Chapter 14 – Chemical Kinetics

• How fast a chemical reaction occurs

• Only need to consider the forward reaction

A. Factors that affect rate

1. Concentration of reactants

2. Temperature

3. Catalysts

4. Surface Area

B. Reaction Rates1. Rate is determined

in the lab by experiment

2. Rate determined by measuring(-) disappearance of reactants(+) appearance of products

t

concR

][

Example 1 – Rates of…

)(

][

if

ifA tt

AAR

)(

][

if

ifC tt

CCR

A + B C + D

Rate of disappearance of ANote the NEGATIVE sign!!

Rate of appearance of CNote the POSITIVE sign!!

C4H9Cl + H2O C4H9OH + HCl

Data Table 14.2 – Disappearance of C4H9Cl

Time

(sec)

[C4H9Cl]

(M)

0.0 0.100

50.0 0.0905

100.0 0.0820

150.0 0.0741

200.0 0.0671

)50150(

]0905.00741.0[

ss

MMR

= 1.64 x 10-4 M/s

Example 2 – Rates with Coefficients

t

A

aRA

][1

t

C

cRC

][1

aA + bB cC + dD

Note that the coefficient becomesa reciprocal value for rate comparison

Example 3 – Rate Comparison

t

NORNO

][

4

1 22

522 2

1

1

4ONNO RR

522 2

1

4

1ONNO RR

2 N2O5 4 NO2 + O2

RN2O5 = 4.2 x 10-7 M/st

ONR ON

][

2

1 5252

Calculate the rate of appearance of NO2

Given:

sMxsMxRNO /104.8)/102.4(2 77

2

Example 3 – Rate Comparison

t

ORO

][ 22

2 N2O5 4 NO2 + O2

RN2O5 = 4.2 x 10-7 M/st

ONR ON

][

2

1 5252

Given:

The rate of O2 appearance is ½ the rate of N2O5 disappearance

sMxsMxRO /101.2)/102.4(2

1 77

2

Rate Law Expression

R = k [reactant]m

• R = rate law expression• k = rate constant units are M-1s-1

Note: k depends upon temperature and nature of reaction

• m = order of reaction– m=0 rate is independent of [ ]0

– m=1 rate is directly related to [ ]1

– m=2 rate is directly related to [ ]2

aA + bB products

• R = k [A]m[B]n

m = order with respect to A

n = order with respect to B

Overall order of reaction is = m + n

Note: order of reaction must be determined experimentally in the lab and cannot be simply concluded from the equation coefficients!!!!

• 2 N2O5 4 NO2 + O2

R = k[N2O5]

• CHCl3 + Cl2 CCl4 + HCl

R = k [CHCl3][Cl2]

• H2 + I2 2 HI R = k [H2] [I2]

Method of Initial RatesA + B C

EXP [ A ] [ B ] Initial Rate (M/s)

1 0.100 M 0.100 M 4.0 x 10-5

2 0.100 M 0.200 M 4.0 x 10-5

3 0.200 M 0.100 M 16.0 x 10-5

First Order Reactions• Using Calculus…

ln [A]t – ln [A]0 = -kt or

ln [A]t /[A]0 = -kt

[A]0=original conc

[A]t=conc @ time, tk = rate constantt = time

][AkRA

][][

Akt

ARA

Graphing First Order Reactions

ln [A]t = -k t + ln [A]0

y = m x + b

[A]

tln [A]

t

This is NOT a linear plot….Scientists like linear plots

Example – 1st Order

• The decomposition of an insecticide in H2O is first order with a rate constant of 1.45 yr -

1. On June 1st, a quantity of 5.0x10-7 g/cm3 washed into a lake.

insect product R = k [insect]

a) What is the concentration on June 1st next year?

ans. [insect]t=1yr = 1.17x10-7 g/cm3

b) How long will it take for the [insect] to drop to 3.0x10-7 g/cm3?

ans. t = 0.35 years = 4 months

1st Order Reactions, Half-Life

21

0

0

][

][21

ln ktA

A

212

1ln kt

21

21

lnt

k

21

693.0t

k

The time that it takes forOriginal concentration to Drop to ½ of its original concentration.

Second Order Reactions

• Using Calculus…

[A]0=original conc[A]t=conc @ time, tk = rate constantt = time

2][AkRA

0][

1

][

1

Atk

A t

y = m x + b

t

[A]

1

slope=k

2nd Order Reactions, Half-Life

t1/2= 1

k[A]0

To Determine Order You Must Graph the Data

y = m x + b

t

[A]

1

slope=k

y = m x + b

ln [A]

t

1st Order 2nd Order

Activation Energy, Ea

1. Molecules must collide to react2. Not all collisions result in a reaction3. The higher the collision frequency, the faster

the reaction ratea. increase temperatureb. increase pressure or decrease volume

(for gas only)c. catalystd. increase [conc]

Activation Energy, Ea

4. Activation energy, Ea – the minimum energy needed to start a reaction

5. Activated complex – intermediate product forming before the reaction is completed

A

A*

B

Ea

E

Activated Complex

Reaction progress

En

erg

y

For A B exothermic E (-)

For B A endothermic E (+) + Ea

The bigger Ea, the slower the rate

Arrhenius Equation – Rate and Temperature

k=rate const

A=frequency

Ea=Activation

energy

R=gas const

8.31 J/mol KT=Temperature

(Kelvin)

RTEaAek /

ART

Ek a lnln

Solving Arrhenius for Two Temperatures

ART

Ek a lnln

11 A

RT

Ek a lnln

22

A

RT

EA

RT

Ekk aa lnlnlnln

2121

122

1 11ln

TTR

E

k

k a

Graphing Arrhenius

122

1 11ln

TTR

E

k

k a

Note: to obtain Ea, you must multiply slope by the gas constant

ln k

1/ T

Yintercept= ln A

Slope = - Ea

R