The macroscopic rate kernel

Before solving eqn. (299) for the singlet density of A, it is worthwhile to consider what the rate coefficient being sought actually is. The reaction between A and B is irreversible and proceeds with a rate kt. The concentration of B is unaffected by reaction and remains at the equilibrium value eQ. By contrast, the reaction leads to a decreasing concentration of A with time. Kapral defined a concentration of A in excess of the equilibrium value of as 

The equilibrium concentration of A is zero if the reaction is irreversible however, it is a useful idea to consider when extending the theory to reversible reactions. All these concentrations are spatially uniform. A rate law t 

In order to develop the spatial average of the singlet density, Kapral first took the Fourier transform of eqn. (299) and considered the limit as the wave vector, k, tends to zero (i.e. the term e 1 is constant throughout the system) and so 

5nA(z) is the average value of the singlet density over the system volume V and over all velocities. The details of the Fourier transformation techniques are left to the interested reader. Kapral found that the rate coefficient is of the form 

In developing this rate kernel [eqn. (303)]. Kapral noted that one term could be ignored because it was small. This is a factor which allows for non-equilibrium flow of A and B towards each other. 

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