1Chemistry 2C Lecture 20: May 17 th, 2010 1)Introduction to Kinetics 2)Rate Laws 3)Orders and Reaction…

1Chemistry 2C Lecture 20: May 17th, 2010

1) Introduction to Kinetics2) Rate Laws

3) Orders and Reaction Constants4) Initial Slopes

5) Zeroth order reactions

Lecture 20: Kinetics

2Chemistry 2C Lecture 20: May 17th, 2010

Chemical Kinetics: VocabularySimple Reaction rate

dtRd

dtPd

rate

For the simple reaction we defined an instantaneous rate:

PR

Rate defined in terms of either gain of products or loss of reactants

3Chemistry 2C Lecture 20: May 17th, 2010

Chemical Kinetics: VocabularyReaction rate Stoichiometrically more complicated reactions

The rate must be expressed in an unambiguous manner!

P2R

dtRd

dtPd

andBoth the ratios

still express the rate of change for the reactant and product concentrations, however they are not equal anymore, because the reactant is used up twice as fast as the product appears.

dtRd

21

dtPd

rate

4Chemistry 2C Lecture 20: May 17th, 2010

Chemical Kinetics: Vocabulary

For example:2Fe3+ + Sn2+ -> 2Fe2+ + Sn4+

Fe3+ disappears twice as fast as Sn2+

disappears

4+ 2+ 3+ 2+d Sn d Fe d Fe d Sn1 1dt 2 dt 2 dt dt

rate

Fe2+ appears twice as fast as Sn4+ disappears

The rate must be expressed in an unambiguous manner!

Each of these equations represent the rate of reaction rate!!

5Chemistry 2C Lecture 20: May 17th, 2010

Chemical Kinetics: Vocabulary2Fe3+ + Sn2+ -> 2Fe2+ + Sn4+

Instantaneous Rate @ a specific time

2+ 2+Fe Fe1 12 t 2 t

drate

d

Averaged Rate over a specific

time interval

Question: What is the averaged reaction rate for this reaction if the concentration of Fe2+ is initially zero and then after 100s, is 0.05M ?

6Chemistry 2C Lecture 20: May 17th, 2010

Chemical Kinetics: Vocabulary2Fe3+ + Sn2+ -> 2Fe2+ + Sn4+

Question: What is the averaged reaction rate for this reaction if the concentration of Fe2+ is initially zero and then after 100 s, is 0.05 M ?

2+Fe12 t

rate

2+ 2+ 2+

@100sec @0secFe Fe Fe

t 100s 0s

=0.05 M-0.00 M=0.05 M

=100 s

1 0.052 100

Mrates

42.5 x 10 M/srate

7Chemistry 2C Lecture 20: May 17th, 2010

Chemical Kinetics: VocabularyReaction rate

In general the rate for a general reaction

Is given by

dDcCbBaA

dtDd1

dtCd1

dtBd1

dtAd1

dcbarate

8Chemistry 2C Lecture 20: May 17th, 2010

Chemical Kinetics: Vocabulary2A -> 3B

Question: [A] drops from 0.5684M to 0.5522M in 2.50 min. What is the average rate for formation of B during this time interval ?

1 B 1 A3 t 2 t

rate

Rate of formation of B is And in terms of A and t:Bt

B 3 At 2 t

B 3 0.5522 M - 0.568 Mt 2 2.50 min

=0.00972 M/min

9Chemistry 2C Lecture 20: May 17th, 2010

Measuring RatesHow do we measure rates?

1) Need a timer2) Method to monitor the concentration

If a gas: can follow the pressure of collect in a buret and follow volume

If colored, can follow in a visible regions using a spectrometer

(Absorption is proportional to concentration)If charged, we can follow conductivityIf slow, we can withdraw aliquots at different

times and measure by titrationIf fast, we can use very fast laser pulses (~fs)

10Chemistry 2C Lecture 20: May 17th, 2010

Using spectroscopy to identify Reaction kinetics

 The reaction of formic acid (HCO2H) and bromine (Br2). As time passes (left to right), the red color of bromine disappears because Br2 is reduced to the colorless Br2 ion. The

concentration of Br2 as a function of time, and thus the reaction rate, can be determined by measuring the intensity of the color.

11Chemistry 2C Lecture 20: May 17th, 2010

Using spectroscopy to identify Reaction kinetics

A sequence of photographs showing the progress of the reaction of hydrogen peroxide (H2O2) and iodide ion (I–). As time passes (left to right), the red color due

to triiodide ion (I3–) increases in intensity.

12Chemistry 2C Lecture 20: May 17th, 2010

13Chemistry 2C Lecture 20: May 17th, 2010

2N2O5 (g) -> 4NO2 (g) + O2(g)Time dependent Concentrations

Increases four times faster

than O2

Conc. of N2O5 decreasing

14Chemistry 2C Lecture 20: May 17th, 2010

Chemical Kinetics: VocabularyReaction order

• The relation ship between the rate of a reaction and the concentrations of reactants and products is usually complex

• In most cases the rate can be expressed in a rate law of the following form:

yx

yx

BAk

BArate

Where x and y are called the reaction order with respect to A and B, respectively.The sum of x and y is called the overall reaction order.

The rate law and the reaction order can NOT be derived from the stoichiometric equation!

There is in general NO connection between the stoichiometric coefficient and the reaction order!

The reaction order can be zero, an integer or even a non-integer!

