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# Chemical Kinetics - PowerPoint PPT Presentation

Chemical Kinetics. The Binary Collision Model. Must actually have a hydrogen molecule bump into a chlorine molecule to have chemistry occur. Reaction during such a collision might look like the following picture:. H. H. H. H. Cl. Cl. Cl. Cl. Cl 2. H 2. +. Collision Frequency.

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## PowerPoint Slideshow about ' Chemical Kinetics' - jasmine-lancaster

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Presentation Transcript

The Binary Collision Model

Must actually have a hydrogen molecule bump into a chlorine

molecule to have chemistry occur. Reaction during such a

collision might look like the following picture:

H

H

H

Cl

Cl

Cl

Cl

Cl2

H2

+

Real gases consist of particles of finite size that bump

into each other at some finite rate.

Assume first that the red molecule has a constant speed

C and the green ones are standing still.

Vc = (AB)2 C

No Collision

Collision

2 A

AB=A + B

B

AB=A + B

Collision

If a green molecule has some piece in this volumeCollision!

AB = A + B

A is the radius of molecule A, B the radius of B

molecule flew through a cloud of motionless green ones at a speed

of C.

In reality, of course, all the molecules are moving.

<urel>is the mean speed of molecule A with respect to molecule B.

Where =mA mB/(mA+mB)

 is called the reduced mass and can be thought of as a kind of

(geometric) average of the masses of A,B.

zNA= (AB)2 <urel>(NB/V)NA

By convention, because we don’t want our results to depend on

the size or volume V of our experimental apparatus, we define ZAB:

ZAB is the total number of collisions between all A and all B

Molecules per liter (or per ml depending on units used for V).

Note that ZAB depends on 4 things:

When we multiply z by NA we count the collisions of all A

molecules with all B molecules. When A=B (all collisions

are of A with other A’s) this turns out to count all collisions

twice!

Thus, <urel>=(2)1/2(8kT/mA)1/2

(8kT/mA)1/2 is the average speed of a molecule even as

(3kT/mA)1/2 is the root mean square speed of a molecule

This gives:

ZAA = (1/2) (2)1/2(AA)2(8kT/mA)1/2(NA/V)2

H

H

Transition

State

Cl

Cl

E

EA

H2 + Cl2

2HCl

E ∆H

Reactants

Products

but rather how much energy is available in the collision

which in turn depends on the relative speed of A,B approach.

Even knowing how Z depends on energy is not

sufficient. We must also know the probability of

reaction at a given energy.

A very simple model for P rate ZR is the “all or nothing”

model where PR(E)=0, E<EA and PR(E)=1, E>EA.

By convention PR is associated with the collision

“cross section” (AB)2:

The reaction cross section, (R)2, is the

product of the reaction probability, PR,

at a given energy and the collision cross

section, (AB)2.

Reaction rate Z“Cross Section” R2

A + B  Products

All or Nothing Model

R2 = PRAB2

PR

1

0

E

EA

PR(E) = 0 when E<EA

PR(E) = (1-EA/E) when E>EA

Reaction Cross Section rate Z

A+B Product

PR=0

E≤EA

PR=(1-EA/E)

E>EA

Arrhenius Model

R2=PRAB2

1

PR

1/2

PR = 1, E>>>EA

PR = 0.9, E=10EA

EA

2EA

3EA

10 EA

E