# Why is Trouton's rule not valid for liquids with boiling points less than 150 K?

This is a question from the last year's semester examination.

Why is Trouton's rule not valid for liquids with boiling points less than 150 K?

I searched the internet but only found that the exceptions mentioned include liquids with strong intermolecular attraction like hydrogen bonding and some similar cases. Can anyone give me a proper answer?

• We prefer to not use MathJax in the title field, see here for details. Dec 15 '16 at 12:13
• Related question: chemistry.stackexchange.com/questions/18967/… Dec 15 '16 at 15:12
• @JonCuster Thanks for the help. However it doesn't answer my question. Dec 15 '16 at 15:19
• Ok, perhaps you could clarify what you need more insight on? The answers in the question I pointed out do at least touch on (perhaps too indirectly) on why the entropy changes might be different at low temperatures. Dec 15 '16 at 15:37
• @JonCuster My question specifically revolves around the temperature 150 K. Low temperatures may cause h bonding or so, but what id so special about 150 K? Dec 15 '16 at 17:01

When a liquid vaporises its entropy goes from a modest value to a significantly larger one. The ratio of $\Delta H_{vap}/T = \Delta S_{vap}$ is found to be approximately constant at the boiling point. Some authors give a value of $80~ \pu{Jmol^{-1}K^{-1}}$ others $90~ \pu{Jmol^{-1}K^{-1}}$.
Experimental values vary rather more than this and for gases such as neon, nitrogen, oxygen and methane whose liquids all boil below $150$ K, have values that are in the range $65 - 75$, benzene, many 'normal' liquids and liquid sodium, lithium and iodine, in the range $80-90$ and ethanol, water, hydrogen fluoride in the range $105 - 115 ~ \pu{Jmol^{-1}K^{-1}}$. Thus there seems to be nothing unusual about $150$ K but rather an influence from intermolecular interactions.
The value of $\approx 80~ \pu{Jmol^{-1}K^{-1}}$ corresponds to a cohesive energy of $\approx 9.5 kT$ per molecule and so the boiling point gives an indication of the strength of the cohesive energy holding molecules together in the condensed phase. When the cohesive energy exceeds this value, as in water, then the ratio $\Delta H/T$ is larger and conversely the ratio is smaller when the cohesive energy is less as in Neon or methane.
The $\approx 9.5 kT$ minimum energy per molecule is quite a modest energy; if a molecule has $6$ near neighbours this corresponds to about $3kT/2$ per interaction between two molecules, roughly the average thermal energy.