The steric effect Steric factor, P, Reactive cross-section, σ*, Harpoon mechanism: Electron transfer preceded the atom extraction. It extends the cross-section for the reactive encounter. K and Br2 reaction

Example 24.1 Estimate the steric factor for the reaction H2 + C2H4 -> C2H6 at 628K given that the pre-exponential factor is 1.24 x 106 L mol-1 s-1. Solution: Calculate the reduced mass of the colliding pair From Table 24.1 σ(H2) = 0.27 nm2 and σ(C2H4) = 0.64 nm2, given a mean collision cross-section of σ = 0.46 nm2. P = 1.24 x 106 L mol-1 s-1/7.37 x 1011 L mol-1s-1 = 1.7 x 10-6

Solution: The above reaction involves electron flip Example 24.2: Estimate the steric factor for the reaction: K + Br2 → KBr + Br Solution: The above reaction involves electron flip K + Br2 → K+ + Br2- Three types of energies are involved in the above process: (1) Ionization energy of K, I (2) Electron affinity of Br2, Eea (3) Coulombic interaction energy: Electron flip occurs when the sum of the above three energies changes sign from positive to negative

24.2 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]

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)

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 (DA + DB). 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*

24.3 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.

(b) Solutions of the equation

Transition State Theory Activated complex theory Using the concepts of statistical thermodynamics. Steric factor appears automatically in the expression of rate constants.

24.4 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]

(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.

(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‡ =

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

(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

Kinetics Salt Effect Ionic reaction A + B → C‡ C‡ → P d[P]/dt = k‡[C‡] the thermodynamic equilibrium constant Then d[P]/dt = k2[A][B] Assuming is the rate constant when the activity coefficients are 1 ( ) Debye-Huckle limiting law with A = 0.509 log(k2) = log( ) + 2AZAZBI1/2 (Analyze this equation)

Experimental tests of the kinetic salt effect

Example: The rate constant for the base hydrolysis of [CoBr(NH3)5]2+ varies with ionic strength as tabulated below. What cab be deduced about the charge of the activated complex in the rate-determining stage? I 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300 k/ko 0.718 0.631 0.562 0.515 0.475 0.447 Solution: I1/2 0.071 0.100 0.122 0.141 0.158 0.173 Log(k/ko) -0.14 -0.20 -0.25 -0.29 -0.32 -0.35

24.6 Reactive Collisions Properties of incoming molecules can be controlled: 1. Translational energy. 2. Vibration energy. 3. Different orientations. The detection of product molecules: 1. Angular distribution of products. 2. Energy distribution in the product.

24.7 Potential energy surface Can be constructed from experimental measurements or from Molecular Orbital calculations, semi-empirical methods,……

Potential energy surfaces, pt. 2.

Various trajectories through the potential energy surface

24.8 Results from experiments and calculations (a) The direction of the attack and separation

Attractive and repulsive surfaces

Classical trajectories