Extensive reading: Levine, pp....

§9.6 Rate Theories of elementary reaction

Extensive reading: Levine, pp. 879-881

Two important empirical rules:

Rate equation (law of mass action)

Arrhenius equation

RT

EAk aexp

Type of

reaction

Unimolecular

reaction

Bimolecular

reaction

Termolecular

reaction

A 1013

s

1011

mol-1dm3s-1

109

mol-2dm6s-1

A seems related to collision frequency.

RT

EaexpBoltzmann distribution term

[A][B]r k


It is obvious that a molecule of A cannot react with a molecule of B

unless the two reactant molecules can somehow interact.

This interaction can only take place if they come within a certain

distance of each other, i.e., collides with each other.

Therefore, the rate constant of the reaction may be predicted by

calculation of the collision frequency of the reactants.

Collision theory is proposed independently by Max Trautz in

1916 and William Lewis in 1918. Thereafter, C. Hinshelwood made

modification on its.

Basic consideration and brief history

http://en.wikipedia.org/wiki/Collision_theory


Basic consideration and brief history


Z. anorg. Chem. 94 (1916), 79

9.6.1 Fundamental assumptions of SCT

For gaseous bimolecular reaction

1) The reaction rate of reaction is proportional to the collision

frequency (Z), which can be solved by kinetic theory of molecule;

ABr Z q

where ZAB is the collision frequency of A with B per unit cubic meter

per second, q is the portion of effective collision.

reaction rate can be expressed as:

2) The collision can be either non-reactive (elastic) collision or

reactive collision. Only the molecules posses energy excess to a

critical value (Ec) can lead to reactive collision. The reaction rate

should be in proportion to the fraction of reactive collision (q).


9.6.2 Calculation of ZAB

SCT assumes that molecules can be taken as rigid ball without inner

structure.

dA dB

dA and dB are the diameter of A and B molecule, respectively.

Definition: mean collision diameter: dAB

ABBA d

dd

2

The way to collide:


Definition:collision cross-section

2

ABdS

2

ABAB dZ V

NB

A

AV

NBmotionless



When the concentration of A is NA/V (molecm-3):

2

ABAB dZ V

N

V

N BAA

When both A and B moves, the relative velocity VAB should be used.

22

BAAB



i

iM

RT

8according to the kinetic theory of gases

A BAB

A B A B

8 8 8 M MRT RT RT

M M M M

AB

8RT

A B

A B

M M

M M

(reduced mass)

2 2A B A BB AB

2 2

8 8

8[A][B]

AB A

AB

N N Ln LnRT RTZ d d

V V V V

RTL d



Decomposition of HI: 2HI = H2 + I2

2 2 2

AA AA

A

2 8[A]

2

RTZ L d

M

2 2

AB AB

8[A][B]

RTZ L d

?

For example

At 1.0 105 Pa and 700 K, d = 3.50 10-10 m, Z HI-HI = ?

53

1 1

1.0 10 Pa[HI] 17.41mol m

8.314J K mol 700K

p

RT

23 2 10 2 2

AA 3

34 3 1

2 8 8.314 7003.1416(6.02 10 ) (3.50 10 ) (17.41)

2 3.1416 128 10

1.017 10 m s

Z

Generally, ZAB of gaseous reactions at ambient temperature and

pressure is of the magnitude of 1035 m-3s-1.



If reaction takes place whenever the molecules collides:

2 2

AB AB

8[A][B]

RTZ L d

A

AB

[A]

Nd

dVr L Z

dt dt

2ABAB

[A] 8[A][B]

Zd RTd L

dt L

[A][A][B]

dk

dt 2

AB

8RTk d L

because

k = 7.88 104 mol-1dm3s-1

When c0 = 1.00 mol dm-3, the half-life of HI is 1.27 10-5 s.

This result differs greatly from the experimental fact. In 1909, Max

Trantz introduced fraction of reactive collision (q) to solve this great

discrepancy.

9.6.3 Calculation of q

Only the molecules posses energy excess to a critical value (Ec) can

lead to reactive collision.

It is apparent that E of translational energy of motion is related to

the relative motion of two molecules. And Ec is thus the minimum

translational energy of motion (critical / threshold energy) along the

connecting line between the mass-point of the two molecules which

are to collide.


If the energy exchange between colliding molecules is much

rapid than reaction, the energy distribution of molecules may still

obey the Maxwell-Boltzmann distribution equation.

RT

E

n

nq cexp

*

Boltzmann factor

If Ec = 120 kJmol-1, T = 300 K, then

q = 1.27 10-21

This suggest than among 7.8 1020 collision only one collision is

effective.

The fraction of the collision with the energy equal to or greater than

Ec is:

9.6.3 Calculation of q


9.6.4 Calculation of k

ABr Z q

2 2 A BAB AB

A B

8[A][B]

M MRTZ L d

M M

2

AB

8exp [A][B]cERT

r d LRT

[A][B]r k

2

SCT AB

8exp cERT

k d LRT

RT

EBTk c

SCT exp2

1

B is a constant independent of T.

