CHM 120CHM 120

CHAPTER 16CHAPTER 16KINETICS: Rates and KINETICS: Rates and

Mechanisms of Chemical Mechanisms of Chemical ReactionsReactions

Dr. Floyd BeckfordDr. Floyd Beckford

Lyon CollegeLyon College

• Two factors control the outcome of chemical

reactions:

1. Chemical Thermodynamics

2. Chemical Kinetics

• Chemical Kinetics: study of rates of chemical

reactions and mechanisms by which they occur

• A reaction may be spontaneous but does not

occur at measurable rates

CHEMICAL KINETICSCHEMICAL KINETICS

REACTION RATESREACTION RATES

• Rate of reaction describes how fast

reactants are used up and products are formed

• There are 4 basic factors that affect

reaction rates

(i)Concentration

(ii) Physical state

(iii) Temperature

(iv) Catalysts

• For every reaction the particles must come into

intimate contact with each other

• High concentrations by definition implies that

particles are closer together (than dilute

solutions)

• So rate increases with concentration

• The degree of intimacy of particles obviously

depends on the physical nature of the particles

• Particles in the liquid state are closer than in

the solid state

• Likewise, particles in a finely divided solid will

be closer than in a chunk of the solid

• In both situations, there is a larger surface

area available for the reaction to take place

• This leads to an increase in rate

• Temperature affects rate by affecting the

number and energy of collisions

• So an increase in temperature will have the

effect of increasing reaction rate

• Rate of reaction is typically measured as the

change in concentration with time

• This change may be a decrease or an increase

• Likewise the concentration change may be of

reactants or products

Rate = ______________ = ______________change in timechange in time

in [products] in [reactants]

Rate =concentration change

time change

• Rate has units of moles per liter per unit time

- M s-1, M h-1

• Consider the hypothetical reaction

aA + bB cC + dD

• We can write

t[A]Rate of

reaction = 1a t

[B]1b

t[C]1

c t[D]1

d

= =

=

- -

• Note the use of the negative sign

- rate is defined as a positive quantity

- rate of disappearance of a reactant is

negative

2N2O5(g) 4NO2(g) + O2(g)

t[N2O5]Rate of

reaction= 12 t

[NO2]14 t

[O2]= =-

C2H4(g) + O3(g)

C2H4O(g) + O2(g)

• Rate may be expressed in three main ways:

1. Average reaction rate: a measure of the

change in concentration with time

2. Instantaneous rate: rate of change of

concentration at any particular instant during the

reaction

3. Initial rate: instantaneous rate at t = 0

- that is, when the reactants are first

mixed

RATE LAWRATE LAW

• Consider the following reaction

aA + bB products

• Rate of reaction changes as concentration of

reactants change at constant temperature

• RATE LAW: equation describing the relationship

between concentration of a reactant and the rate

Rate = k[A]m[B]n

where k is called the rate constant

• m, n are called reaction orders

- they indicate the sensitivity of the rate to

concentration changes of each reactant

• NOTE: the orders have nothing to do with the

stoichiometric coefficients in the balanced

overall equation

• An exponent of 0 means the reaction is zero

order in that reactant - rate does not depend

on the concentration of that reactant

• An exponent of 1 rate is directly proportional

to the concentration of that reactant

- if concentration is doubled, rate doubles

- reaction is first order in that reactant

• An exponent of 2 rate is quadrupled if the

concentration of that reactant is doubled

- reaction is second order in that reactant

• The overall reaction order is the sum of all the

orders

Rate = k[A][B]0 m = 1 and n = 0

- reaction is first order in A and zero order

in B

- overall order = 1 + 0 = 1

- usually written: Rate = k[A]

• Remember: the values of the reaction orders

must be determined from experiment; they

cannot be found by looking at the equation

DETERMINATION OF THE RATE LAWDETERMINATION OF THE RATE LAW• The method of initial rates may be used

- involves measuring the initial rates as a

function of the initial concentrations

- avoids problems of reversible reactions

- initially there are no products so they

cannot affect the measured rate

• In this method the experiments are chosen so

as to check the effect of a single reactant on

the rate

THE RATE CONSTANTTHE RATE CONSTANT

1. The units of k depends on the overall order of

reaction

2. The value of k is independent of concentration

and time

3. The value refers to a specific temperature

and changes if we change temperature

4. Its value is for a specific reaction

THE INTEGRATED RATE EQUATION• This is the equation that relates concentration

and time

• Consider a first-order reaction

aA products

Rate = k[A]

