Bimolecular rate constant, hard spheres

This is identical with the expression previously obtained (Section 2-2) for the bimolecular rate constant for a reaction involving dissimilar elastic hard spheres with a steric factor of unity, since -h AEq /RT =... 

The above discussion shows that very good agreement of observed and calculated exchange rate constants can be obtained using the semiclassical formalism. In the bimolecular reactions discussed in this paper the reactants were treated as hard spheres and an outer-sphere mechanism was assumed. If the... 

Collision theory is based on the concept that molecules behave like hard spheres during a collision of two species, a reaction may occur. To estimate a rate constant for a bimolecular reaction between reactants A and B based on this theory, one needs first to calculate the number of collisions occurring in a unit volume per second (ZA1 ) when the two species, A and B, having radii rA and ru, are present in concentrations jVa and Aru, respectively. From gas kinetic theory, this can be shown to be given by Eq. (I) ... 

Since any quenching action is a bimolecular process, it is essential that the molecules M and Q should be in relatively close contact, but not necessarily in hard sphere (van der Waals) contact. Theoretical models lead to the distance dependence of the quenching rate constants as exponentials or sixth powers of r, the centre-to-centre distance of M and Q. Since these distance dependences are very steep, it is convenient to define a critical interaction distance r at which the quenching efficiency is, this being the distance at which 50% of the molecules M decay with emission of light (or undergo a chemical reaction) and 50% are quenched by some nearby molecule Q. 

The pre-exponential factor of a bimolecular reaction is related to the reaction cross-section (see Problem 2.3). A relation that is fairly easy to interpret can be obtained within the framework of transition-state theory. Combining Eqs (6.9) and (6.54), we can write the expression for the rate constant in a form that gives the relation to the (hard-sphere) collision frequency ... 

Collision theory for a bimolecular reaction in the gas phase treats the individual reactant species as hard spheres and introduces a threshold energy for the reaction. The expression derived for the temperature dependence of the bimolecular second-order rate constant is of the same form as that for the Arrhenius equation. The theoretical A-factor is related to the rate at which reactant species collide and is calculated to be of the order of 10 dm mol s , although experimental values can be smaller than this by several orders of magnitude. 

The value of fcg was 10 = = exp [(—450 300)/r] cm mol s between 293 and 573 K the frequency factor is surprisingly large, and is closely similar in magnitude to the hard-sphere bimolecular collision frequency for 2BrO. The rate constant for the reaction... 

Reaction (36) has been used to measure absolute [F observed in resonance fluorescence in the far vacuum-u.v. (Section 2). Rate constants approaching the hard-sphere bimolecular collision frequency at 298 K have been reported (Table 7). 

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