# Activated Carbons as Effective Adsorbents of Non-Steroidal Anti-Inflammatory Drugs
## 3 Results
### Adsorption Kinetics  
As part of a comprehensive analysis of the adsorption of ibuprofen sodium, diclofenac sodium, and naproxen sodium on GAC activated carbon, adsorption kinetics measurements were also performed. Figure 3 shows a comparison of the kinetic curves of the experimental systems. It can be underlined that both at 25 \({}^{\circ}\)C and 35 \({}^{\circ}\)C, the highest adsorption rate (the fastest concentration loss and the fastest achievement of the equilibrium state) was recorded for naproxen sodium and the lowest for diclofenac sodium. The smaller dimensions of the NPX molecule compared to D and its greater hydrophobicity compared to IBP enabled highly effective and rapid adsorption of this drug on GAC activated carbon. Figure S1 (Supplementary Material) shows a comparison of kinetic curves for the adsorption of naproxen sodium, ibuprofen sodium, and diclofenac sodium at different temperatures: 25 \({}^{\circ}\)C and 35 \({}^{\circ}\)C. A larger adsorption rate accompanying an increase in temperature was noticed. The observed phenomenon is a consequence of the larger kinetic energy of the elements present in the adsorption system and the increased dehydration of adsorbate molecules and adsorbent grains [8]. Figure S2 (Supplementary Material) presents the kinetic data in linear Bangham coordinates. This made it possible to initially determine the adsorption mechanism [37]. The graphs are practically linear, and their initial slopes, in the interval from 10 to 500 min, are \begin{table}
\begin{tabular}{c c c c} \hline \hline
**System** & \(\Delta\)G\({}^{\circ}\) a [k]/mol [k]/mol [k]/mol [k]/mol [k]/mol [k]/mol [k]/mol [k]/mol [k]/mol [k]/mol [k]/mol] \\ \hline IBP/GAC\_15 \({}^{\circ}\)C & \(-\)2.66 & & \\ IBP/GAC\_25 \({}^{\circ}\)C & \(-\)3.07 & 22.73 & 0.07 \\ IBP/GAC\_35 \({}^{\circ}\)C & \(-\)3.97 & & \\ D/GAC\_15 \({}^{\circ}\)C & \(-\)1.98 & & \\ D/GAC\_25 \({}^{\circ}\)C & \(-\)2.72 & 21.61 & 0.06 \\ D/GAC\_35 \({}^{\circ}\)C & \(-\)3.25 & & \\ NPX/GAC\_15 \({}^{\circ}\)C & \(-\)0.10 & & \\ NPX/GAC\_25 \({}^{\circ}\)C & \(-\)0.73 & 26.41 & 0.087 \\ NPX/GAC\_35 \({}^{\circ}\)C & \(-\)1.62 & & \\ \hline \hline \end{tabular}  
* \(\Delta\)G\({}^{\circ}\)—the Gibbs free energy, b AH\({}^{\circ}\)—enthalpy, c AS\({}^{\circ}\)—entropy.  
\end{table} 
Table 3: Thermodynamic parameters for the adsorption of ibuprofen sodium, diclofenac sodium, and naproxen sodium on GAC activated carbon. 0.76-0.77, 0.76-0.84, and 0.78-0.80 for naproxen sodium, ibuprofen sodium, and diclofenac sodium, respectively. As is known, in the case of a pure intramolecular diffusion model (IDM), the slope is equal to 0.5. Therefore, it can be concluded that the adsorption of the tested pharmaceuticals on GAC can not be described using a diffusion model. The obtained experimental data of the adsorption rate were estimated using numerous equations and models of adsorption kinetics. The relative deviations are listed in Table 4, which shows that the best quality of fitting is achieved for the multi-exponential equation and the fractal-like MOE equation, the parameters of which are presented  
Figure 3: The adsorption kinetic at 25 and 35 \({}^{\circ}\)C for ibuprofen sodium, diclofenac sodium, and naproxen sodium on GAC activated carbon presented as changes in concentration (**a,c**) and adsorption (**b,d**) over time. The adsorption of naproxen sodium, ibuprofen sodium, and diclofenac sodium on GAC activated carbon is a sophisticated process, the rate of which can be described by two (NPX) or three (IBP and D) terms of the multi-exponential equation (Table 5). Moreover, half-times t\({}_{1/2}\) were determined for all experimental systems tested. This parameter is the time it takes to achieve half the change in concentration. Thus, in this particular case, the loss of adsorbate from the solution is 100% (u\({}_{\text{eq}}\) = 1), and the half-time will correspond to the time after which the pharmaceuticals concentration value was 0.5-c\({}_{0}\).