What makes you think it would be a kinetic model rather than a steady state? It will be difficult to do for a cell, unless you have an estimate of the area of a cell. Most people would do this per unit area, and probably in a derivative of SI units - so mm2. I would guess that unless something is actively happening to the solute in terms of concentration gradient or active transport, that the answer will be a constant and written in terms of molecules per area per second.
I have no idea how to do this mathematically, but I can guess that the parameters will be concentration of the solute, volume you have over your surface, surface area of the cell/unit area and diffusion rate (which in turn is dependent on temperature...) and time.
You probably also need to define what is happening in the system - is the solute transported across the cell membrane? If so, how fast does this occur, and within what parameters?