CHEMICAL KINETICS

Prepared by

Prof. Odyssa Natividad R. Montoya-Molo

Chemical Kinetics

• The area of chemistry that is concerned with the speeds or rates at which reactions occur.

• Reaction rate is the measure of how quickly a reactant is consumed or how quickly a product is produced.

Chemical Kinetics

• A chemical reaction may either give off (exothermic) or absorb (endothermic) heat.

Collision Theory

• States that molecules must collide to react. Upon collision, the kinetic energy of the molecules can be used to break bonds leading to chemical reactions.

–Effective collision• Leads to products

–Ineffective collision• Does not lead to formation of products

Factors that determine the effectiveness of collision:

• Energy of the colliding particles

– Sufficient kinetic energy to achieve the threshold or minimum energy required for a chemical reaction

to occur

(activation energy,

Ea)

Factors that determine the effectiveness of collision:

• Orientation of the molecules at the time of collision

Why are some reactions slow,other fast?

• Whether the reaction takes place slowly or rapidly

depends on the number of molecules reaching the

activated state in a given time.

Why are some reactions slow,other fast?

• If the Ea is high only few molecules are activated. As a result, reaction occurs slowly.

• If the Ea is low, many molecules are activated & reaction occurs faster.

• Some reactions do not occur at all because the Ea is too large. Under certain conditions,

it cannot be satisfied.

Ex (decay of plastic)

Importance of Ea

• The Ea in every chemical reaction is important for life. Imagine what would happen if Ea is needed to start a reaction.– Many reactions would occur instantly & at a very

fast rate. (Ex: decay, burning, rusting)– Food would be spoiled fast.– It would be impossible to store combustible

materials such as gasoline, alcohol & even paper.– Life would be too short (too long)

• Nature has a way of protecting people; the Ea in chemical reactions.

Factors Affecting Rates of Reactions

• Nature of the Reactants– Depends on the number of bonds that have to be

broken & formed

• Reactions between ionic are generally more rapid than between covalent.

– States of the reactants

• Homogeneous reactions (same state) are likely to proceed more quickly than heterogeneous reactions

• Reaction rate: Gases > liquids > solid

Factors Affecting Rates of Reactions

• Concentration– Increase concentration means an increase in the

number of molecules or particles per unit volume& thus a decrease in spaces between the reacting particles.

– With less distance to travel inside the vessel, the more frequent the collision, the faster the rate of reaction.• Ex: Treatment of tonsillitis may need 250 mg of antibiotic but

meningitis requires 2 – 5 times of 250 mg. Increasing the dosage increases the rate of absorption in the bloodstream, resulting in effective concentration in the blood.

Factors Affecting Rates of Reactions

Effect of Concentration on Rate(a) When heated in

air, steel wool glows red-hot but oxidizes slowly.

(b) When the red-hot steel wool is placed in an atmosphere of pure oxygen, it burns vigorously, forming Fe2O3 at a much faster rate.

Factors Affecting Rates of Reactions

• Temperature

– The higher the temperature, the faster the molecules move, and the more frequent they collide. Hence, the faster the reaction rate.

– When concentration of reactants are kept constant, an increase of 10°C doubles or triples the reaction rate.

• Food spoils faster at room temperature especially on warm summer days. That is why we refrigerate our food.

Factors Affecting Rates of Reactions

• Surface area (of solid reactant)– The smaller the size of particles, the larger the

surface area exposed, the more frequent the collision is, the faster the reaction.• A number of medicines are produced in the form of

fine powder or small crystals to increase the reaction rate in the body.

• Some finely divided substances can produce dangerous results. Suspended flour in flour mills or coal dust in coal mines is very reactive & presents explosion hazard. This is why smoking is strictly prohibited in the work areas.

Factors Affecting Rates of Reactions

• Effect of catalyst– Presence of catalysts speeds up a reaction.

– Catalyst provides an alternative pathway of lowerEa. It increases the rate of reaction but is not used up in the reaction.• Enzymes = catalysts in the body

• Catalytic converter in cars = removes toxic gases (CO & NOx) by mixing these gases in air & passing them over catalysts Pt or Rh

– Inhibitors = substances that slow down the rate of reaction. (Ex: preservatives)

Factors Affecting Rates of Reactions

• Effect of catalyst

Reaction rates

• The measure of how quickly a reactant is consumed or how quickly a product is produced.

Reaction rates

• in terms of concentration

Average rate =

Instantaneous rate (rate at a particular time)

• in relation to stiochiometry

Given: aA + bB cC + dD

Rate =

Sample Exercises

1) Using the data in the table, calculate the average rate of disappearance of C4H9Cl for each time interval.

