## 3 Experimental Evidence for Trouton's Rule
### Salt Hydrates
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Salt** & **H\({}_{2}\)O** & **\(\Delta\)s (J/molK)** & **Alternative \(\Delta\)s (J/molK)** \\ \hline Ca(H\({}_{2}\)PO\({}_{4}\))\({}_{2}\) & 1-0 & 69 & \\ MnI\({}_{2}\) & 2-1 & 77 & \\ CuSO\({}_{4}\) & 1-0 & 81 & \\ MnSeO\({}_{4}\) & 1-0 & 82 & \\ MgSeO\({}_{4}\) & 1-0 & 84 & \\ CsCd(SO\({}_{4}\))\({}_{2}\) & 6-2 & 90 & \\ SrCl\({}_{2}\) & 2-1 & 91 & 148 \\ MnI\({}_{2}\) & 1-0 & 95 & \\ Na\({}_{2}\)HPO\({}_{4}\) & 12-7 & 99 & 149 \\ CaCl\({}_{2}\) & 6-4 & 182 & 142, 166 \\ SrCl\({}_{2}\) & 1-0 & 184 & \\ Tl(Al(SO\({}_{4}\)))\({}_{2}\) & 12-0 & 184 & \\ LiBr & 2-1 & 185 & 171 \\ BaCl\({}_{2}\) & 1-0 & 190 & 100, 145 \\ Na\({}_{2}\)B\({}_{4}\)O\({}_{7}\) & 5-0 & 192 & 149 for 10-0 \\ CsCr(SeO\({}_{4}\))\({}_{2}\) & 12-0 & 196 & \\ HD\({}_{3}\) & 1-0 & 201 & \\ CH\({}_{3}\)NH\({}_{2}\)Cr(SO\({}_{4}\))\({}_{2}\) & 12-0 & 204 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Hydration transitions with lowest and highest \(\Delta\)s.  
We now arrive at a discussion of the issues mentioned at the end of the introduction. In short, the validity of [PERSON]'s rule for salt hydrates is illustrated by Figures 10 and 11. We have seen that to some extent, [PERSON]'s rule can be used to identify suspicious pT-lines. Predicting the pT-line of a salt hydrate transition for which only the sorption enthalpy \(\Delta h\) is known can be done by Equation (4), taking for \(\Delta\)s the average of collection of similar transitions. Finally, for a given \(T_{d}\) of dehydration, one can predict that no more heat than about \(\Delta h=T_{d}\Delta s\) per mole of sorbent molecules can be released. For estimating the heat storage density per volume of hydrate \(Q/V\) (J/m\({}^{3}\)), we also need the molar mass \(M\) (kg/mol) and density \(\rho\) (kg/m\({}^{3}\)) of the hydrate. Figure 12 shows the correlation between \(Q/V\) and \(T_{d}\). This figure was constructed from Figure 10 with available values for \(M\) and \(\rho\)[28]. With a regression coefficient of only \(r^{2}=0.19\), Figure 12 does not seem to be very valuable for predictions. The correlation is considerably improved by including process water, which is the water extracted from the salt at dehydration, to the material volume. Figure 13 shows the correlation between \(Q/(V_{H}+V_{W})\) and \(T_{d}\), where \(V_{H}\) is the hydrate volume and \(V_{W}\) is the volume of process water. For this figure, a considerably better correlation with \(r^{2}=0.64\) is obtained. Including the process water in the heat storage density is fair when implementing a closed system such as in Figure 1.  
Figure 11: Transition entropy at 1 atm for hydration transitions of salts. Orange points with highest and lowest transition entropies correspond to the orange points in Figure 10. The transition entropy of 118.9 J/mol for water evaporation is also plotted as the left-most point and differs considerably from the average, as expected. Figure 10: [PERSON]’s rule for salt hydrates. Orange points are entries with highest and lowest transition entropy. The regression coefficient \(r^{2}=0.8757\) is considerably smaller than for chloride ammoniates.