[lullu]

if the adsorption isotherm represents partial pressure (gas, vapour) or concentration (liquid) of the adsorbate in the fluid and the solute loading on the adsorbent, why during the adsorption the concentration of the adsorbate increase?

[Stepan]

If I understand you question correctly:

While the adsorption is in progress (kinetics of adsorption), the adsorbate amount grows with time, and solute concentration drops to the point when the system reaches equilibrium. In equilibrium point, concentrations do not change. The equilibrium point can be plotted on the chart as C(ads) vs C(sol). If one collects enough points (at the same temperature), and plot them on a chart, it is called Isotherm. 

Isotherm is a representation of equilibrium between adsorbate and solute.

[lullu]

Thanks a lot!