[A]0

[A]t = - ktln

time

initialconc.

conc. aftertime = t

2.303[A]0

[A]t =log - kt

• The equation may be written in the form for a

linear plot

• A plot of log [A]t vs. t is linear plot with slope

= -k/2.303

• Note that this plot gives a straight line ONLY

if the reaction is first-order

2.303 - ktlog [A]t = + log [A]0

Half-life

• The half-life, t1/2, is defined as the time it

takes for the reactant concentration to drop

to half its initial value

• Note: the half-life for a first order reaction

does not depend on the initial concentration

• The value of the half-life is constant

t = ln 2 = 0.693kk

1/2

Second order reactions

• Consider a reaction that is 2nd order in reactant

A and 2nd overall

aA products and Rate = k[A]2

• A plot of 1/[A]t vs. t gives a straight line with

slope = k

t =1/2 k[A]0

1

[A]t1 = kt + 1

[A]0

RATES AND TEMPERATURERATES AND TEMPERATURE

• Recall that temperature is the only factor that

affects the rate constant

• In general rates increase with temperature

k = Ae- (Ea/RT)

rate constant

absolute temperature

activation energy

constant (related to collision frequemcy)

• This is ARRHENIUS’ EQUATION

• Can be arranged in the form of a straight line

ln k = (-Ea/R)(1/T) + ln A

• Plot ln k vs. 1/T slope = -Ea/R

Ea/RTdecreases

- Ea/RTincreases

e- Ea/RT

increases kincreases

REACTI ONSPEEDS UP

I f Tincreases

• Another form of Arrhenius’ equation:

k2

k1=ln

Ea 1T2

1T1

-R

-

COLLISION THEORY: a reaction results when

reactant molecules, which are properly oriented

and have the appropriate energy, collide

• The necessary energy is the activation energy,

Ea

• Not all collisions leads to a reaction

• For effective collisions proper orientation of

the molecules must be possible

TRANSITION STATE THEORY

• During a chemical reaction, reactants do not

suddenly convert to products

• The formation of products is a continuous

process of bonding breaking and forming

• At some point, a transitional species is formed

containing “partial” bonds

• This species is called the transition state or

activated complex

• The transition state is the configuration of

atoms at the maximum of the reaction energy

diagram

• The activation energy is therefore the energy

needed to reach the transition state

• Note also that the transition state can go on

to form products or break apart to reform the

reactants

REACTION MECHANISMSREACTION MECHANISMS

• MECHANISM: the step-by-step pathway by

which a reaction occurs

• Each step is called an elementary step

NO2(g) + CO(g) NO(g) + CO2(g)

Mechanism:

NO2(g) + NO2(g) NO(g) + NO3(g)

NO3(g) + CO(g) NO2(g) + CO2(g)

• NO3 is a reaction intermediate

• Elementary reactions are classified by the

molecularity

A B + C unimolecular

A + B C + D bimolecular

A + 2B E termolecular

• Termolecular reactions are very unlikely

• For ANY SINGLE ELEMENTARY

REACTION – reaction orders are equal to the

coefficients for that step

Rate = kelem[A][B]

• The slow step is called the rate-determining

step (RDS)

• A reaction can never occur faster than its

slowest step

1. Overall reaction = sum of all elementary steps

2. The mechanism proposed must be consistent

with the rate law

A + B C + Dkelem

• There may be more than one plausible

mechanism

• The experimentally determined reaction orders

indicate the number of molecules of the reactants

- in the RDS (if it occurs first)

- the RDS and any fast steps before it

NO2(g) + NO2(g) NO(g) + NO3(g)

NO3(g) + CO(g) NO2(g) + CO2(g)

k1

k2

NO2(g) + CO(g) NO(g) + CO2(g)

CATALYSISCATALYSIS

• Reaction rates are also affected by catalysts

• Catalyst: a substance that increases the rate of

a reaction without being consumed in the reaction

• Catalysts work by providing alternative pathways

that have lower activation energies

•A catalyst may be homogeneous or heterogeneous

• Homogeneous: catalyst and reactants are in the

same phase

• Heterogeneous: catalyst in a different phase

• Typically: a solid in a liquid

• An important example: catalytic converters in

automobile

- convert pollutants to CO2 H2O, O2, N2

- usually Pt, Pd, V2O5, Cr2O3, CuO

• Cars must use unleaded fuels – lead poisons the

catalytic bed

2Ce4+(aq) + Tl+(aq) 2Ce3+(aq) + Tl3+(aq)Mn2+