Equations to describe the amount and rate of sorption

The partition of materials that react with soil between the solid and the solution phase, and how this changes with time, can often be described by a simple equation: S = a cb1tb2 where S is the amount sorbed, c is the solution concentration, t the time of contact, and a, b1 and b2 are parameters. However, when the range of values for sorption is large, it is apparent that both b1 and b2 increase with decreasing sorption. At low values for sorption, b1 approaches 1, and sorption plots are nearly linear. These observations are consistent with a mechanistic model in which it is postulated that the materials react with heterogenous sites. As the amount of sorption decreases, the heterogeneity of the occupied sites decreases. This is why b1 increases. Because there is heterogeneity of occupied sites, there is a range of rates for the subsequent reaction. This is why the rates are proportional to a fractional index of time. It is better to describe the effects of time this way than by using several first‐order equations.