## 3 Results and Discussion
### Solubilities  
Calculated values of \(x_{1}\) are compiled in Table 4 together with the quartiles Q\({}_{1}\) and the span ratio (Q\({}_{3}\)/Q\({}_{1}\)) as determined from the MC simulation. Because symmetric boxcar probability distributions were used and \(x_{1}=\text{f}(\Delta H_{1},\,T_{m,1},\,V_{1},\,\delta_{1},\,\delta_{2})\) is a monotonous function with regard to each variable, the median solubility from simulation is expected to meet Q\({}_{2}\approx x_{1}\) within statistical scatter, which was confirmed by the results. Also, as is expected from Equation (1), increasing solubility is matched by a decreasing absolute solubility parameter difference \(\Delta\delta=|\delta_{1}-\delta_{2}|\). The numerical effect the material parameter uncertainties have on solubility will be analyzed in the following. \begin{table} \begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Solvent**} & \multirow{2}{*}{\(\mathbf{\delta_{2}}\) (**MPa**)\({}^{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{   }}}}}}}}}}}}}}\) & \(\mathbf{x_{1}}\) * & \multicolumn{2}{c}{**Interquartile Range of \(\mathbf{x_{1}}\)\({}^{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{  }}}}}}}}}}}}}}}\) **} & **95\% CI**\({}^{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{ \text{\text{ \text{ \text{ }}}}}}}}}}}}}}}}}\) \\ \cline{3-6}  & & **Q\({}_{1}\)** & **Q\({}_{3}\)** & **Q\({}_{1}\)** & **Q\({}_{2}\)** \\ \hline Pentane & 14.50 & \(1.13\times 10^{-11}\) & \(3.30\times 10^{-12}\) & \(3.63\times 10^{-11}\) & 11.0 & 483.2 \\ \hline n-Hexane & 14.90 & \(2.34\times 10^{-11}\) & \(8.46\times 10^{-12}\) & \(7.22\times 10^{-11}\) & 8.5 & 424.9 \\ \hline Heptane & 15.30 & \(4.79\times 10^{-11}\) & \(1.67\times 10^{-11}\) & \(1.37\times 10^{-10}\) & 8.2 & 313.9 \\ \hline Dieethyl ether & 15.49 & \(6.65\times 10^{-11}\) & \(2.27\times 10^{-11}\) & \(1.96\times 10^{-10}\) & 8.6 & 363.4 \\ \hline Cyclohexane & 16.80 & \(6.19\times 10^{-10}\) & \(2.23\times 10^{-10}\) & \(1.74\times 10^{-9}\) & 7.8 & 282.9 \\ \hline n-Butyl acetate & 17.41 & \(1.65\times 10^{-9}\) & \(5.52\times 10^{-10}\) & \(4.19\times 10^{-9}\) & 7.6 & 209.0 \\ \hline Xylene & 18.10 & \(4.79\times 10^{-9}\) & \(1.74\times 10^{-9}\) & \(1.25\times 10^{-8}\) & 7.2 & 171.9 \\ \hline Ethyl acetate & 18.15 & \(5.24\times 10^{-9}\) & \(1.88\times 10^{-9}\) & \(1.37\times 10^{-8}\) & 7.3 & 174.1 \\ \hline Toluene & 18.16 & \(5.33\times 10^{-9}\) & \(1.93\times 10^{-9}\) & \(1.24\times 10^{-8}\) & 6.4 & 165.0 \\ \hline Benzene & 18.51 & \(8.92\times 10^{-9}\) & \(3.63\times 10^{-9}\) & \(2.44\times 10^{-8}\) & 6.7 & 161.9 \\ \hline Tetrahydrofuran & 19.46 & \(3.53\times 10^{-8}\) & \(1.36\times 10^{-8}\) & \(8.00\times 10^{-8}\) & 5.9 & 128.3 \\ \hline Acetone & 19.94 & \(6.80\times 10^{-8}\) & \(2.82\times 10^{-8}\) & \(1.61\times 10^{-7}\) & 5.7 & 106.7 \\ \hline Acetic acid & 21.37 & \(4.35\times 10^{-7}\) & \(2.08\times 10^{-7}\) & \(9.37\times 10^{-7}\) & 4.5 & 62.2 \\ \hline Propan-2 ol & 23.58 & \(5.35\times 10^{-6}\) & \(2.75\times 10^{-6}\) & \(1.03\times 10^{-5}\) & 3.7 & 38.9 \\ \hline Acetonitrile & 24.40 & \(1.22\times 10^{-5}\) & \(6.66\times 10^{-6}\) & \(2.32\times 10^{-5}\) & 3.5 & 34.8 \\ \hline
1-Propanol & 24.60 & \(1.48\times 10^{-5}\) & \(8.17\times 10^{-6}\) & \(2.96\times 10^{-5}\) & 3.6 & 30.4 \\ \hline Ethanol & 26.52 & \(7.76\times 10^{-5}\) & \(4.55\times 10^{-5}\) & \(1.27\times 10^{-4}\) & 2.8 & 19.8 \\ \hline Methyl hydroperoxide & 29.40 & \(5.03\times 10^{-4}\) & \(3.46\times 10^{-4}\) & \(7.76\times 10^{-4}\) & 2.2 & 9.9 \\ \hline Methanol & 29.41 & \(5.03\times 10^{-4}\) & \(3.38\times 10^{-4}\) & \(7.26\times 10^{-4}\) & 2.1 & 10.4 \\ \hline Ethylene glycol & 32.95 & \(1.83\times 10^{-3}\) & \(1.20\times 10^{-3}\) & \(2.49\times 10^{-3}\) & 2.1 & 2.8 \\ \hline \hline \end{tabular}