Plate Theory and Extensions - The Plate Theory > Page 4
Differentiating equation (1),
dXs = KdXm (2)
Consider three consecutive plates in a column, the (p-1), the (p) and the (p+1) plates and let there be a total of (n) plates in the column. The three plates are depicted in Figure 2.
Figure 2. Three Consecutive Theoretical Plates in a Column
Let the volumes of mobile phase and stationary phase in each plate be (vm) and (vs) respectively, and the concentrations of solute in the mobile and stationary phase in each plate be Xm(p-1), Xs(p-1), Xm(p), Xs(p), Xm(p+1), and Xs(p+1), respectively. Let a volume of mobile phase, dV, pass from plate (p-1) into plate (p) at the same time displacing the same volume of mobile phase from plate (p) to plate (p+1). As a result, there will be a change of mass (dm) of solute in plate (p) which will equal the difference in the mass entering plate (p) from plate (p-1) and the mass of solute leaving plate (p) and entering plate (p+1). It is now possible to apply a simple mass balance procedure to the plate (p).