## 3 Experimental Evidence for Trouton's Rule
### Salt Hydrates  
Figure 10 illustrates [PERSON]'s rule for a collection of salt hydrate transitions, calculated from collections of parametrized pT-lines [5; 10]. Instead of the normal boiling point at 1 atm,  
Figure 8: [PERSON]’s rule for ammoniates of chloride salts. This plot was constructed from the pT-lines of chloride ammoniates transitions of Figure 7. The regression coefficient \(r^{2}=0.9958\) is even better than for the vapor-liquid transitions of common liquids of Figure 6.  
Figure 7: Vapor pressure lines of chloride ammoniates (black) and ammonia (red). This plot is an extension of an earlier plot of Neveu [11], which we extrapolated towards \(1/T=0\). Here, an approximate intersection of the pT-lines of the chloride ammoniates becomes apparent, which confirms [PERSON]’s rule for the collection. As anticipated, the vapor pressure line of ammonia does not intersect at \(1/T=0\) and therefore does not belong to this collection. Figure 9: Transition entropy at 1 atm for ammoniate transitions of chloride salts, corresponding to Figures 7 and 8. The orange point is the transition entropy between ammonia vapor and liquid, which differs considerably from the average value for ammoniate transitions, as expected. we considered a pool evaporator-condenser at 20 \({}^{\circ}\)C, giving an H\({}_{2}\)O vapor pressure of 23.4 mbar. Thus, the temperature in Figure 10 is the dehydration temperature at 23.4 mbar. The fit provides \(\Delta h/T_{d}\) = 171.6 J/molK = 20.6\(R\) = \(\Delta\)s at 23.4 mbar. Figure 11 shows \(\Delta\)s\({}_{j}\) for transitions \(j\) of the collection, with an average of about 145 J/molK at \(p_{0}\) = 1 atm. The first entry in orange is the transition entropy of 119 J/molK between water vapor and liquid at 1 atm, which differs considerably from the average value for hydration transitions, as expected. Figure 10 was obtained after elimination of the most obvious outliers, e.g., with negative \(\Delta\)s, negative hydration states, etc. Remaining transitions with remarkably low and high \(\Delta\)s are plotted in orange in both Figures 10 and 11. Table 2 shows \(\Delta\)s for these transitions. Sometimes different values of \(\Delta\)s are given [5]. For these cases, the last column gives the alternative \(\Delta\)s values. In some cases, the alternative value is close to the average 145 J/molK, making the outlier particularly suspicious. We do not see an obvious correlation with cation or anion type for the transitions with particularly low or high \(\Delta\)s. This may be due to the limited number of transitions in the table. The corresponding regression coefficient \(r^{2}\) = 0.8757 of [PERSON]'s rule for salt hydrates is considerably worse than for chloride ammoniates. One possible explanation might be that this collection contains salts of many different anions and cations. We checked this by fitting [PERSON]'s rule separately for the largest sub-collections of chlorides and sulfates with 21 and 150 members, respectively. For chlorides we obtained \(\Delta h/T_{d}\) = 21.4\(R\) with \(r^{2}\) = 0.8866 and for sulfates \(\Delta h/T_{d}\) = 20.9\(R\) with \(r^{2}\) = 0.9717. For the rather large sulfate collection, the regression coefficients are considerably higher, but the fitted \(\Delta h/T_{d}\) hardly differs from the value of 20.6\(R\) for the whole collection. Thus, this collection does not provide evidence that the type of anion makes much difference for obeying [PERSON]'s rule. We add that measurements of salt hydrates are calculated at typically lower pressure, around 10 mbar, than the typical value of around 1 bar for salt ammoniates. Experiments at low pressures may be more difficult as leakage may influence the measured pressure. In addition, driving forces for vapor transport may be lower at lower pressures, so that it may take considerably longer to measure equilibrium states.