Present research describe applicability of tin oxide hydroxide nanoparticles loaded on activated carbon (Sn 6 O 4 (OH) 4 -NPs-AC) which recognized via by Field emission scanning electron microscopy (FE-SEM) and X-ray diffraction (XRD) for the rapid simultaneous removal of Methyl orange (MB) and methylene blue (MB) in mixture in the presence of ultrasonic wave. The central composite design (CCD) pattern as branch of response surface methodology (RSM) give useful information about influence of five most important operating variables is separate and combination nature namely pH (4.0-8.0), initial MO (8-24 mg L −1 ) and MB concentration (4-12 mg l −1 ), sonication time (2-6 min) and adsorbent mass (0.01-0.03 g) on the ultrasound under study dyes assisted adsorption. After surveying the experiment data and finding regression analysis correspond to experimental data, mathematical model and equation was constructed and derived which applied for optimizing ultrasound assisted adsorption and revel serious dependency of response to variables like adsorbent mass and sonication time s. F values of 114.5 and 165.5, coefficient of determination (R 2 ) of 0.9978 and 0.9985, adjusted-R 2 of 0.9891 and 0.9925, adequate precision (AP) of 39.11 and 40.23, coefficient of variation (CV) of 0.653 and 1.988% for MB and MO respectively, implied the satisfactory adjustment of the quadratic model. Based on CCD, the optimum conditions was set as pH of 6.0; 0.02 g adsorbent; 20 and 12 mg l −1 of MO and MB concentration and 2 min sonication time. The predicted removal of MO and MB in binary system were 98.19 and 98.02% which was good agreement with their experimental R% MOand MB value of 98.00% for both at optimum condition. The equilibrium data has good agreement with Langmuir with maximum monolayer adsorption capacity of 30.90 and 25.70 mg g −1 for MO and MB respectively. Investigation of time dependency of adsorption data revel more applicability pseudo-second order in cooperation with intraparticle diffusion description of the mechanism and adsorption rate.KEYWORDS isotherm and kinetic studies, methyl orange, methylene blue, optimization, Sn 6 O 4 (OH) 4 -NPs-AC, ultrasonic wave

S-doped and Cu- and Co-doped TiO was synthesized by a sol-gel method and characterized by FE-SEM, XRD, EDX and FTIR. The Co/Cu/S-TiO nanocomposite loaded on the activated carbon as new nanoadsorbent was used for simultaneous removal of methylene blue (MB) and sunset yellow (SY) from aqueous solution by ultrasonic-assisted adsorption method. In this work, central composite design (CCD) and adaptive neuro-fuzzy inference system (ANFIS) as a support tool for examining data and making prediction are used to recognize and predict the removal percentage in MB and SY dye solution of different concentrations. The predictive capabilities of CCD and ANFIS are compared in terms of square correlation coefficient (R), root mean square error (RMSE), mean absolute error (MAE) and absolute average deviation (AAD) against the empirical data. It is found that the ANFIS model shows the better prediction accuracy than the CCD model. In addition to, the optimization of ultrasound-assisted simultaneous removal of methylene blue (MB) and sunset yellow (SY) on the Co/Cu/S-TiO/AC nanocomposite by response surface methodology (RSM) for the optimization of the process variables, such as MB and SY concentrations, Co/Cu/S-TiO/AC nanocomposite dose and sonication time, was investigated. Various isotherm and kinetic models were used in the experimental data. The results revealed that the langmuir isotherm and pseudo-second-order model had a better correlation than the other models.