tinoco chapter 7

CHEM 2880 - Kinetics

Chemical Kinetics

Tinoco Chapter 7


2

What is kinetics?

Kinetics is the study of rates of reactions. • How fast does a reaction proceed under specific

conditions?• What factors (concentration, temperature, etc) effect

the rate of reaction?

Studying reaction rates can provide valuable informationabout the mechanism by which a reaction proceeds.


3

Rates of reaction

Rates of reaction are always measured as the change inconcentration (of reactants and/or products) per unit time(M s or M min ).-1 -1

For the reaction: A 6 B

the reaction rate (v) can be expressed in terms of:• the disappearance of reagent A or• the appearance of product B

Thus:


4

For the reaction: 2A 6 B

A disappears twice as fast as B appears

Thus:

In general to account for the stoichiometry of a reactionsuch as:

aA + bB 6 cC + dD

the rate of change of concentration for each component isdivided by its stoichiometric coefficient. Thus for thisreaction:

this is the average rate over the time period )t. As thetime interval is decreased and approaches zero, thisbecomes the instantaneous rate :


5

What effects reaction rates?

Reaction rates are generally dependant in some way onthe concentrations or amounts of the species involved inthe reaction.

Species which effect rates can be sorted into two groups:

Species whose concentrations changes during thecourse of the reaction• reactants• products• intermediates

Species whose concentrations do not change duringthe course of the reaction• catalysts• intermediates in a steady-state process• components that are buffered by a large reservoir• solvents etc.


6

Rate Laws

The relationship between rate and concentration is knownas the rate law.

v = f(concentrations)

These functions can be simple or quite complex and mustbe determined experimentally.

Often, (but not always), for a reaction such as:aA + bB 6 cC + dD

the rate law can be expressed as

where k is the rate constant and the exponents x and yare determined experimentally.

The rate law shows that the rate is dependant on k (whichin turn is dependant on a number of factors, includingtemperature) and the concentration of the reagents.


7

Order of Reaction

For the example given above where: aA + bB 6 cC + dD

with the rate law:

x is the order of reaction with respect to reagent Ay is the order of reaction with respect to reagent Band (x+y) is the overall order of reaction


8

Examples:

L-isoleucine 6 D-isoleucinev = k[L-isoleucine]first order in L-isoleucinefirst order overall

2Proflavin 6 proflavin dimerv = k[proflavin]2

second order in proflavinsecond order overall

2 2 2HemoglobinC3O + O 6 Hb C4O

2 2v = k[HbC3O ][O ]

2first order in HbC3O

2first order in Osecond order overall

Table 7.1 presents some more examples of reactions, theirrate laws and their kinetic order.


9

Pseudo orders

The third example above can be used to illustrate amethod used to simplify some rate laws by reducing theirorder. For the reaction:

2 2 2HemoglobinC3O + O 6 Hb C4O

with the rate law:

2 2v = k[HbC3O ][O ]

2 2If the HbC3O is reacting with atmospheric O , i.e. it is

2exposed to the atmosphere, the absolute amount of O itcan react with is insignificant compared to the total

2amount of O available. In essence, the reaction with the

2 2 2HbC3O will not change the [O ] and thus the [O ] isconstant throughout the reaction. The rate law can thenbe written as:

2v = k’[HbC3O ]

2where k’ = k[O ]

This is known as a pseudo first order rate law .


10

Reducing the overall order of a reaction to a pseudo lowerorder can be useful for any reaction where theconcentration of one of the reagents is essentially constantthroughout the reaction. This can occur in a number ofways, for example:

• a reagent may be present at a much higherconcentration than the other(s) and thus there is nosignificant change in its concentration during thereaction

• a reagent may be constantly being produced byanother reaction, and thus as it is consumed by thereaction under study, it is replaced by a secondreaction and its concentration does not change

Pseudo orders of reaction are particularly useful forreactions with higher orders, allowing the overall order tobe reduced to 1 or 2.


11

Please note:

The exponents in the rate law can only be determinedexperimentally. They cannot be determined based on thecoefficients in the stoichiometric reaction expression. The exponents depend on the mechanism of the reactionas we will see later.

Kinetic experiments allow the researcher to determine theorder of reaction which in turn can provide insight intothe mechanism of the reaction.

Rate laws can be very complex. They can includeconcentrations of both reactants and products, and canhave exponents that are integers, including 0, or fractions.


12

For example:

For the reaction:

2 2 H + I 6 2HI

the rate law is:

2 2v = k[H ][I ]

2 2First order in both H and I , second order overall whichcorresponds to the stoichiometric reaction.

However for the similar reaction:

2 2H + Br 6 2HBr

the rate law is much more complex and includes theproduct.


13

Zero-Order Reactions

The rate law for a zero-order reaction such as:A 6 products

is given by:

The units for k are M s .-1


14

A plot of concentration of reagent A versus time lookslike:


15

and

integrating this gives us:

1 1 2 2Setting the limits of [A] , t and [A] , t gives us:

which is the integrated rate law.


