Molecular Reaction Dynamics

Reactions occur because atoms/molecules collide and interact with each other

Collision theory relates rates of gas phase reactions to their rate

Basis is that, for bimolecular reactions, products are formed only if the collision is sufficiently energetic

Consider a simple reaction : A + B -> P

Rate : v = k[A][B]

Second order reaction

Rate constant dependent on a number of physical requirements relting to the collisions which occur

Rate of collisions- reaction rate a rate of collisions

Related to the mean molecular speed c (c a (T/M)0.5) ,M is the molar mass

If s is the collisional cross sectio, then

v a s (T/M)0.5NANB a s (T/M)0.5[A][B] or k a s (T/M)0.5

Energy - a minimum kinetic energy is required for a successful collision, thus a Boltzman factor must be included in the rate constant

k a s (T/M)0.5{exp(-Ea/Rt)}

Finally, molecules may need to collide in a particular orientation, so a steric factor, P, needs to be applied or

k a Ps (T/M)0.5{exp(-Ea/Rt)}

Thus, the form of rate constant: k a steric factor x encounter rate x minimum energy requirement

Each of these factors will now be considered

Collision density (ZAB) = # of collisions/volume/time

Units: m-3 s-1

Related to the collision frequency, z, discussed in section of gases (Chapter 1)

ZAB = s (8kT/πµ)0.5Na 2[A][B]

s = collision cross section = πd2; d =1/2(dA +dB)

Area subtended by a circle of diameter, d

Assumes elastic hard spheres ( see next page)

Na is Avagodro’s number

Na[A] is the number density of A

µ is the reduced mass = (mAmB)/(mA + mB)

If A=B, ZAB = s (4kT/πµ)0.5Na 2[A]2

Reduced by 1/2 because you would double count collisions

Collision densities can be large - N2 @RT Z= 5 x 10 34 m-3 s-1 (d = 280 pm)

...