Time (s) [C4H9Cl] (M)

0.0 0.1000

50.0 0.0905

100.0 0.0820

150.0 0.0741

200.0 0.0671

Answer:

• From 0 to 50 s • 1.9 x 10-4 M/s

• From 50 to 100 s• 1. 7 x 10-4 M/s

• From 100 to 150 s• 1.58 x 10-4 M/s

• From 150 s to 200 s• 1. 4 x 10-4 M/s

Sample Exercise

2) How is the rate of disappearance of ozone related to the rate of appearance of oxygen in the ff equation: 2 O3(g) 3 O2(g)?

3) If the rate of appearance of O2 is 6.0 x 10-5 M/s at a

particular instant, what is the value of the rate of

disappearance of O3 at this time?

4) The decomposition of N2O5 proceeds according to the equation: 2 N2O5(g) 4NO2(g) + O2(g). If the rate of decomposition in a reaction vessel is 4.2 x 10-

7 M/s, what is the rate of appearance of NO2? O2?

Answer:2) ∆ [O3]/∆t = 2/3 ∆[O2]/∆t3) 4.0 x 10-5 M/s 4) ∆[NO2]/∆t = 8.4 x 10-7

M/s; ∆[O2]/∆t = 2.1 x 10-7 M/s

Practice Exercise

• The isomerization of methyl isonitrile, CH3NC,

to acetonitrile, CH3CN, was studied in the gas

phase at 215°C, and the ff data in the table were

obtained. Calculate the average rate of reaction,

M/s, for the time interval between each measurement.

Time (s) [CH3NC], (M)

0 0.0165

2,000 0.0110

5,000 0.00591

8,000 0.00314

12,000 0.00137

15,000 0.00074

Answer:

Time (s) Time interval (s)

Concentration(M)

∆M Rate (M/s)

0 0.0165

2,000 2,000 0.0110 -0.0055 28 x 10-7

5,000 3,000 0.00591 -0.0051 17 x 10-7

8,000 3,000 0.00314 -0.00277 9.23 x 10-7

12,000 4,000 0.00137 -0.00177 4.43 x 10-7

15,000 3,000 0.00074 -0.00063 2.1 x 10-7

Practice Exercise

• Consider the combustion of H2(g): H2(g) + O2(g) 2 H2O(g). If hydrogen is burning at the rate of 4.6 mol/s, what is the rate of consumption of oxygen? What is the rate of formation of water vapor?

• The reaction 2 NO(g) + Cl2(g) 2 NOCl(g) is carried out in a closed vessel. If the partial pressure of NO is decreasing at the rate of 30 torr/min, what is the rate of change of the total pressure of the vessel?

• Answer: 2.3 mol/s; 4.6 mol/s

• Answer: Ptotal decreases by 15 torr/min

Dependence of Rate on Concentration

• Rate law– An expression which shows how the rate

depends on the concentration of reactants

• Rate constant, k– The constant in the rate law– Unit depends on the overall reaction order

• Reaction order– The exponents in the reactants; determined

experimentally

• Example: aA + bB cC + dD– Rate law: rate = k [A]m [B]n

Sample Exercises

• The initial rate of a reaction A + B C was

measured for several different starting

concentrations of A & B, with the results given in

the table. Using these data, determine (a) the

rate law of the reaction; (b) magnitude of the rate

constant; (c) rate of the reaction when [A] =

0.050M & [B] = 0.100M.

Expt # [A],(M)

[B], (M)

Initial rate, (M/s)

1 0.100 0.100 4.0 x 10-5

2 0.100 0.200 4.0 x 10-5

3 0.200 0.100 16.0 x 10-5

• Answer:(a)Rate = k[A]2[B]0 =

k[A]2

(b) 4.0 x 10-3 M-1s-1

(c)1.0 x 10-5 Ms-1

Sample Exercises• STEPS

1) Write the rate law/eqn:• Rate = k [A]x[B]y

2) Find x (use constant y/[B])• Rate3/Rate1 = [A]x

3/[A]x1

3) Find y (use constant x/[B])• Rate2/Rate1 = [B]y

2/[B]y1

4) Re-write rate law/eqn with values of x & y

Order of rxn: (values of x & y)• x order with respect to [A]

• y order with respect to [B]

Expt#

[A],(M)

[B], (M)

Initial rate, (M/s)

1 0.100 0.100 4.0 x 10-5

2 0.100 0.200 4.0 x 10-5

3 0.200 0.100 16.0 x 10-5

• To find k:

• Derive from rate law

• Use any set of given data.

Practice Exercise

• The ff data in the table were collected for the rate of disappearance of NO in

the reaction 2 NO(g) + O2(g) 2 NO2(g). (a)

What is the rate law of the reaction? (b) What are the units of the rate constant?

(c) What is the average value of the rate constant calculated from the three data sets? (d) What is the

order of the rxn?

