This preview shows page 1. Sign up to view the full content.
Unformatted text preview: se standard Ea’ for second expression
L Grondahl CHEM2056 Collision theory for 2nd order
reactions E / RT
k Ae a The product of A and e(-Ea/RT) gives the rate of successful collisions
The pre‐exponential factor, A, is a measure of the rate at which collisions occur irrespective of their energy
The fraction of collisions with a kinetic energy greater than that of Ea is given by the Boltsmann distribution as e(-E/RT) L Grondahl CHEM2056 Energy requirement k Ae E a / RT The thermal energies of molecules increases with temperature, so according to the collision theory for chemical reactions, the number of collisions with energy greater than Ea would increase at higher temperatures. I.e. rate constant should increase with temperature.
Kinetic theory of a gas:
Fraction of molecules with sufficient energy for collisions to be successful increases exponentially with increasing temperature.
The fraction of collisions with a kinetic energy greater than that of Ea is given by the Boltsmann distribution as e(-E/RT) L Grondahl CHEM2056 L Grondahl CHEM2056 Interpretation of parameters
2nd order E / RT
k Ae a The pre‐exponential factor, A, is a measure of the rate at which collisions occur irrespective of their energy
1: Encounter rate – i.e. molecules must collide and do so at a certain
2: Steric requirement – i.e. molecules must be suitably oriented on
collision Encounter rate
A+B k k Ae E a / RT P Relative mean speed of molecules at collision: 1/ 2 8k T crel b ‐where kb is the Boltzmann’s constant, and is the reduced mass: = mAmB/(mA + mB) (molecular masses).
‐If reaction between two same molecules then = ½ mA
L Grondahl CHEM2056 Encounter rate k Ae E a / RT L Grondahl CHEM2056 Second order rate constant
Experimentally observed relationship: The collision cross‐section, , which is average of two cross‐sections (approximation for non‐spherical species)
Theoretically derived relationship:
Area which molecule A must enter around molecule B in order for collision to occur
Values for σ for single molecules can be looked up in tables
σ for the collision is the mean: σ = ½ (σA + σB) L Grondahl CHEM2056 k Ae E a / RT
k crel e E a / RT Theoretically derived expression for pre‐exponential factor: 1/ 2 8k T A N A b NA is Avogadro constant; included in order to get theoretical expression of the same form as the observed rate constant (i.e. unit of A is L mol‐1 s‐1)
L Grondahl CHEM2056 Examples of values for the “A” factor
Reaction A (L mol-1 s-1) Steric Requirement, P. P Experimental Theory 2NOCl 2NO +
Cl2 9.4 x 109 5.9 x 1010 0.14 2 HI H2 + I2 4.6 x 1010 4.6 x 1010 1.0 H2 + C2H4 C2H6 1.24 x 106 7.4 x 1011 1.7 x 10-6 Expression for pre‐exponential factor accounting for steric requirement: Reaction can occur 1/ 2 Reaction
cannot occur 8k T A P N A b L Grondahl CHEM2056 L Grondahl CHEM2056 Steric Requirement, P. Example: Estimating a steric factor (P)
The collision cross-section
is the target area that
results in simple deflection
of the colliding molecule.
The reaction cross-section
is the area for chemical
change to occur on
View Full Document