RT

E

n

nq cexp

*


RT

EAk aexp

ca ERTE 2

1

RT

EBTk c

SCT exp2

1

The experimental activation energy (Ea) depends on temperature.

Using Ea for substitution of Ec,

2

AB

8exp c

SCT

ERTk d L

RT

2

AB

8exp a

SCT

ERTek d L

RT

The pre-exponential factor

corresponds to the collision

frequency. This is the reason

why A is also named as

frequency factor.

9.6.4 Calculation of k


9.6.5 Comment on SCT

1) The expression for the rate coefficient given by SCT conforms

qualitatively to the Arrhenius equation observed experimentally. This

suggests that SCT reveal the principal features of the reaction, i.e., in

order to react, molecules have to collide (the pre-exponential term) and

the collision should be sufficiently energetic (the exponential term)

(1) Success

SCT gives a vivid physical image of the reaction process:


2) As pointed out by SCT, the pre-exponential factor, dependent

only on the masses of the species involved in the collision, can be

calculated easily.

ca ERTE 2

1

SCT reveals the physical meaning of the pre-exponential factor,

i.e., the collision frequency.

3) SCT demonstrated theoretically that experimental activation

energy depends on temperature.



(2) Shortcomings

1) For calculating k, Ec is needed. However, SCT can not give Ec.

Calculation of k depends on the experimental determination of Ea.

Therefore, SCT can not predict the kinetic features of the reaction

theoretically.

2) The quantitative agreement between SCT and experiments is poor.

Reaction Ea Acal Aexp Acal./Aexp.

2NOCl2NO+Cl2 107.8 2.95109 3.23109 0.91

H+Br2 HBr+Br 3.76 4.61010 6.76109 6.76

NO+O3NO2+O2 9.61 7.94109 6.31107 1.25102

CH3+CHCl3 CH4+CCl3 24.2 1.51010 1.26106 1.19104

2-cyclopentadiene dimer 60.6 8.13109 2.45103 3.32106



In some cases, the agreement between experimental and calculated A

values can be quite good. However, in many cases, the observed rate is

definitely too small. It was found that the more complex of the reactant

molecules, the greater the discrepancy between Acal and Aexp.

In fact, the reactant is of complex molecular structure. To take reactant

molecules as rigid balls without inner structure will spontaneously result

in systematic error.

?

2 ONBr Br2 + 2 NO



Substitution

OH¯+ CH3Br CH3OH + Br¯



图片1.gif

图片1.gif

The great discrepancies between experimental and calculated A

were recognized around 1925. The equation

RT

EAk a

SCT exp

was then modified by introduction of an empirical factor P called

the steric factor / probability factor.

RT

EPAk a

SCT exp.

.exp

calA

AP

Steric factor (P), ranging between 1~10-9, represents the fraction of

energetically suitable collisions for which the orientation is also

favorable, can be only determined experimentally.

SCT can not give any clue to calculate P.

9.6.6 Modification of SCT


,

AB expcERT

k d LRT

12 8

,

AB expcERT

k L dRT

22 8

1, ,

2

log log log a a

kE E

k RT

1 1

1 2

2 2

1

9.6.7 Application of SCT is solution reactions


（a）碰撞频率。大量溶剂分子的存在会导致反应物分子与溶剂分子间产生

频繁碰撞，致使反应物分子间的碰撞几率降低，指前因子（A）下降；

（b）分子间的阻滞作用。溶质分子与溶剂分子之间存在的作用力致使反应

物分子的运动速率（v）降低--微观黏度（micro-viscosity）作用[6-10]；

（c）反应物活度。由于溶剂—溶质分子间存在作用力，导致溶液偏离理想

行为，使反应物的活度系数（）降低，反应速率随之下降。--“原盐效应

（primary salt effect）”；

（d）溶剂化。包围在反应物、中间产物或者过渡态、反应产物周围的溶剂

分子会构成一个静电场，影响这些物质的结构、尺寸、电子分布 [2, 3, 10-16]，

进而影响反应的活化能（Ea）。这种影响通常与溶剂分子的偶极矩相关；

（e）溶剂催化。溶质和溶剂分子间的作用力可能使某些化学键被活化，从

而改变反应途径和活化能（Ea），使得反应产物的种类或者比例发生改变；

（f）溶剂分子的运动速率。分子的热运动速率与分子量有关。如果溶剂分

子的分子量小于反应物分子的，则溶剂分子的运动速率高于反应物分子，反

应物分子的运动会被加速，呈现“负黏度”（negative viscosity）现象。

9.6.7 Application of SCT is solution reactions


Extensive reading: Levine, pp....

Documents

Transcript of Extensive reading: Levine, pp....