In this study, we evaluated the use of prickly pear seed cake, a by-product of prickly pear seed oil extraction, as a new precursor for producing activated carbon by phosphoric acid activation, and the obtained carbon’s capacity for heavy metal removal from aqueous solution. Response surface methodology based on the full factorial design at two levels (2⁴) was developed to reduce the number of experiments and reach optimal preparation conditions for the removal of cadmium and lead ions from aqueous solutions. Design Expert 11.1.2.0 Trial software was used for generating the statistical experimental design and analyzing the observed data. Factors influencing the activation process, such as carbonization temperature, activation temperature, activation time, and impregnation ratio, were studied. Responses were studied in depth with an analysis of variance to estimate their significance. Each response was outlined by a first-order regression equation demonstrating satisfactory correspondence between the predicted and experimental results as the adjusted coefficients of correlation. Based on the statistical data, the best conditions for the removal of heavy metals from aqueous solution by the obtained activated carbon were indicated. The maximum iodine number and methylene blue index were 2527.3 mg g⁻¹ and 396.5 mg g⁻¹, respectively, using activated carbon obtained at the following conditions: Tc = 500 °C, Ta = 500 °C, impregnation ratio = 2:1 (g H₃PO₄: g carbon), and activation time of two hours. The maximum adsorption reached 170.2 mg g⁻¹ and 158.4 mg g⁻¹ for Cd²⁺ and Pb²⁺, respectively, using activated carbon obtained at the following conditions: Tc = 600 °C, Ta = 400 °C, impregnation ratio = 2:1 (g H₃PO₄: g carbon), and activation time of one hour. The activated carbon obtained was characterized by Boehm titration, pH of point of zero charge (pH_PZC), Brunauer–Emmett–Teller surface area (S_BET), and scanning electron microscopy. Adsorption was performed according to different parameters: pH solution, adsorbent dosage, temperature, contact time, and initial concentration. Regeneration experiments proved that the obtained activated carbon still had a high removal capacity for Cd²⁺ and Pb²⁺ after five regeneration cycles.

Experimental Design Analysis of Murexide Dye Removal by Carbon Produced from Waste Biomass Material: The aim of this work is to investigate the adsorption of an anionic dye, the Murexide (MX) present in aqueous solution, on activated carbon, derived from prickly pear seed cake biomass after bio-oil extraction. The obtained adsorbent used was characterized by Bohem titration, pH of point of zero charge (pH_PZC), FTIR spectroscopy, BrunauerEmmettTeller surface area (S_BET), and scanning electron microscopy (SEM). The different experimental parameters of the adsorption process, such as temperature, contact time, initial dye concentration, and adsorbent dose, were studied. For the optimization of the process, the effects of these parameters were investigated using the full factorial experimental design methodology. Design Expert 11.1.2.0 Trial software was used for generating the statistical experimental design and analysing the observed data. Langmuir and Freundlichs adsorption models were employed to provide a description of the equilibrium isotherm. The adsorption process was found to obey Langmuir, which indicates that the Murexide had formed a monolayer onto activated carbon. Furthermore, according to the regression coefficients, it was observed that the kinetic adsorption data can fit better by the pseudo-second-order model compared to the first-order Lagergrens model. The thermodynamic studies indicated that the adsorption of Murexide occurs in a spontaneous and exothermic process. The regeneration process of the exhausted adsorbent was studied to assess the economic and operational feasibility. According to the obtained findings, it is proposed that the activated carbon prepared from prickly pear seed cake retains a high potential for Murexide removal and is suitable for repetitive usage.