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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Chapter 15 Kinetics

• The speed with which the reactants disappear and
  the products form is called the rate of the
  reaction
• A study of the rate of reaction can give detailed
  information about how reactants change into
  products
• The series of individual steps that add up to the
  overall observed reaction is called the reaction
  mechanism

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• There are five principle factors that influence
  reaction rates
• Chemical nature of the reactants
• Ability of the reactants to come in contact with
  each other
• Concentration of the reactants
• Temperature
• Availability of of rate-accelerating agents
  called catalysts

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• Chemical nature of the reactants
• Bonds break and form during reactions
• The most fundamental difference in reaction rates
  lie in the reactants themselves
• Some reactions are fast by nature and others slow
• Ability of the reactants to meet
• Most reactions require that particles (atoms,
  molecules, or ions) collide before the reaction
  can occur
• This depends on the phase of the reactants

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• In a homogeneous reaction the reactants are in
  the same phase
• For example both reactants in the gas (vapor)
  phase
• In a heterogeneous reaction the reactants are in
  different phases
• For example one reactant in the liquid and the
  second in the solid phase
• In heterogeneous reactions the reactants meet
  only at the intersection between the phases
• Thus the area of contact between the phases
  determines the rate of the reaction

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Effect of crushing a solid. When a single solid
is subdivided into much smaller pieces, the total
surface area on all of the pieces becomes very
large.
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• Concentration of the reactants
• Both homogeneous and heterogeneous reaction rates
  are affected by reactant concentration
• For example, red hot steel wool bursts into
  flames in the presence of pure oxygen
• Temperature of the system
• The rates for almost all chemical reactions
  increase as the temperature is increased
• Cold-blooded creatures, such as insects and
  reptiles, become sluggish at lower temperatures
  as their metabolism slows down

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• Presence of a catalyst
• A catalysts is a substance that increases the
  rate of a chemical reaction without being
  consumed
• Enzymes are biological catalysts that direct our
  body chemistry
• A rate is always expressed as a ratio
• One way to describe a reaction rate is to select
  one component of the reaction and describe the
  change in concentration per unit of time

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• Molarity (mol/L) is normally the concentration
  unit and the second (s) is the most often used
  unit of time
• Typically, the reaction rate has the units

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• By convention, reaction rates are reported as a
  positive number even when the monitored species
  concentration decreases with time
• If the rate is known with respect to one species,
  the coefficients of the balanced chemical
  equation can be used to find the rates with
  respect to the other species

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• Consider the combustion of propane
• Compared to the rate with respect to propane
• Rate with respect to oxygen is five times faster
• Rate with respect to carbon dioxide is three
  times faster
• Rate with respect to water is four times faster
• Since the rates are all related any may be
  monitored to determine the reaction rate

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Learning Check

• In the reaction 2A 3B ?5D We measured the rate
  of disappearance of substance A to be
  3.510-5M/s. What is the rate of appearance of
  D?
• In the reaction 3A 2B ?C, we measured the rate
  of B. How does the rate of C relate?

8.7510-5 M/s
Rate of C1/2 rate of B
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• A reaction rate is generally not constant
  throughout the reaction
• Since most reactions depend on the concentration
  of reactants, the rate changes as they are used
  up
• The rate at any particular moment is called the
  instantaneous rate
• It can be calculated from a concentration versus
  time plot

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The progress of the reaction A ? B. The number of
A molecules (in red) decreases with time while
the number of B molecules (in blue) increases.
Some reaction rates are not dependent on the
concentrations
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Instantaneous Rates Changes With Time

• As reactants are consumed , the reaction slows
• The process of determining rates is important for
  reproducibility

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The Rate Law Depends On The Concentrations Used

• rate kreactantorder
• k is a reaction rate constant, a measure of time
  efficiency. (high values of k mean high
  efficiency).
• k must be determined experimentally
• Each experiment has its own rate law
• The rate law must be determined experimentally

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Learning Check

• The rate law for the reaction 2A B?3C is
• rate 0.045M-1s-1 AB
• if the concentration of A is 0.2M and that of B
  is 0.3M, what will be the reaction rate?

rate0.045 M-1 s-1 0.20.3
rate0.0027 M/s
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Determining The Rate Law

