Ch 15 Rates of Chemical Reactions

Ch 15 Rates of Chemical Ch 15 Rates of Chemical ReactionsReactions

Chemical Kinetics is a study of the rates of chemical reactions.

Part 1 macroscopic levelwhat does reaction rate mean?how are reaction rates determined experimentally?how do factors like temp and conc influence rates?

Part 2 microscopic levelreaction mechanism detailed pathway taken by atoms and

molecules in the reaction in order to control the reaction

The rate of a chemical reaction is the change The rate of a chemical reaction is the change of concentration of a substance (reactant) per of concentration of a substance (reactant) per unit time.unit time.

Generally Generally conc reactant conc reactant

timetime

Slope of the line changes Slope of the line changes

When Conc is large, Time is small, When Conc is large, Time is small,

When Conc is small, Time is long.When Conc is small, Time is long.

Reaction Rate TermsReaction Rate Terms

Concentration in mol/L Concentration in mol/L [ square [ square brackets ]brackets ]

Changes Changes X = XX = Xfinal - final - XX initial initial

Units for reaction rates mol / L Units for reaction rates mol / L .. time time Rate Expression for this reactionRate Expression for this reaction

2 N2 N22OO55 -> 4 NO -> 4 NO2 2 + O + O22

1 1 [N[N22OO55]]1 1 [NO[NO22]][O[O22]]

4 4 t t 2 2 t t tt

For a chemical reaction to occur, reactants For a chemical reaction to occur, reactants must must physically collide, physically collide, with sufficient energy, with sufficient energy, With appropriate geometry With appropriate geometry For the reaction to occur. Rates are dependent For the reaction to occur. Rates are dependent

on these variables. on these variables.

Factors that affect the speed of a reactionFactors that affect the speed of a reaction

Concentration - greater concentration of Concentration - greater concentration of reactions results in the faster rate.reactions results in the faster rate.

Temperature - for endothermic reactions, Temperature - for endothermic reactions, faster moving molecules react at a faster rate.faster moving molecules react at a faster rate.

Catalyst - substances that accelerate a Catalyst - substances that accelerate a chemical reaction, but but are not transformed chemical reaction, but but are not transformed by the reaction.by the reaction.

Effect of Concentration on Reaction Effect of Concentration on Reaction RateRate

The rate of a reaction is proportional to the The rate of a reaction is proportional to the concentration of reactants concentration of reactants

aA + bB -> xXaA + bB -> xX Rate = k [A]Rate = k [A]mm[B][B]nn

k is the proportionality constant called k is the proportionality constant called the rate constantthe rate constant [A] and [B] are the concentrations of [A] and [B] are the concentrations of A and BA and B

m and n are determined experimentallym and n are determined experimentally

Rate = k [A]Rate = k [A]mm[B][B]nn

The order of a reactant is the exponent m or nThe order of a reactant is the exponent m or n The order of a reaction is the sum of the The order of a reaction is the sum of the

exponentsexponents If the exponent is 1, doubling the concentration, If the exponent is 1, doubling the concentration,

doubles the ratedoubles the rate If the exponent is 2, doubling the concentration, If the exponent is 2, doubling the concentration,

quadruples the rate.quadruples the rate. If the exponent is 0, doubling the concentration If the exponent is 0, doubling the concentration

has no effect on the rate.has no effect on the rate.

Rate = k [A]Rate = k [A]mm[B][B]nn

The rate constant is kThe rate constant is k k is a proportionality constant that relates rate k is a proportionality constant that relates rate

and concentration at a given temperature.and concentration at a given temperature.

Determining the Rate Equation for a Determining the Rate Equation for a Reaction.Reaction.

Rate = k [CO]Rate = k [CO]mm[NO[NO22]]nn

Determining the Rate Equation for a Determining the Rate Equation for a Reaction.Reaction.

Rate = k [NO]Rate = k [NO]mm[O[O22]]nn

Determining the Rate Equation

for a Reaction.

