The binding of heavy metals by a biosorbent with binary functional groups was mathematically modeled. An FT-IR spectrophotometer analysis was employed to determine the stoichiometry between the protons in the functional groups of alginic acid and lead ions as a model system. The results calculated using an equilibrium constant agreed well with the experimental results obtained under various operating conditions, such as pH and metal ion concentration. It was also shown that the overall adsorption phenomenon of alginic acid was mainly due to its carboxyl groups. The equilibrium constants for each functional group successfully predicted the lead adsorption of ${alpha}$-cellulose. Furthermore, the biosorption model could predict the adsorption phenomena of two metal ions, lead ions and calcium ions, relatively.