• Determined by running the reaction under the same
  conditions, varying only the concentrations of
  reactants
• A ratio of rate laws for each experiment allows
  us to determine the orders of each reactant
• The rate law is unique to temperature and
  concentration conditions
• The rate law cannot be predicted from the
  chemical equation, but must be determined
  experimentally

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Orders

• Are indicated for each reactant
• The overall reaction order is the sum of
  individual reactant orders
• May be negative, fractional or integers, but in
  this course we will usually encounter positive
  integers
• Must be determined from experimental data

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• The rate of a homogeneous reaction at any instant
  is proportional to the product of the molar
  concentrations of the reactants raised to a power
  determined from experiment

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• Consider the following reaction
• From experiment, the rate law (determined from
  initial rates) is
• At 0oC, k equals 5.0 x 105 L5 mol-5 s-1
• Thus, at 0oC

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• The exponents in the rate law are generally
  unrelated to the chemical equations coefficients
• Never simply assume the exponents and
  coefficients are the same
• The exponents must be determined from the results
  of experiments
• The exponent in a rate law is called the order of
  reaction with respect to the corresponding
  reactant

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• For the rate law
• We can say
• The reaction is first order with respect to
  H2SeO3
• The reaction is third order with respect to I-
• The reaction is second order with respect to H
• The reaction order is sixth order overall
• Exponents in a rate law can be fractional,
  negative, and even zero

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Use Rate Laws To Determine Orders

• Suppose the experimental concentration-rate data
  for five experiments is

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• For experiments 1, 2, and 3 B is held constant,
  so any change in rate must be due to changes in
  A
• The rate law says that at constant B the rate
  is proportional to Am

Thus m1
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Use Rate Laws To Determine Orders 2NO(g)
O2(g) ? 2NO2(g)

• Select 2 rate laws that vary in concentration for
  only one of the substances
• Next choose 2 rate laws where the unknown changes
• Since we know the exponent on the other, at this
  stage it doesnt matter if it changes

ratekNO2O2
y1
x2
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Determining The Value Of k

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

ratekNO2O2
0.048M/s k0.015M20.015M
1.410-4 M-2s-1 k
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• The relationship between concentration and time
  can be derived from the rate law and calculus
• Integration of the rate laws gives the integrated
  rate laws
• Integrate laws give concentration as a function
  of time
• Integrated laws can get very complicated, so only
  a few simple forms will be considered

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Zero-Order Reactions

• Ratek
• Plot of reactant vs. time will be linear
• The equation of the line will be AA0-kt
• A amount remaining after elapsed time, t.
• Aooriginal amount
• Diffusion controlled - usually are fast reactions
  in viscous media
• Rate is independent of concentrations of
  reactants, but the reaction still requires
  reactants

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Learning Check

• The rate law for the reaction of A?B is zero
  order in A and has a rate constant of 0.02 M/s.
  If the reaction starts with 1.50 M A, how much is
  present 15 seconds after the reaction begins?

• AA0-kt
• A1.3M

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Learning Check

• The rate law for the reaction of A?2B is zero
  order in A and has a rate constant of 0.12 M/s.
  If the reaction starts with 1.50 M A, after what
  time will the concentration of A be 0.90M?

• AA0-kt
• t5 s

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First Order Reactions

• RatekA1
• 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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Learning Check

• The radioactive decay of a new atom occurs so
  that after 21 days, the original amount is
  reduced to 33. What is the rate constant for
  the reaction in s-?

k 0.0528 da-1
k 6.1110-7 s-1
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• Graphical methods can be used to determine the
  first-order rate constant, note

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• A plot of lnAt versus t gives a straight line
  with a slope of -k

The decomposition of N2O5. (a) A graph of
concentration versus time for the decomposition
at 45oC. (b) A straight line is obtained from a
logarithm versus time plot. The slope is negative
the rate constant.
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• The amount of time required for half of a
  reactant to disappear is called the half-life,
  t1/2
• The half-life of a first-order reaction is not
  affected by the initial concentration

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Half-Life Of First Order Rxn

• In monitoring decay processes, a half-life (t
  1/2) is often recorded, rather than k. (carbon
  dating)
• t 1/2 is the time needed for exactly half of the
  substance to decay. At this time, AA0/2

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Learning Check

• The half-life of I-132 is 2.295h. What
  percentage remains after 24 hours?

