APPENDIX A1

Refractive Index of the Reaction Mixture as a Function of the Extent of Reaction

If a, b, and c are defined as the number of moles of glycidol, water and glycerol, respectively, at any given time, then

and

We can also define a_o, b_o, c_o as the initial number of moles of each species and a parameter z to represent the extent of the reaction according to

Note that z ranges from zero, before any of the glycidol has reacted, to one, if the reaction goes to completion. Substituting these expressions into equations A1-1 and  A1-2 gives the mole fractions of water and glycerol as a function of the extent of the reaction:

and

These two expression can then be substituted into equation A1-5 to obtain an analytical expression for the index of refraction of the reaction mixture in terms of the parameter z, the initial number of moles of each reagent, and their indices of refraction:

Figure A1-1 shows a graph of this function evaluated using the reaction conditions specified in the procedure. Note that the function is very nearly linear over the entire course of the reaction.