Equation (9) describes the rate of change of concentration of solute in the mobile phase in plate (p) with the volume flow of mobile phase through it. Integrating equation (9) will provide the elution curve equation for any solute eluted from any plate in the column.
First consider the conditions of the above equation when an initial charge of concentration Xo(m) has been placed on the first plate of the column, but chromatographic development has not commenced, i.e., v=0.
The first condition states that before development commences, the concentration in plate p=0 is merely that resulting from the injection of the sample onto the column. The second condition states that the remainder of the column is free of solute.