Expt [NO] (M) [O2] (M) Initial Rate (M/s)

1 0.0126 0.0125 1.41 x 10-2

2 0.0252 0.0250 1.13 x 10-1

3 0.0252 0.0125 5.64 x 10-2

• Answer: a) Rate =k [NO]2[O2]b) M-2s-1

c) 7.11 x 103 M-2s-1

d) Order of rxn:2nd wrt [NO]1st wrt [O2]3rd overall order

Practice Exercise

• A particular reaction was found to depend on the concentration of the hydrogen ion. The initial rates varied as shown in the table. (a) What is the order of the reaction? (b) Predict the initial reaction rate when [H+] = 0.400 M

[H+], (M) Initial rate (M/s)

0.0500 6.4 x 10-7

0.100 3.2 x 10-7

0.200 1.6 x 10-7

• Answer: a) -1b) 0.80 x 10-7 M/s

Change of Concentration with Time

• 1st order reactions:

Rate law:

Rate = = k [A]

Conc & time:

ln [A]t – ln [A]0 = - kt

Half-life:

t1/2 = 0.693/k

• 2nd order reactions:

Rate law:

Rate = = k [A]2

Conc & time:

[A]t-1 = kt +[A]0

-1

Half-life:

t1/2 = (k[A]0)-1

Sample Exercises

• The 1st-order rate constant for the decomposition of a certain insecticide in water at 12°C is 1.45 yr-

1. A quantity of this insecticide is washed into a lake on June 1, leading to a concentration of 5.0 x 10-7 g/cm3. Assume that the effective temperature of the lake is 12°C. (a) What is the concentration of the insecticide on June 1 of the following year? (b) How long will it take for the concentration of the insecticide to drop to 3.0 x 10-7 g/cm3?– Answer: (a) 1.2 x 10-7 g/cm3; (b) 0.35 yr

Sample Exercises

• The decomposition of HI(g) at 700K is followed for 400s yielding the ff data in the table. What are the reaction order & the rate constant for the rxn: HI(g) ½ H2(g) + ½ I2(g)? Write the rate law for the reaction at 700K.

Time (s) [HI] (M)

0 1.00

100 0.90

200 0.81

300 0.74

400 0.68

• Answers: Rate = k [HI]2; 2nd order in HI; overall k = 0.00118

M-1s-1

Practice Exercise

• The decomposition of dimethyl ether (CH3)2O, at 510°C is a 1st-order process with a rate constant of 6.8x10-4s-1. If the initial pressure is 135 torr, what is its partial pressure after 1420 s? its half-life?– Answer: 51 torr; 1.02 x 103 s

• In 3 different experiments, the following results were obtained for the reaction A products: [A]0 = 1.00M, t½

= 50 min; [A]0 = 2.00M, t½ = 25 min; [A]0 = 0.50M, t½ = 100 min. Write the rate equation for this reaction & indicate the value of k.– Answer: rate = k[A]2; k = 0.020

M-1min-1

Temperature & Rate

• Svante Arrhenius’ Equation

k = Ae-Ea/RT

where k = rate constant

Ea = activation energy

R = gas constant (8.314 J/mol-K)

T = temp (K)

A (frequency factor)

• Simplified Arrhenius equation

ln (k1/k2) = (Ea/R)(T2-1-T1

-1)

Reaction Mechanism

• The complete description of how the reactants are converted to products.

• Presented as a series of single-step changes (elementary process/reaction)– Unimolecular: decomposition of single

molecule• O3(g) O2(g) + O(g) 1st order

– Bimolecular: 2 molecules collide• O3(g) + O(g) 2 O2(g) 2nd order

– Termolecular: 3 molecules collide• A + B product rate = k [A]2 [B] 3rd order

Reaction Mechanism cont…

• The elementary steps in a mechanism do not have the same rate.

• rate-determining step

– determines the rate of the overall reactions ; one of the steps which is much slower than the others

• reaction intermediate/intermediate product

– A specie that is formed in one step of the reaction mechanism & consumed in a subsequent step.

Reaction mechanism example:

• Original Eqn: H2(g) + 2 ICl(g) I2(g) + 2 HCl(g)

– Rate = k [H2] [ICl]

• Mechanism:

(1) Slow: H2 + ICl HI + HCl rate = k1 [H2][ICl]

(2) Fast: HI + ICl I2 + HCl rate = k2 [HI][ICl]

Net: H2 + 2 ICl I2 + 2 HCl

Equation (1) is the rds since the rate law of original equation is also the rate law of equation (1).

HI is the reaction intermediate.

BUBBLE ACTIVITY

GRAPHIC ORGANIZER (p 408)

• Global Warming

– Issues

– Chemical rxn explanation

– Data on rates of this rxn

– Propose solutions