K2.1 collision theory

why may a theory be needed for bimolecular reactions

• may otherwise need to extrapolate k to non-lab conditions e.g. combustion, atmosphere, space

• may need to estimate k e.g. if there are too many reactions to measure

• some reactions are just hard to measure, e.g. if there is no detection scheme (no absorption in UV/vis, no dipole moment etc), e.g. no LIF for detection but reaction too fast for other methods

how does collision theory work

uses sizes and velocities of A and B to calculate the number of collisions per second which is then related to the Arrhenius A factor

the fraction of collisions with sufficient energy to react will be related to E_a

assumptions of collision theory

• reagents can be treated as hard spheres

• atomic radii

• no interactions between molecules

• impenetrable spheres so no distortion on collision

• use relative velocity and assume B is stationary

impact parameter

impact parameter, b, is defined as the closest perpendicular distance between the 2 centres at the point of collision

each collision has b somewhere between 0 and d

how is a collision defined

if b < d

collision cross section equation, symbol and units

how is collision volume calculated

in 1 unit time (1 second), a collision volume is swept out by each moving A molecule which is moving at the relative velocity v_rel

collision rate calculation for a single molecule and for the total collision rate

assumption for this calculation?

how is the assumption made in collision rate calculations corrected?

is collision rate greater than or less than reaction rate? why?

collision rate > reaction rate as not all collisions are reactive - some have insufficient energy to surmount the activation barrier

what is required for the collision to be reactive in terms of:

• energy

• velocity - give equation

relate to impact parameter

θ is the angle between v_rel and the line of centres

how is reaction rate calculated from collision rate

how is rate coefficient calculated from reaction rate

what can this equation be used to show

what is the temperature dependence of k_CT?

how is A_EXP determined

how are A_CT and A_EXP compared

how will they usually differ

CT usually overestimates the A factor by orders of magnitude - many collisions are ineffective as the reactive parts of the molecule do not collide due to incorrect orientation

exceptions to usual observation of A_CT vs A_EXP

P can be > 1 - the Harpoon mechanism