PLENTIFUL ENERGY

The free energy of the reaction of plutonium or PuCd 6 in cadmium with the
uranium chloride in the electrolyte still favors exchanging plutonium for uranium in
uranium chloride. Not all the difference in free energies of formation of plutonium
and uranium chloride can be eliminated by the formation of plutonium
intermetallic. Some difference remains in the direction of removal of the plutonium
metal by exchange with uranium in uranium chloride. Drawing down the uranium
chloride concentration in the electrolyte well below the plutonium chloride
concentration allows useful concentrations of plutonium to be deposited, always
along with higher actinides and substantial amounts of uranium.
Chemical reactions result from collisions between molecules, and the more
energetic molecules undergo reactions. The fraction of molecules with kinetic
energies sufficient to cause a reaction is proportional to an exponential of the form
exp((E f -E b )/RT), where (E f -E b ) is the difference between the free energies of
forward and back reactions and RT is the energy corresponding to temperature T. In
addition to the principal reaction in the ―forward‖ direction, there is always some
―back‖ reaction; it may be small or very small if the free energy differences are
substantial, but always there is some. The exponential allows calculation of the
balance between the forward and backward reactions. In our case, because the back
reaction—Pu metal forming from PuCl 3 in the presence of UCl 3 —is what we want,
the smaller (E f -E b ) can be made (again in our case by use of a liquid cadmium
cathode), the easier it is to deposit plutonium metal.
The PuCl 3 /UCl 3 ratio in the electrolyte must be high enough to give a back
reaction sufficient for a useful rate of Pu metal deposition. The PuCl 3 /UCl 3 ratios
necessary for useful depositions can be calculated from equilibrium considerations.
In fact, what goes where, and how much, and in what form is extremely important,
and it is possible to calculate it from the simple principles of equilibrium in
the rates of the reactions of each of the elements.
Pu metal (just created by electrorefining) reacts with UCl 3 in the electrolyte to
form U metal and PuCl 3 (returning the plutonium once more to the electrolyte.) At
equilibrium the rates of the two reactions—the forward reaction Pu + UCl 3 , and the
back reaction U + PuCl 3 —are equal. The concentrations given by the back reaction
must increase until this is so.
Pu +UCl 3 U + PuCl 3 .
The reaction rates are directly proportional to the ―activities‖ denoted by the
symbol ―a‖ The activities in turn are approximately proportional to concentrations.
Where they are not, they are corrected by altering the concentrations by an amount
given by an ―activity coefficient,‖ essentially a fudge factor, known and tabulated
for our reactions of interest. The concentrations corrected in this way are the
―activities‖ or ―chemical activities‖ that determine the reaction rates.
205