Introduction: In studies of the adsorption of pollutants onto different adsorbents, determining the adsorbent dose of the most important characteristics must be considered. The aim of the study was the determination and modeling of dose-response bone char fluoride removal from aqueous solutions and comparison of the adsorption isotherm models with dose-response models from the perspective of adsorption.

Methods: In this experimental study, bone char was prepared by using an electric furnace at 450˚C in two hours. Sorting the adsorbent was conducted by standard sieve ASTM in the range of 18-35 meshes and its characteristics were determined with conventional methods. The concentration of fluoride was measured according to the recommendation of manufacturer (HACH) with Dr-5000 of regent fluoride. Dose-response models were fit to the data and parameters were estimated. Based on the quality of fitness indicators, the adsorption isotherm models were compared with dose-response models. Analysis of the data in this study was performed using the R software version 3.1.2 and stats package.

Results: Fit indexes (AIC and R²) showed that the most appropriate model for the data in pH= 10, concentration = 10 and pH = 7, concentration = 20 was the Emax model and in pH = 7, concentration = 10 and pH = 7, concentration = 15 the quadratic model. According to these models, the median of effective dose on bone char at removal of fluoride was determined 0.11 g in concentration of 10 mg/L and pH = 10. The maximum effective dose was determined 1.25 g in concentration of 20 mg/L and pH = 7. The index (AIC) showed that quadratic dose-response models better fit to adsorption data than adsorption isotherm models.

Conclusions: The median and maximum effective doses of bone char at removal of fluoride were estimated by statistical models more accurately. In addition, determining the goal dose was performed using modeling method, which was more economic than repeated testing, and the performance time was also more cost-effective. Quadratic dose-response model can be a good alternative for adsorption isotherm models in the adsorption behavior.