General Chemistry - 3e - Hill/Petrucci

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Chapter 14Chemical Kinetics
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• Chemical kinetics is the study of
• - The rates of chemical reactions
• - The factors (variables) that affect rates
• - The reaction mechanisms
• Variable in Reaction Rates
• - Concentrations of reactants
• - Temperature
• - Surface area
• - Catalysts
• - Inhibitors

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Contents in Chapter 14
14-1 Rate of a Chemical Reaction 14-2 Measuring
Reaction Rates 14-3 Effect of Concentration on
Reaction Rates The Rate Law 14-4 Zero-Order
Reactions 14-5 First-Order Reactions 14-6 Second-O
rder Reactions 14-7 Reaction Kinetics A
Summary 14-8 Theoretical Models for Chemical
Kinetics 14-9 The Effect of Temperature on
Reaction Rates 14-10 Reaction Mechanisms 14-11 Cat
alysis
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14-1 Rate of a Chemical Reaction

• Rate of a chemical reaction the change in
  concentration for formation of product or
  disappearance of reactant per unit of time.
• Unit in general mol L1 s1 (M s1)

Example 2 Fe3(aq) Sn2(aq) ? 2 Fe2(aq)
Sn4(aq) and, 38.5 s after reaction starts,
Fe2 0.0010 M
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• General rate of reaction
• (average rate of reaction)

Example 2 Fe3(aq) Sn2(aq) ? 2 Fe2(aq)
Sn4(aq) and, 38.5 s after reaction starts,
Fe2 0.0010 M
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14-2 Measuring Reaction Rates

• Decomposition of H2O2 For Example
• H2O2(aq) ? H2O(l) ½ O2(g)
• Monitoring H2O2 disappearance for example
• remove small samples of the reaction mixture
  then titration with KMnO4
• 2MnO4-(aq) 5H2O2(aq) 6H(aq)
• ? 2Mn2(aq) 8H2O(l) 5O2(g)

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• Example of experimental data and derived rate data

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• Graphical representation and explanation

Average rate The concentration change in a given
time interval (dash)
Initial rate The instantaneous rate at t 0.
(black)
Instantaneous rate The slope of the tangent to
the curve at a precise point in the reaction.
(blue)
Raw data (red)
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14-3 Effect of Concentration on Reaction
Rates The Rate Law

• Rate law (rate equation)
• An expression for a reaction relates the
  reaction rate to the concentrations of the
  reactants.
• For a hypothetical reaction
• aA bB ? gG hH
• Rate law for this reaction can be expressed as
• Rate of reaction kAmBn
• A and B The molarities of the reactants.
• m and n Reaction order of A and B,
  respectively.
• m n Overall order of reaction
• k Rate constant
• Exponents m and n are determined by experiment,
  irrelevant to the stoichiometric coefficients a
  and b.

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• Units for rate constants M(1 overall reaction
  order) s1

Overall order Of Reaction Unit for k
Zero M s1
First s1
Second M1 s1
Third M2 s1
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• Distinction between rate and rate constant
• Rate of a reaction The change in concentration
  with time. Except for zero-order reaction, the
  rate of a reaction varies as concentration vary.
• Rate constant Remains constant throughout a
  reaction, regardless of the initial
  concentrations of the reactants
• Value of the rate constant (k) depends on
• The specific reaction
• The temperature
• The presence or absence of a catalyst.

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• Method of initial rates
• A method of establishing the rate law for a
  reaction, i.e., finding the values of the
  exponents in the rate law, and the value of k.
• (It is performed by a series of experiments in
  which the initial concentration of one reactant
  is varied, other reactants are held constant.)

Double the concentration of a reactant A, if
reaction is zero-order in A no effect on rate.
(20) first-order in A the rate doubles
(21). second-order in A the rate quadruples
(22). third-order in A the rate eightfold (23)
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Example of Establishing a Rate Law
For the reaction 2 HgCl2(aq) C2O42(aq) ? 2
Cl(aq) 2 CO2(g) Hg2Cl2(s) Experimental
results
Experiment Initial HgCl2 Initial C2O42 Initial rate, Ms1
1 0.105 M 0.15 M 1.8105
2 0.105 M 0.30 M 7.1105
3 0.052 M 0.30 M 3.5105
Solution rate of reaction kHgCl2mC2O42n
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(Continuous)

• Comparing Exp. 2 and Exp.3
• Rate2/Rate3 2 21 HgCl2Exp2/HgCl2Exp3m
  2m, m 1
• Order in HgCl2 is 1.
• Comparing Exp. 1 and Exp.3
• Rate2/Rate1 4 22 C2O42Exp2/C2O42Exp1
  n 2n, n 2
• Order in C2O42 is 2.
• The rate law of this reaction is
• Rate k HgCl2C2O422
• Overall order of this reaction is 3.
• Calculate the rate constant (k), e.g., from
  Exp.1

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14-4 Zero-Order Reactions

• Rate of reaction remains constant (independent of
  the concentration of the reactant)
• Concentration versus time is a straight line with
  a negative slope.

