1. Lecture 21

2. 27.2 Diffusion-controlled reactions
Cage effect: The lingering of one molecule near another on account of the hindering presence of solvent molecules.
Classes of reaction
Suppose that the rate of formation of an encounter pair AB is first-order in each of the reactants A and B:
A + B →AB v = kd[A][B]
The encounter pair, AB, has the following two fates:
AB → A B v = kd’[AB]
AB → P v = ka[AB]
The net rate of change of [AB]:
= kd[A][B] - kd’[AB] - ka[AB]

3. Invoking steady-state approximation to [AB]
The net rate of the production:
When kd’<< ka k2 = kd (This is diffusion-controlled limit)
When kd’>> ka (This is activation-controlled reaction)

4. Reaction and Diffusion
where R* is the distance between the reactant molecules and D is the sum of the diffusion coefficients of the two reactant species.
where η is the viscosity of the medium. RA and RB are the hydrodynamic radius of A and B.
If we assume RA = RB = 1/2R*

5. 27.3 The material balance equation
(a) The formulation of the equation
the net rate of change due to chemical reactions
the over rate of change
the above equation is called the material balance equation.

6. (b) Solutions of the equation

7. 27.4 The Eyring equation
The transition state theory pictures a reaction between A and B as proceeding through the formation of an activated complex in a pre-equilibrium:
A + B -> C‡
K‡ = ( `‡` is represented by `±` in the math style)
The partial pressure and the molar concentration has the following relationship:
pJ = RT[J]
thus
[C‡] = K‡ [A][B]
The activated complex falls apart by unimolecular decay into products, P,
C‡ → P v = k‡[C‡]
So v = k‡ K‡ [A][B]
Define k2 = k‡ K‡
v = k2[A][B]

8. (a) The rate of decay of the activated complex
k‡ = κv
where κ is the transmission coefficient. κ is assumed to be about 1 in the absence of information to the contrary. v is the frequency of the vibration-like motion along the reaction-coordinate.

9. (b) The concentration of the activated complex
Based on Equation 20.54, we have
with ∆E0 = E0(C‡) - E0(A) - E0(B)
are the standard molar partition functions.
provided hv/kT << 1, the above partition function can be simplified to
Therefore we can write
qC‡ ≈
where denotes the partition function for all the other modes of the complex.
K‡ =

10. (c) The rate constant
combine all the parts together, one gets
k2 = k‡ K‡ = κv
then we get
k2 = κ (Eyring equation)

11. (d) The collisions of structureless particles
A B → AB
Because A and B are structureless atoms, the only contribution to their partition functions are the translational terms:
k2 = κ
k2 = κ NA