A .0711
0.302 h-1 k
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Second Order Reaction

• Are of several types RatekA2, RatekA1B1
  and RatekA2B0, etc
• The integrated equation is of the form

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Learning Check

• The rate constant for the second order reaction
  2A?B is 5.310-5 M-1s-1. What is the original
  amount present if, after 2 hours, there is 0.35M
  available?

A00.40 M
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Second Order Half-Life

• Depends 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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Learning Check

• The rate constant for a second order reaction is
  4.510-4 M-1s-1. What is the half-life if we
  start with a reactant concentration of 5.0 M?

t1/2 440 s 7.4 min
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Collision Theory Of Reactions

• For a reaction to occur, three conditions must be
  met
• Reactant particles must collide
• Collision energy must be enough to break
  bonds/initiate
• Particles must be oriented so that the new bonds
  can form

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• The minimum energy kinetic energy the colliding
  particles must have is called the activation
  energy, Ea
• In a successful collision, the activation energy
  changes to potential energy as the bonds
  rearrange to for products
• Activation energies can be large, so only a small
  fraction of the well-orientated, colliding
  molecules have it
• Temperature increases increase the average
  kinetic energy of the reacting particles

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• Transition state theory explains what happens
  when reactant particles come together
• Potential-energy diagrams are used to help
  visualize the relationship between the activation
  energy and the development of total potential
  energy
• The potential energy is plotted against reaction
  coordinate or reaction progress

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Formation of the activated complex in the
reaction between NO2Cl and Cl.
NO2ClCl?NO2Cl2
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Kinetic energy distribution for a reaction at two
different temperatures. At the higher
temperature, a larger fraction of the collisions
have sufficient energy for reaction to occur. The
shaded area under the curves represent the
reacting fraction of the collisions.
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• The activation energy is related to the rate
  constant by the Arrhenius equation
• k rate constant
• Ea activation energy
• e base of the natural logarithm
• R gas constant 8.314 J mol-1 K-1
• T Kelvin temperature
• A frequency factor or pre-exponential factor

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Working With The Arrhenius Equation

• Linear Form To determine the Ea and A value

Ratio form Can be used when A isnt known.
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Learning Check

• Given that k at 25C is 4.6110-1 M/s and that at
  50C it is 4.6410-1, what is the activation
  energy for the reaction?

208 J/molEa
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Reaction Mechanisms

• Tell what happens on the molecular level, and in
  what order
• Tell us which steps in a reaction are fast and
  slow
• The rate determining step is the slowest step of
  the reaction that accounts for most of the
  reaction time
• Elementary steps sum to the overall reaction

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Elementary Steps
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Intermediates And Catalysts

• Because catalysts interact with the reactant,
  they will appear in the mechanism recognizable by
  their presence in an early step and their
  regeneration in subsequent step
• Intermediates are temporary products recognizable
  by their formation in an early step and their
  subsequent reaction in a later step

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Learning Check

• The reaction mechanism that has been proposed for
  the decomposition of H2O2 is
• H2O2 I- ? H2O IO- (slow)
• H2O2 IO- ? H2O O2 I- (fast)
• Which is the rate determining step?
• Are there any intermediates?

step 1
IO-
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Rate Laws And Mechanisms

• The majority of the reaction time is taken by the
  rate determining step
• Those substances which appear in this step have
  the greatest effect on the reaction rate
• The observed rate law usually matches the rate
  law based on the rate determining step where the
  order of each reactant is its stoichiometric
  coefficient

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Learning Check

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

ratekH2O2I-
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Learning Check

• The reaction A 3 B ? D F was
  studied and the following mechanism was finally
  determined
• A B ? C (fast)
• C B ? D E (slow)
• E B ? F (very fast)
• What is the expected rate law?

ratekCB or kAB2
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• Consider the reaction
• The mechanism is thought to be

• The second step is the rate-limiting step, which
  gives

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• N2O2 is a reactive intermediate, and can be
  eliminated from the expression
• The first step is a fast equilibrium
• At equilibrium, the rate of the forward and
  reverse reaction are equal

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• Substituting, the rate law becomes
• Which is consistent with the experimental rate law

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Catalysts

• 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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Catalytic Actions

• May serve to weaken bonds through induction
• May serve to change polarity through amphipathic
  / surfactant effects
• May reduce geometric orientation effects
• Heterogeneous catalyst reactant and product
  exist in different states.
• Homogeneous catalyst reactants and catalyst
  exist in the same physical state

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Heterogeneous catalysts