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Module 7 : Theories of Reaction Rates

Lecture 32 : Theories Of Reaction Rates : Collision Theory

At large distances, neutral K and Br₂ have lower energy than ionic K ⁺ and Br₂^- because more energy is needed to separate the ionic species. For all r greater than r^, the potential energy curve for the neutral reactants lies lower than the potential energy for the ionic reactants. At r = r^, the two potential energies are equal and for r values less than r^*, the ionic potential energy curve is lower than the neutral reactants curve, because of the strong electrostatic attraction between K⁺ and Br₂^-. The difference in the energy (E) between the charged pair ( K⁺ and Br₂^-) and the neutral pair is

E = ( I - E_a - e² / r ) - E _{neutral pair}	(32.24)

Where I is the ionization energy of K, E_a, the electron affinity of Br₂ and - e²/r, the electrostatic attraction. For r < r ^, E is negative (more attractive) and therefore the distance at which the electron jumps from K to Br₂ is when r = r , where the term in brackets goes to zero, i.e.,

e² / r ^* = I - E _a or r ^* = e²/ ( I - E_a)	(32.25)

Since the electron or the harpoon shoots across from K to Br₂ when r = r^, ( r^) ² may be identified as the reaction cross section. It is after this transfer that the reactants are further accelerated towards each other and finally depart as products KBr and Br. This reaction cross section may be compared with the collision cross section d² where d is the contact distance between K and Br₂. This ratio is is the steric factor P discussed earlier.

P = / = ( r^* / d ) ² = { e² / d ( I - E_a ) ]} ²	(32.26)

For K, I = 420 kJ / mol, E_a of Br₂ is 250 kJ/ mol and d = contact distance = [ d (K) + d (Br₂)] / 2 = 400 pm. d(K) is the diameter of K and d(Br₂) is the average diameter of Br₂. We note that this calculated value of P 5 which matches with the experimental value of P.

To find the reaction cross section of reactions, one needs to know the potential energy curves (surfaces when more than one independent variable like r above are involved) and other details such as probabilities of passage from reactants to products. These involve detailed microscopic calculations. Experiments involve crossed molecular beams which will be outlined in a later lecture.