A0 at tf

• Integrated rate law equation of zero order
  reaction
• At kt A0
• Half-life of zero order reaction t½ A0/2k
• Half-life ( t½ ) The time in which one-half of
  the reactant originally present is consumed.

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(Continuous)

• Integrated rate law (equation) Derived from a
  rate law (equation) by the calculus technique of
  integration. It relates the concentration of a
  reactant to elapsed time from the start of a
  reaction.

• Zero-order integrated rate law derivation
• A ? products, the rate can be expressed as

y mx b
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14-5 First-Order Reactions
First- order integrated rate law derivation
Ao initial conc. of A At conc. of A at time
"t" k rate constant
or
Finally,

• Integrated rate law equation of first-order
  reaction
• lnAt kt lnA0
• y mx b

• Half-life of first-order reaction

t½ 0.693/k
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Example Decomposition of H2O2
2H2O2(aq) ? 2H2O(l) O2(g)
lnAt kt lnA0 y mx b
It is a first-order reaction!!
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Skilled your calculator!!
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14-5 (Continuous)

• Reaction involving gases

Example
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14-5 (Continuous)
The constancy of the half-life is proof that the
reaction is first order.
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14-5 (Continuous)

• Examples of first-order reactions

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14-6 Second-Order Reactions
Second- order integrated rate law derivation

• Integrated rate law equation of second-order
  reaction

• Half-life of second-order reaction

A B ? C, i.e., Rate kAB, tedious work, no
further discussion in this course
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14-6 (Continuous)

• Pseudo First-Order Reactions

For example CH3COOCH2CH3 H2O ? CH3COOH
C2H5OH The molarity of the water remains
essentially constant throughout the reaction
(55.5 M). The reaction appears to be zero order
in H2O, first order in CH3COOCH2CH3. First order
overall.
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14-7 Reaction Kinetics A Summary

• Determine the order by straight line
• A vs time zero order
• lnA vs. time first order
• 1/A vs. time second order

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14-8 Theoretical Models for Chemical Kinetics

• Collision Theory The rate of a reaction is
  proportional to the number of effective collision
  per unit of volume per unit of time.

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(Continuous)

• Variables for effective collisions
• Activation energy (Ea) the minimum energy that
  must be supplied for an effective collisions,
  i.e., for a reaction to occur.
• Temperature effect increasing temperature
• increases molecules with enough KE to react
• increases the collision frequency.
• Spatial orientations (steric factor).

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(Continuous)

• Temperature effect Distribution of Kinetic
  Energies of Molecules

At the higher temperature T2 (red), the fraction
is considerably larger than at the lower
temperature T1 (blue).
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(Continuous)

• Spatial orientation effect

Orientation is not a factor
Orientation is an important factor
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(Continuous)

• Steric factor The probability of favorable
  orientations of colliding molecules.

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14-8 (Continuous)

• Transition state theory The theory assumes a
  chemical equilibrium between reactants and
  activated complex in transition state, and the
  theory can explains the reaction rates as well as
  the elementary step of a chemical reactions.
• Transition state An intermediate state between
  the reactants and products.
• Activated complex An intermediate in a chemical
  reaction formed through collisions.
• Reaction profile A graphical representation of a
  chemical reaction in terms of the energies of the
  reactants, activated complex(es), and products.

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(Continuous)
Activated complex
Partial bond
Heat of reaction, ?H Ea(forward) Ea(reverse)
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14-9 The Effect of Temperature on Reaction Rates

• Arrhenius equation for the rate constant (k)
• k Zope-Ea/RT Ae-Ea/RT
• A frequency factor, expression of collision
  frequency (Z0) and steric factor (p) , i.e., the
  number of collisions per unit volume per unit
  time that are capable of leading to reaction.
• e-Ea/RT fraction of collisions with sufficiently
  energetic to produce a reaction.
• Ea activation energy (kJ/mol)
• R gas constant (8.3145 J/K?mol)
• T absolute temperature (K)

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Extending of the Arrhenius equation

• When plotting ln k (y) vs. 1/T (x)

k AeEa/RT
y mx b where m Ea/R
Ea (mR) (slope)R

• Rates at different temperature

or
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14-10 Reaction Mechanisms

• Reaction mechanism A set of elementary processes
  by which a reaction is proposed to occur.
• A proposed mechanism must
• consistent with the experimentally determined
  rate law.
• consistent with the stoichiometry of the overall
  reaction.
• Steps in the study of a reaction mechanism
• 1. Measuring the reaction rate
• 2. Formulating the rate law
• 3. Postulating plausible reaction mechanism

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(Continuous)

• Elementary process A single step at the
  molecular level in the progress of the overall
  reaction.
• Molecularity The number of free atoms, ions, or
  molecules that collide or dissociate in an
  elementary reaction.

