Order
reaction.

• Are of several types RatekA2, RatekA1B1
  and RatekA2B0, etc
• Integrating the equation

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Half-Life of First Order Rxn

• In monitoring decay processes, in lieu of k, a
  half-life (t 1/2) is often recorded.
• t 1/2 is the time needed for exactly half of the
  substance to decay. At this time, AtA0/2

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Relationship of t1/2 to k
At t1/2, A0/2At
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Second Order Half-Life

• Dependent on the amount present at the start of
  the time period.
• What is the relationship between k and t1/2 for
  this reaction type?

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15.6 Reaction Mechanisms

• Tell what happens on the molecular level, and in
  what order
• Tell us which steps in a reaction are fast and
  slow
• Rate determining step (RDS) is the slowest step
  of the reaction. Accounts for most of the rxn
  time.
• Elementary steps sum to the overall reaction.

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Elementary Steps
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Sample Mechanism

• The reaction mechanism that has been proposed for
  the decomposition of H2O2 is
• H2O2 I- ? H2O IO- (slow)
• H2O2 IO- ? H2O O2 I- (fast)

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Potential Energy Diagrams

• Demonstrate the energy needs and products as a
  reaction proceeds.
• Tell us whether a reaction is exothermic or
  endothermic
• Tell us if a reaction occurs in one step or
  several steps
• Show us which step is the slowest

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Potential Energy Diagrams
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Features of PE Diagrams
Activation Energies
Activated Complexes
Product Energy
P.E.
Enthalpy of reaction
Reactant Energy
Reaction Coordinate (progress of reaction)
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15.7 Temperature Effects

• Changes in temperature affect the rate constant,
  k, according to the Arrhenious equation

• Where p is the steric factor
• Z is the frequency of collisions.
• Ea is the activation energy
• R is the Ideal Gas Constant (8.314 J/mol K)
• T is the temperature (K)

• A is the frequency factor

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Working with the Arrhenious Eqn.

• Linear Form To determine the Ea and A value

Ratio form Can be used when A isnt known.
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15.8 Rate laws and Mechanisms

• The slowest step in the reaction is termed the
  rate determining step (RDS)
• Because the majority of the reaction time is
  taken by the RDS, those substances which appear
  in the RDS have the greatest effect on the rxn
  rate.
• The observed rate law usually appears to be the
  rate law based on the RDS, where the order of
  each rxtnt is its stoichiometric coefficient.

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Mechanisms 1

• The reaction A 3 B ? D F was
  studied and the following mechanism was finally
  determined
• A B b C (fast)
• C B D E (slow)
• E B F (very fast)
• The step with largest activation energy is

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Mechanisms2

• Suppose the reaction A B ? D followed
  the mechanism
• A B ? C (fast)
• C ? D (slow)
• The rate law for the reaction would be

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Catalysts

• Are used to speed a reaction, but are not
  consumed by the reaction
• May appear in the rate law
• Lower the Ea for the reaction.
• May be heterogeneous or Homogeneous

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15.9 Catalytic Actions

• May serve to weaken bonds through induction
• May serve to change polarity through
  amphipathic/surfactant effects
• May reduce geometric orientation effects
• Are consumed in one step and regenerated in a
  subsequent step

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Heterogeneous catalysts