Kinetics

How fast does your reaction go?

Reaction rates

• Rate is how fast a process occurs

• Rates are measured in units of

Results

Time

• Example: speed is measured in m/s (or mi/hr). A remote control car covers 125 meters in 15 seconds. What is its rate of speed?

Reaction rates

• Example #2: Lucy wraps chocolates at a rate of 5 pieces/minute. The conveyor belt moves chocolates by at a rate of 9 pieces/minute. At what rate does Lucy have to eat chocolates to keep them from piling up on the conveyor belt?

• Chemical reaction rates are often mol/s or mol/Ls.

Reaction rates

• Average rate is the (total results)/(total time).

• MgO + H2 Mg + H2O

• Average rate =

([H2Ofinal]-[H2Oinitial])/(tf-ti)

= [H2O]/t

Reaction rates

• Instantaneous rate is the results for an infinitesimally small amount of time divided by that time

• Instantaneous rate = d[H2O]/dt

• Rates can also be for the disappearance of reactants

• Average rate = -[H2]/t

Reaction rates

• Measured in units of

amount of product formed

time

• The amount of product can be any convenient unit (grams, moles, liters of gas, etc.)

Reaction rates

• Example:

MgO + H2 Mg + H2O

• If the concentration of water vapor in the above reaction increases from 1.0x10-3 moles/liter to 8.8x10-3 moles/liter in 3.5 seconds, What would be the average reaction rate?

• (8.8-1.0)x10-3/3.5 = 2.2x10-3 mol/L∙s

Graphing rates

• Results (dependent variable) are plotted on the y axis, and time (independent variable) is plotted on the x axis.

• The rate at any time is the slope of the graph at that time.

• The rate of a straight line plot is just the slope of the whole line (rise/run).

Graphing rates

• Curved plots– Instantaneous rate at any time is the

slope of the tangent to the curve at that point.

– Average rate for any time period is the slope of the straight line connecting the two desired time points on the graph.

Collision theory

• Particles must collide in order to react.

• Particles must be oriented correctly when colliding in order to react

• Correct orientation results in a temporary high-energy arrangement called an activated complex or transition state.

Collision theory

Collision theory

Activated complex for SN2 substitution of bromomethane with hydroxide to make methanol

• Transition state may form products or break apart and re-form reactants

Activation energy

• Particles must collide with sufficient energy to cause a reaction

• Activation energy is the difference in energy between the reactants and the transition state

Activation energy

Activation energy

• If reactants do not have enough kinetic energy, the reaction will not start.

Factors affecting reaction rates• Free energy and reaction rate are

unrelated

• Surface area– More surface area (smaller pieces or

finer powder) means a faster reaction. All reactions involving a solid phase take place at the surface of the solid.

Factors affecting reaction rates• Concentration

– Higher concentration means a faster reaction.

• Nature of reactants– Rate of reaction depends on what is

reacting.

• Temperature – The activation energy is supplied by

the kinetic energy of the particles.

Factors affecting reaction rates

Factors affecting reaction rates• Higher temperature means that

more particles will have enough energy to react.

Catalysts

A reaction will proceed faster in the presence of a catalyst because the activation energy is lowered.

Catalysts

• A catalyst speeds a reaction without being used up.

• Transition metals and their oxides often have catalytic properties – used in catalytic converters in automobiles

Catalysts

• For solid catalysts, the reaction usually takes place on the surface of the catalyst, therefore the more surface area the catalyst has, the faster the reaction

• Biological catalysts are called enzymes

Rate Laws

• Rate varies with concentration of reactants

A B

Rate = k[A]

where k is the rate constant. • The rate constant is temperature

dependent.• Rate constant is experimentally

determined.

Reaction order

• Expresses how rate depends on concentration as an exponent

• Zero order: rate = k[A]0 = k

• First order: rate = k[A]

• Second order: rate = k[A]2

• Reactions beyond second order in one reactant are extremely rare.

Reaction order

A + B AB

Rate = k[A][B]

• Reaction is first order in A, first order in B and second order overall.

• In a simple reaction the order represents the molecularity of the reaction.

Reaction order

• Molecularity is the number of particles that have to collide to make a reaction

• Zero order – generally reactions that happen at a surface and depend only on surface area.