Concentration-Time Relationships:Concentration-Time Relationships:Integrated Rate LawIntegrated Rate Law

ln ln [R][R]tt = - kt = - kt

[R][R]oo

Second-Order Reactions suppose R -> is Second-Order Reactions suppose R -> is second order then second order then

- - [R][R] = k[R] = k[R]22 tt

1 1 _ _ 1 1 = kt = kt

[R][R]tt [R] [R]oo

1 1 _ _ 1 1 = kt = kt

[R][R]tt [R] [R]oo

1 1 _ _ 1 1 = kt = kt

[R][R]tt [R] [R]oo

Zero-Order Reactions suppose R -> is zero Zero-Order Reactions suppose R -> is zero order then order then

- - [R][R] = k[R] = k[R]00 tt

[R][R]oo - [R] - [R]tt = kt = kt

Concentration-Time Relationships:Concentration-Time Relationships:Graphical Analysis MethodGraphical Analysis Method

[R][R]oo - [R] - [R]tt = kt = kt

[R][R]oo

1 1 _ _ 1 1 = kt = kt

[R][R]tt [R] [R]oo

Concentration-Time Relationships:Concentration-Time Relationships:Graphical AnalysisGraphical Analysis

Half-Life and First-Order ReactionsHalf-Life and First-Order Reactions

ln [R]t = - kt

Concentration-Time Relationships:Concentration-Time Relationships:

[R][R]oo

Particulate View of Reaction RatesParticulate View of Reaction RatesCollision TheoryCollision Theory

The reacting molecules must collide with The reacting molecules must collide with one anotherone another

The reacting molecules must collide with The reacting molecules must collide with one another with sufficient energyone another with sufficient energy

The reacting molecules must collide in an The reacting molecules must collide in an orientation that can lead to rearrangement orientation that can lead to rearrangement of the atoms.of the atoms.

Particulate View of Reaction RatesParticulate View of Reaction RatesCollision TheoryCollision Theory

The reacting molecules must collide with The reacting molecules must collide with one anotherone another

The rate of reactions is primarily related to the The rate of reactions is primarily related to the number of collisions which is related to the number of collisions which is related to the concentration of molecules.concentration of molecules.

The rate of a reaction is related to the The rate of a reaction is related to the concentration of each reactant.concentration of each reactant.

Collision Theory: Concentration and Collision Theory: Concentration and Reaction Rate.Reaction Rate.

The rate of molecular reactions is related to the number of collisionsWhich is related to the concentration. Collisions directly related to Concentrations

Collision Theory: Temperature, Reaction Collision Theory: Temperature, Reaction Rate and Activation EnergyRate and Activation Energy

Recall the Boltzman distribution of molecular Recall the Boltzman distribution of molecular energiesenergies

The reacting molecules must collide with one another The reacting molecules must collide with one another with sufficient energy with sufficient energy

Activation Energy, EActivation Energy, Eaa, minimum energy required for , minimum energy required for molecules to react.molecules to react.

Collision Theory: Temperature, Reaction Collision Theory: Temperature, Reaction Rate and Activation EnergyRate and Activation Energy

Increasing the Temperature Increases the Increasing the Temperature Increases the number of number of molecules with sufficient energy to react.molecules with sufficient energy to react.

Temperature, Reaction Rate and Activation Temperature, Reaction Rate and Activation EnergyEnergy

The reacting molecules must collide in an orientation The reacting molecules must collide in an orientation that can lead to rearrangement of the atoms. A that can lead to rearrangement of the atoms. A graph of this is described as the reaction pathway.graph of this is described as the reaction pathway.

Reactant molecules approach each other with Kinetic Reactant molecules approach each other with Kinetic energyenergy Kinetic energy decreases, potential increasesKinetic energy decreases, potential increases

Reactant Molecules collide and bonds rearrangeReactant Molecules collide and bonds rearrange Highest potential energyHighest potential energy

Transition stateTransition state Activated complexActivated complex

Product molecules convert potential energy to Kinetic Product molecules convert potential energy to Kinetic energy as they move apart from each other.energy as they move apart from each other.

Reaction Pathway diagramsReaction Pathway diagrams

Example:Example:

The following are the data from an experiment to assess the The following are the data from an experiment to assess the disinfection of wastewater with a given dose of chlorine. disinfection of wastewater with a given dose of chlorine. Assuming first-order kinetics, determine the rate constant.Assuming first-order kinetics, determine the rate constant.

