## 3 Results and Discussion
An analysis of the individual values in Table 2 reveals irregular scatterings, which are challenging to describe methodically. However, qmax increases with increasing temperatures. With increasing phosphate concentrations in the solution, as shown in Figure 9, the most important parameter with a practical dimension is the maximum amount of phosphate that can be absorbed by a gram of analyzed material. The average values as a function of temperature depending on the grain size of the adsorbent for all four linearizations are shown in Figure 3:0  
Upon analyzing the graphs in Figure 9, it can be assumed that in the winter, at wastewater temperatures below 10 \({}^{\circ}\)C, 1 g of the test material can absorb 0.6-0.8 mg of phosphate, while in the summer, at 20-25 \({}^{\circ}\)C, it can absorb 0.8-1.0 mg. Scientific reports note opoka's tremendous variation in phosphate absorption capacity and its modifications. The type of opoka and its source are essential aspects. With high proportions of silica (light opoka) and carbonates (heavy opoka), the sorption volumes of phosphate obtained from the Langmuir isotherm were 80 mg P/g and 137-181 mg P/g, respectively [12]. After the firing of opoka, the content of iron oxides is an essential aspect, and this is especially the case for calcium oxides, which, in amounts between 238.6 and 520.1 g of Ca/kg, stimulate the absorption of 12.3-25.5 mg of P-PO\({}_{4}\)\({}^{-3}\)/g [35]. [PERSON] et al. [8; 29] studied two materials, rock with high CaCO contents (M1) and Rockfos\({}^{\otimes}\) material (M2), which showed considerable differences in sorption. The sorption values obtained from the Langmuir isotherm were qmax = 256.41 mg/g for the M1 material and 0.36 mg/g for the M2 material. [PERSON] and [PERSON] [45] and [PERSON] et al. [46] showed that the type of rock is not the only parameter that affects phosphate sorption; they noted a dependence on sorbent particle size and pH and a robust correlation with phosphate concentrations in solution. Laboratory results are not always fully translated into the practical performance of sorbents working in the final stage of wastewater treatment plants. [PERSON] [70], studying phosphate sorption on blast furnace slag, found that, compared to laboratory results from field studies, phosphorus sorption decreased significantly by about twofold. The calculations made for LI and LII linearization (Figure 9A) show more excellent stabilization, while those obtained for LIII and LIV linearization (Figure 9B) show overestimated results with such substantial scattering that they can hardly be considered reliable. Since these results were obtained from the exact measurements, it can be seen that the  
Figure 3:1 Maximum sorption capacity (qmax) as a function of temperature and adsorbent grain size for Langmuir LI and Lineweaver–Burke LII linearization (**A**) and Scatchard LIII and Eadie–Hofste LIV (**B**). linearization method has a significant impact on the conclusions. The above analyses show that sorption analysis using Langmuir linearization should be used, with Lineweaver-Burke constituting a secondary option. The linearization of the general formula, approximation with a linear function, and, finally, the determination of \(\mathrm{K_{L}}\) and \(\mathrm{q_{max}}\) naturally introduce errors, partially expressed by the determination coefficient, \(\mathrm{R^{2}}\), shown for all cases in Figure 3:2 As can be seen, the highest values of \(\mathrm{R^{2}}\) were obtained from Langmuir linearization, which means that this mode of operation and this way of determining \(\mathrm{K_{L}}\) and \(\mathrm{q_{max}}\) generates the least significant errors. The two graphs shown in Figure 10 show a comparison of such cases. To more precisely determine the goodness of fit of the function with respect to the measurement results, error functions were determined for all the cases, described in Table 2 as optimization criteria.