The general equation for calculating \(\Delta S\) is
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| \begin{equation*} \Delta S = \int \frac{\delta q_{rev}}{T} \label{eq:DS_general} \end{equation*} | (3.17) |
For first order phase transitions \(T = const.\) while \(\Delta H\) changes. Using here \(\Delta H\) instead of \(\delta q\) implies that the pressure is kept constant. Thus we find
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| \begin{equation*} \Delta_{trs} S = \frac{\Delta_{trs}H}{T_{trs}} \quad \mbox{thus for an endothermic process} \quad \Delta_{trs} S \gt 0 \label{eq:DtrsS} \end{equation*} | (3.18) |
According to Trouton’s rule the standard entropy for vaporization of liquids is
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| \begin{equation*} \Delta_{vap}S = \Delta S(gas) - \Delta S(liquid) \approx 85 \; \mbox{J/(K mol)} \label{eq:DvapS} \end{equation*} | (3.19) |
The main assumption for this rule is that the structures of all liquids and of all gases is roughly the same, thus, \(\Delta_{vap} S\) is roughly the same. Essentially one looks at the liquid state as being less chaotic compared to vapor.
| \(\Delta_{vap} H^{0}\) [kJ mol\(^{-1}\)] | \(\Theta_B\) [\(^\circ\)C] | \(\Delta_{vap} S^{0}\) [kJ K\(^{-1}\) mol\(^{-1}\)] | |
| Benzene | 30.8 | 80.1 | 87.2 |
| Carbon tetrachloride | 30.0 | 76.7 | 85.8 |
| Cyclohexane | 30.1 | 80.7 | 85.1 |
| Hydron sulfide | 18.7 | -60.4 | 87.9 |
| Methane | 8.18 | -161.5 | 73.2 |
| Water | 40.7 | 100 | 109.1 |
As can be seen in the table above Trouton’s rule holds for a number of liquids quite well. Water has a significantly larger value for \(\Delta_{vap} S^{0}\) since the liquid state is more ordered than expected, thus more entropy change is found. In contrast e.g. methane shows a negative deviation since the energy in the vapor state is not as dispersed as expected (due to a low population of higher rotational energy levels for light molecules at low \(T\)).
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© J. Carstensen (TD Kin I)