Time, min % E. coli remaining Time, min % E. coli remaining

00 100100

1010 7070

2020 2121

3030 6.36.3

6060 0.60.6

Time, min % E. coli remaining Time, min % E. coli remaining

00 100100

1010 7070

2020 2121

3030 6.36.3

6060 0.60.6

Effect of temperature on biological reaction rate

The effect of temperature on reaction rate is given by the Arrhenius equation:

EA= activated energy, J/mol

R = Universal gas constant 8.31J/mol-K

T = Temperature in Kelvin = (oC + 273)

A = Constant (not significantly affected by small temp. change

Arrhenius EquationArrhenius Equation

Arrhenius Equation Describes all variablesArrhenius Equation Describes all variables Describes the dependence of reaction rates on Describes the dependence of reaction rates on

energy, frequency of collisions, temperature energy, frequency of collisions, temperature and collision geometryand collision geometry

rate constant = k = Arate constant = k = Aee-Ea/RT-Ea/RT

Where A represents the frequency factor andWhere A represents the frequency factor andThe rest of the equation represents the fraction of the The rest of the equation represents the fraction of the molecules with minimum energy for collisionmolecules with minimum energy for collision

R = 8.31 x 10R = 8.31 x 10-3-3 kJ/mol kJ/mol..KK

Reaction Rates: Arrhenius EquationReaction Rates: Arrhenius Equation

rate constant = k = Arate constant = k = Aee-Ea/RT-Ea/RT

R = 8.31 x 10R = 8.31 x 10-3-3 kJ/mol kJ/mol..KK

Arrhenius Equation and Activation EnergyArrhenius Equation and Activation Energy

Graph the data above and calculateThe slope. The slope = - Ea / R

Arrhenius Equation and Activation EnergyArrhenius Equation and Activation Energy

Effect of Catalysts on Effect of Catalysts on Reaction RateReaction Rate

Substances that speed up the rate of a Substances that speed up the rate of a chemical reaction by lowering the reaction chemical reaction by lowering the reaction barrier (changing the mechanism)barrier (changing the mechanism)

Heterogeneous catalysts (solid in solution)Heterogeneous catalysts (solid in solution) Homogeneous catalysts -same phaseHomogeneous catalysts -same phase

A catalyst effects the rate of reaction by A catalyst effects the rate of reaction by impacting collision geometryimpacting collision geometry

http://www.800mainstreet.com/7/0007-http://www.800mainstreet.com/7/0007-005-rea-t-cat.html005-rea-t-cat.html

Reaction MechanismReaction Mechanism

Most reactions are bimolecularMost reactions are bimolecular An intermediate molecule is produced and An intermediate molecule is produced and

then used in the subsequent reaction(s) then used in the subsequent reaction(s) Each elementary step has its own EEach elementary step has its own Ea a and and k k

which combine to give the overall reactionwhich combine to give the overall reaction

Reaction MechanismReaction Mechanism

Mechanisms are postulated from Mechanisms are postulated from experimental data.experimental data.

Molecularity unimolecular, bimolecular Molecularity unimolecular, bimolecular and termolecularand termolecular

Reaction Mechanism, Reaction Mechanism, Molecularity, and Rxn RateMolecularity, and Rxn Rate

The molecularity of an elementary step The molecularity of an elementary step and its order are the sameand its order are the same

The rate is determined by the slowest step The rate is determined by the slowest step The rate law included all reactions The rate law included all reactions up to up to

the rate determining stepthe rate determining step

The rate is determined by the slowest step The rate is determined by the slowest step Step 1 A + B -> X + M Step 1 A + B -> X + M kk11 slow rate E slow rate Eaa is large is large

Step 2 M + A -> Y Step 2 M + A -> Y kk2 2 fast rate E fast rate Eaa is small is small

Overall Reaction 2A + B -> X + YOverall Reaction 2A + B -> X + Y

Rate = kRate = k11 [A] [B] [A] [B]

The first bimolecular step is the rate-determining step, theRate equation is Rate = k [NO2] [F2]F is an intermediate, produced in # 1 and used in #2

If this were bimolecular, this would beThe rate equation

Reaction Mechanism and Reaction Reaction Mechanism and Reaction Rate EquationsRate Equations

Experiments determine effect of conc on Experiments determine effect of conc on raterate

Proposed reaction mechanism is used to Proposed reaction mechanism is used to derive a rate equation (no intermediates)derive a rate equation (no intermediates)

A rate equation can only be based on A rate equation can only be based on elementary steps (not over all rate elementary steps (not over all rate equations)equations)

More than one mechanism can be More than one mechanism can be proposed.proposed.

Ch 15 Rates of Chemical Reactions

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