Molecularity Reactant(s) in elementary step Image
Unimolecular one
Bimolecular Two
Termolecular three
unfavorable
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• Rate-determining step The elementary process in
  establishing the rate of the overall reaction. It
  is usually the slowest step.
• Intermediate A substance that is produced in one
  elementary process in a reaction mechanism and
  consumed in another elementary process.
• The intermediate does not appear in the overall
  reaction.
• Catalyst A substance that increase the rate of a
  reaction without itself being consumed in the
  overall reaction.
• A catalyst changes a reaction mechanism with a
  lower activation energy.
• The catalyst does not appear in the overall
  reaction.

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• Mechanism-with a slow step followed by a fast step

• Q For the reaction
• Experiment resulted in rate law Rate
  kH2ICl
• Postulating a possible mechanism.
• Possible mechanism

Step 1
(slow, rate determine step)
Step 2
(fast)
Overall

• Step 1 consist with the rate law rate
  k1H2ICl kH2ICl.
• HI is the intermediate in this reaction.

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(Continuous)
Reaction profile
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• Mechanism-with a fast reversible step followed by
  a slow step

• Q For the reaction 2NO(g) O2(g) ? 2NO2(g)
• Experiment resulted in rate law Rate
  kNO2O2
• Intermediate N2O2 is detected during the
  experiment.
• Postulating a possible mechanism.
• Possible mechanism

(fast)
Step 1 2NO N2O2
(slow, rate determine step)
Step 2 N2O2 O2 2NO2
Overall 2NO(g) O2(g) ?? 2NO2(g)
Step1 represent a fast reaching dynamic
equilibrium k1NO2 k1N2O2 or N2O2
(k1/k1)NO2 Substitute into step 2
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• Smog-An Environmental Problem with Roots in
  Chemical Kinetics

A photochemical smog for example
PAN peroxyacetyl nitrate, a powerful lacrimator
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• Catalytic Converters
• A dual catalyst system for example

• 2CO(g) unburned hydrocarbons 2NO(g)
• 2CO2(g) 2N2(g)
• CO(g) unburned hydrocarbons O2(g)
• CO2(g) H2O(g)

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14-11 Catalysis

• The role of catalyst
• Catalyst increases the reaction rate without
  itself being used up in a chemical reaction.
• A catalyst works by changing the mechanism of a
  chemical reaction.
• The catalyst is consumed in one step of the
  mechanism, but is regenerated in another step.
• The pathway of a catalyzed reaction has a lower
  activation energy than that of an uncatalyzed
  reaction, i.e., more molecules at a fixed
  temperature have the necessary activation energy.

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• Homogeneous Catalysis (reactants and catalyst are
  in single phase)
• Example for homogeneous catalysis

- The reactants and products of this reaction are
all present throughout the solution, or
homogeneous mixture.
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• Heterogeneous Catalysis (reactants and catalyst
  are in different phases)
• Solid surface-catalyzed reaction for example, its
  catalytic processes involves
• (1) adsorption of reactants
• diffusion of reactants along the surface
• reaction at an active site to form adsorbed
  product
• desorption of the product.

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• Example for heterogeneous catalysis

(1)
(2)
(3) and (4)
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• Concentration of catalyst on reaction rate

• Neither catalyst (I) nor intermediate (OI)
  appear in the overall equation.
• Decomposition of H2O2(aq) is affected by the
  initial concentration of I.
• I is constant throughout a given reaction.

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• Enzymes as Catalysts
• Enzymes High-molecular-mass proteins, usually
  catalyze one specific reaction or a set of
  quite similar reactions but no others.
• The reactant called the substrate (S), attaches
  itself to an area on the enzyme (E) called the
  active site, to form an enzyme-substrate complex
  (ES).
• The rates of enzyme-catalyzed reactions are
  influenced by factors such as
• concentration of the substrate
• concentration of the enzyme
• acidity of the medium
• temperature.

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• Lock-and-key model of enzyme action

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• Mechanism of enzyme Kinetics

High S V k, zero order
Low S V kS, first order
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• The Steady-State Steady-State Approximation

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End of Chapter 14