15Chemistry 2C Lecture 20: May 17th, 2010

Chemical Kinetics: VocabularyReaction order: An example

(g)O(g)4NO(g)O2N 2252

252ONkrate NO!

52ONkrate

Experiment shows that:

The reaction order and the rate law MUST be determined by experiment

16Chemistry 2C Lecture 20: May 17th, 2010

Chemical Kinetics: Non-Constant ratesFor the N2O5 reaction, the slope rate is decreasing with time!

Thus, the reaction rate is changing as the reaction proceeds.

Instantaneous Rate: is the slope of the tangent at point t.Average Rate: is is over a specified interval of time t.

17Chemistry 2C Lecture 20: May 17th, 2010

Chemical Kinetics Determination of the reaction Order and Rate Law

Differential Method or Initial rates method. We measure the reaction rate at several starting concentration of reactant. Using the general form of the rate law we can write:

nAkrate kAnrate logloglog and

The slope of a plot of log [A] vs. log the initial reaction rate gives us the reaction order

18Chemistry 2C Lecture 20: May 17th, 2010

Determining reaction ordersFor example

Rate=k [HgCl2]m [C2O42-]n

m and n must be determined experimentally. If m or n is 0, then reaction doesn’t depend on their concentration

2HgCl2 (aq) + C2O42- -> 2Cl- (aq) + 2CO2 (g) + Hg2Cl2(s)

Experiment [HgCl2] [C2O42-] Initial Rate

(M/min)1 0.105 M 0.15 M 1.8 x 10-5

2 0.105 M 0.3 M 7.1 x 10-5

3 0.052 M 0.3 M 3.5 x 10-5

19Chemistry 2C Lecture 20: May 17th, 2010

Determining reaction ordersRate=k [HgCl2]m [C2O4

2-]n

Experiment [HgCl2] [C2O42-] Initial Rate

(M/min)1 0.105 M 0.15 M 1.8 x 10-5

2 0.105 M 0.3 M 7.1 x 10-5

3 0.052 M 0.3 M 3.5 x 10-5

By inspection:A) 1 vs. 2: Double [C2O4

2-] with a constant [HgCl2]: the rate increases by 4Rate ~ [C2O4

2-]2 B) 2 vs. 3: Halve [HgCl2], with a constant [C2O4

2-]: the rate decreases by 2Rate ~ [HgCl2]1

C) Combine to get Rate =[HgCl2][C2O4

2-]2 What is the order of reaction? 1st order in

20Chemistry 2C Lecture 20: May 17th, 2010

Determining reaction ordersRate=k [HgCl2]1 [C2O4

2-]2

What is the order of reaction?

1st order in HgCl22nd order in C2O4

2-

3rd order overall (1+2)

21Chemistry 2C Lecture 20: May 17th, 2010

Chemical Kinetics: Reactions of integral order

Zero-Order Reactions

PA kAkdtAdrate 0

Reaction Rate Lawk is the zero-order rate constant in M s-1

We want to be able to calculate the concentration of A or P at any time:We have to integrate the rate law!

ktAA

ktAA

tkA

tkAtA

A

0

0

0

dd

dd

0

Integrated form of the zero order rate law

22Chemistry 2C Lecture 20: May 17th, 2010

Chemical Kinetics: Reactions of integral order

Zero-Order Reactions

In a zero-order reaction the rate is independent of the reactant concentration

Reactions are not of zero-order under all conditions

A common example are catalyzed reactions when the catalyst is saturated with substrate

23Chemistry 2C Lecture 20: May 17th, 2010

Chemical Kinetics: Reactions of integral order

First-Order ReactionsIn a first-order reaction the rate depends only on the concentration of the reactant raised to the first power:

AktA

d

drate k is the first-order rate constant in s-1

We get the integrated form of the rate law by integrating between t=0 and t=t

kt

tA

A

eAA

ktAA

tkAA

tkAA

0

0

0

ln

dd

dd

0

Integrated form of first-order rate law

24Chemistry 2C Lecture 20: May 17th, 2010

Chemical Kinetics: Reactions of integral order

First-Order Reactions

kteAA

ktAA

0

0

ln

First-order reactions are very common. Typical examples are:

βSP 01

3216

3215 Radioactive decay of phosphorous

Growth of E.Coli bacteria in culture

Isomerization of Acetonitrile CNCHNCCH 33

25Chemistry 2C Lecture 20: May 17th, 2010

Chemical Kinetics: Reactions of integral order

First-Order Reactions

• How long do I have to wait until the radioactivity of my samples has decayed enough to make it safe for disposal?

• How long does an antibiotic stay active in a patient?• How much time does it take for the bacteria in my culture to double

in cell mass?

The rate describes the process of the reaction accurately and allows us to calculate the concentration of reactants or products at any given time. However, from a practical point of view we are often interested in questions like:

The half-life of a reaction or process provides a convenient measure for this kind of question.

The half-life of a reaction is defined as the time it takes for the concentration of the reactant to decrease to half its original value.

26Chemistry 2C Lecture 20: May 17th, 2010

Chemical Kinetics: Reactions of integral order

First-Order Reactions

The half-life of a reaction is defined as the time it takes for the concentration of the reactant to decrease to half its original value.

kkt

ktA

A

693.02ln

20ln

21

21

0

The half-life of a first-order reaction is independent of the original concentration!

The half-life of a first-order reaction is constant!Measuring the half-life provides an easy way to determine k!