PLENTIFUL ENERGY

Eventually the amount of product will build up enough that the backward rate
(and there will always be a backward rate) equals the forward rate of product
formation. The backward rate—the rate at which the product of a reaction
dissociates into the original components of the reaction—may be small, as we have
noted. In fact it may be microscopically small, and present only due to highly
unlikely statistical fluctuations. But equality of forward and backward rates comes
when the concentrations of reactants have so decreased and the amount of product
has so increased that the two rates overall are equal. In those reactions where the
backward rate is extremely small and present only because of statistical
fluctuations, reactions go to almost perfect completion. And where clean
separations are important, that's what is wanted.
A fission product can go entirely (well, almost) into the electrolyte and stay there
because this is the equilibrium result. And importantly, we can calculate its
distribution—where it is and in what quantity. Equating the forward and backward
rates, and taking the ratio of the two gives the ―equilibrium constant.‖ From the
equilibrium constant we can predict the degree of separation of each element, and
that is exactly what the IFR chemists do, in a computer program that handles
the multitude of elements.
To the present time, the rates of electrorefining do not appear to affect the
assumption of equilibrium, at least to the accuracy the distributions could be
measured. Running the process faster may bring in issues that lessen the accuracy
of the equilibrium assumption. Today the process can be run fast enough to be
practical, and equilibrium distributions seem to hold but the rates at present may not
be optimal. Eventually there may be economic pressure to run the process faster,
perhaps to a point where the kinetics of the process do become important.
The things that matter to the rate of a reaction are not surprising: They are the
concentrations of the reactants, or rather the concentrations that actually contribute
effectively to the reaction, along with the factor that accounts for the fraction of
molecules actually having high enough energies to surmount the activation barrier.
Concentrations are relevant because reactions depend on collisions taking place,
and the more tightly packed the reactants are—the higher the concentrations—the
more collisions there will be. And the factor that accounts for the necessity of
molecular energies to equal or exceed the activation energy is just the familiar
Arrhenius exponential, exp(-Ea/RT).
The rate of a reaction then is given by the relationship Aexp(-Ea/RT) multiplied
by the concentrations contributing to the reaction. In this expression A is a constant
(the pre-exponential constant) which cancels out in the important concept that we
have been coming to—that of the equilibrium constant.
358