## 3 Results and Discussion
### Solubilities

Table 5: Influence of variable uncertainty on molar solubility \(x_{1}\) of l-ascorbic acid at 25 \({}^{\circ}\)C.  
Additionally, in Figure 1, experimental solubilities at 20 \({}^{\circ}\)C and 25 \({}^{\circ}\)C from [34; 35; 36] are plotted (See Table S3 for numerical data). A difference of 5 \({}^{\circ}\)C in solution temperature results in an 8% to 30% change in solubility dependent on solvent and study. The inter-study variability of \(\mathrm{x}_{1}\) was found to be marked, reaching even 435% (!) for some solvents for unresolved reasons. Here, despite their magnitude, these discrepancies can be disregarded when compared with the 'intrinsic' uncertainty as evaluated above or with the systematic offset of the measured data. Compared with the 100% (50%) percentile the experimental values are larger by a factor 5 to 10\({}^{3}\) (20 to 2:10\({}^{4}\)). Generally, higher solubility can be caused by a decrease of \(\Delta H_{1}\), \(T_{m,1}\), \(V_{1}\), or \(\Delta\delta=|\delta_{1}-\delta_{2}|\), or any combination thereof. The first three causes are ruled out on the grounds of uncertainties of these material parameters being already bracketed by the 100% CI as displayed in Figure 1. Considering the solubility parameters, it is evident that shifting all \(\delta_{2}\) values equally by some \(-5\) (MPa)\({}^{0.5}\) could make the estimated and experimental data match. This would correspond to a systematic and equally large error of the same sign for all solvents, which is considered extremely improbable. On the other hand, \(\Delta\delta\) also decreases if \(\delta_{1}\) (solute) becomes smaller. A non-linear least-squares fitting of Equation (1) to the experimental values optimizing \(\delta_{1}\)  
Figure 1: Molar solubility \(x_{1}\) of \(\mathrm{\iota}\)-ascorbic acid at 25 \({}^{\circ}\)C from simulation (solid lines) and analytical computations (\(\blacksquare\)). Experimental data at 20 \({}^{\circ}\)C (\(\Circ\)) and 25 \({}^{\circ}\)C (\(\bullet\)) from references [34; 35; 36]. Dashed vertical line indicates the total solubility parameter of \(\mathrm{\iota}\)-ascorbic acid \(\delta_{1}=35.3\) (MPa)\({}^{0.5}\). Figure 2: Relative width of the confidence intervals (CI) of \(\mathrm{\iota}\)-ascorbic acid solubilities at 25 \({}^{\circ}\)C from the Monte Carlo simulation. The width is expressed as ratio = UCL/LCL of the respective upper and lower confidence limit of the numerical simulation results. and leaving all other parameters fixed at their respective mid-range values, consistently arrives at \(\delta_{1}\approx 27\) (MPa)\({}^{0.5}\), some 24% below the value of 35.3 (MPa)\({}^{0.5}\) and derived according to HVK. Apparently, a too high solute solubility parameter could, in principle, explain the observed differences, but other reasons, such as a general insufficiency of the underlying theory or oversimplification due to dropping the heat capacity term in deriving Equation (1), could also play a role. Normally, this term is positive and effectively increases solubility to some extent making, in principle, predicted and experimental data match better. Because, (a) there is no indication as to the actual value of this term, and (b) it is considered very unlikely that a difference of 3 to 4 \(\log(x_{1})\)-units can be consistently explained along this line, this point needs to be left unaddressed. Another explanation for systematically predicting too low solubilities could be a solute activity coefficient that is consistently overestimated by the model for all solvents. With due caution, this could possibly hint at some specific solute-solvent interactions playing a role in this context [37]. Exploring this issue further would be beyond the scope of this study. Overall, the results show that the scatter of the deterministically calculated solubility values is strong due to the inherent inaccuracies of the material data. The quality of the material data of LAA is well within the usual range and can be classified as typical.