• First order – depends only on concentration of reactant

Reaction order

• Second order

Rate = k[A]2

• Two molecules of A must collide.• Probability of a collision is n(n-1)/2. If

the concentration is doubled to 2n (and n is large) the probability increases by a factor of four, so the rate depends on the square of the concentration.

Determining reaction order

• Method of initial rates– Reaction is run for short periods of time and

stopped before reactant concentrations change much

– Initial concentrations are changed and rates compared

– If initial concentration is doubled, the rate will• zero order: not change • first order: 2x • second order: 4x

Determining reaction order

• Rate constant can also be determined

• Example. A + B C

Determine rate law for this reaction, rate constant, and rate when [A] = 0.050 M and [B] = 0.100 M

Experiment [A] [B] Initial rate (M/s)

1 0.100 0.100 4.0x10-5

2 0.100 0.200 4.0x10-5

3 0.200 0.100 16.0x10-5

Determining reaction order

• Rate law for B: Use exp. 1 & 2• Rate2/rate1 = 4.0x10-5/4.0x10-5

= k(0.100)m(0.200)n = 1 k(0.100)m(0.100)n

• Rate law for A: Use exp. 1 & 3 • Rate2/rate1 = 16.0x10-5/4.0x10-5 = 4

= k(0.200)m(0.100)n k(0.100)m(0.100)n

• rate = k[A]2[B]0 = k[A]2

n = 0

m = 2 = 2m = 4

Determining reaction order

• Determining k: use any experiment

• k = rate/[A]2 = 4x10-5/0.1002 = 4.0x10-3M-1s-1

• Rate at given concentrations: Use the rate law equation

• rate = k[A]2 = (4x10-3)(0.200)2 = 1.6x10-4 M/s

Determining reaction order

• Example:

2NO + 2H2 N2 + 2H2O

Determine the rate law and rate constant, and the rate when [NO] =

0.050 M and [H2] = 0.150 MExperiment [NO] [H2] Initial rate (M/s)

1 0.10 0.10 1.23x10-3

2 0.10 0.20 2.46x10-3

3 0.20 0.10 4.92x10-3

Answer: rate = k[NO]2[H2]; k = 1.2 M-2s-1; rate = 4.5x10-4M/s

Integrated rate laws

• Concentration expressed in terms of time

• Zero order: • [A] = -kt + [A]0

• Graph of [A] vs t is a straight line.• 1st order: • ln[A] = -kt + ln[A]0

• Graph of ln[A] vs t is a straight line.

Integrated rate laws

• 2nd order:

• 1/[A] = kt + 1/[A]0

• Graph of 1/[A] vs t is a straight line.

• 3rd order reactions are practically non-existent.

Reaction mechanisms

• Complex reactions are made of several simple steps.

• Example:

NO2 + CO NO + CO2 occurs in two steps:

i. NO2 + NO2 NO3 + NO

ii. NO3 + CO NO2 + CO • Overall process is sum of steps.

Reaction mechanisms

• Intermediates are short-lived species that are temporarily formed as the reaction proceeds.

• The rate-determining step is the slowest step of the mechanism.

• Intermediates are short-lived species that are temporarily formed as the reaction proceeds.

• The rate-determining step is the slowest step of the mechanism.

Reaction mechanisms

• Changing components of this step changes the reaction rate; changing components of other steps does not.

• Rate laws for complex reactions include the components of the slow step and critical components of earlier steps.

Reaction mechanisms

• Example: 2NO + 2H2 N2 + 2H2Ooccurs in three steps:

2NO N2O2 (fast)N2O2 + 2H2 N2O + H2O (slow)

N2O + H2 N2 + H2O (fast)• Rate law is rate = k[NO]2[H2]. [H2]

appears in the slow step, and [N2O] depends on [NO]2, so [NO]2 appears in the rate law as well.

Reaction mechanisms

• Further examples:• Example 1

HBr + O2 2H2O + 2Br2

Step 1 (slow)

HBr + O2 HOOBrStep 2

HOOBr + HBr 2HOBrStep 3

2HOBr+ 2HBr 2H2O + 2 Br2

Reaction mechanisms

• Choose the most likely rate law:

a. rate = [HBr]

b. rate = [O2]

c. rate = [HBr][O2]

d. rate = [HBr]2

Reaction mechanisms

• Example 2

(CH3)3CBr + H2O (CH3)3COH + HBr