16

1 1If [A] , and t are the initial concentration and time

1respectively (t = 0) then the integrated rate law simplifiesto:

t 0[A] -[A] = -kt or

t 0[A] = [A] - kt

This is the equation of a straight line with a slope of -kand a y-intercept corresponding to the initialconcentration of A.


17

Example (Tinoco p.322):

Ethanol is converted to acetaldehyde by the liver enzymealcohol dehydrogenase (LADH) using nicotinamideadenine dinucleotide (NAD ) as the oxidizing agent. The+

reaction is:

The [NAD ] is buffered by metabolic reactions that+

rapidly restore it. So if the [alcohol] is in excess over theenzyme, the reaction is pseudo-zero-order overall, and therate law is:


18

1 Order Reactionsst

The rate law for a 1 order reaction such as:st

A 6 products

is given by:

The units for k are s .-1


19



20

and

Integrating this gives us:

1 1 2 2Setting the limits of [A] , t and [A] , t gives us:



21



or

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

or

0[A] = [A] e-kt


22

The plots that result from these equations look like:

an exponential decay curve, and

0a linear plot with a slope of -k and an intercept of ln[A] .


23

Some examples of 1 order reactions:st

• radioactive decay (See Tinoco example 7.1)

• decomposition of the antibiotic penicillin (Tinoco p.324)


24

2 Order Reactionsnd

There are two types of 2 order reactions:nd

Type I: 2A 6 products

and

Type II: A + B 6 products

The respective rate laws are:

Type I

and

Type II

The units for k are M s .-1 -1


25



26

Type I

2A 6 products

and

integrating this gives us:

1 1 2 2setting the limits of [A] , t and [A] , t gives us:



27



or


28

The plots that result from these equations look like:

a steeper decay curve than the first order plot, and

0a linear plot with a slope of k and an intercept of 1/[A] .


29

Some examples of Type I 2 order reactions:nd

2• 2 proflavin 6 [proflavin]v = k [proflavin]2

4 2 2• NH OCN 6 NH CONH (ammonium cyanate 6urea)

4v = k [NH OCN]2

• see Tinoco p. 330


30

Type II

A + B 6 products

This type of reaction is 1 order in A, 1 order in B andst st

2 order overall.nd

The integrated rate law for this type of reaction is slightlymore complicated than that for type 1.

0 0If [A] = [B] , then at any time t [A] = [B] and theintegrated rate law for Type 1 can be used.


31

0 0If [A] � [B] , the integrated rate law is:

or

A plot of vs t has

0 0a slope of ([B] - [A] ) and an intercept of .


32

Example

Renaturation of DNA (Tinoco p. 334)

This experiment is used to provide information about thesequence of a DNA sample. A large piece of DNA isbroken down into smaller segments (using sonication)and then denatured into single strands (by heating to90°C). Then as the solution cools, the strands recombine(renature) to form double-stranded segments. The rate ofthis process depends on the complexity of the originalpiece of DNA.

If there are no repeating sequences in the DNA, thenevery segment will be unique, and the chances of itfinding it’s complementary strand are small. In thiscase renaturation will be slow.

If there are many repeating sequences, then there willbe many similar strands and the chances of each onefinding a complimentary strand are higher, andrenaturation will be faster.

There is an extreme case of synthetic DNAconsisting entirely of one set of complementary basepairs. This results in the fastest renaturation process.


33


34


35

Kinetic analysis:

A+B 6 AB

[A] = [B]

v = k[A][B] = k[A]2

0[A] is the initial concentration (in moles of nucleotide/L)of fragment A, and [A] is the concentration of thatfragment at time t. Thus f is the fraction of strands thatare denatured.


36

0Let C be the total concentration of all the single strandsbefore renaturation occurs.

N is the smallest repeating sequence and ranges from 1for the synthetic DNA mentioned above, to the totalnumber of base pairs present for DNA with no repeatingsequence (on the order of 10 or greater).6

½When f = ½, t = t and:


37

Note: k is the same for renaturation of all DNA.

k can be determined for one sample such as the syntheticDNA for which N is known, and then used to determineN for other samples.

On this plot, for each curve, where f = 0.5:

0 0 ½C t = C t = N/k’


38

Half-life

The half-life of a reaction is the time it takes for theconcentration of the reagent to drop to half of it’s original

0concentration, for [A] to decrease to ½[A] .

Zero-order

1 orderst

2 ordernd

In general, for any reaction of order n:

½Note: 1 -order reactions are the only ones where t is notst

dependant on the initial concentration.


39

Summary

Zero-order 1st-order 2nd-order

rate law

integratedrate law

linear plot [A] vs t ln[A] vs t 1/[A] vs t

slope -k -k k

intercept 0 0 0[A] ln[A] 1/[A]

½t

units of k M s s M s -1 -1 -1 -1

tinoco chapter 7

Documents