[Miffymycat]

Ethanol has a higher ΔHvap than water (43.5 vs 41.3 kJ/mol).  But water has a higher boiling point (373 vs 352K). How do we explain this?!

[ramboacid]

It makes sense if we consider entropy as well. Remember that
 :delta: G =  :delta: H - T :delta: S

The system is in equilibrium between the liquid and gaseous phases at the boiling point, so :delta: G_vap=0 and we can rewrite the equation as
T =  :delta: H/ :delta: S

The boiling point is therefore the ratio between the enthalpy change and the entropy change of the process, which in this case is vaporization. Using your values of the enthalpy change and boiling points, the :delta: S_vap of ethanol is +123.5 J/K and the :delta: S_vap of water is  +110.7 J/K. As the change in entropy is simply the difference in the entropies of the liquid and gaseous phases, we see that there is a larger entropy difference between liquid and gaseous ethanol than there is between liquid and gaseous water.

Water has a higher boiling point because its intermolecular forces are stronger than those of ethanol. The values of  :delta: S_vap are also somewhat fixed, as they are the differences in entropy between the initial and final states. Using the formula for Gibb's free energy, we can see that the enthalpy of vaporization, :delta: H_vap, is therefore a consequence of those two values.

An interesting topic relating to your question is Trouton's Rule: http://en.wikipedia.org/wiki/Trouton's_rule

[Miffymycat]

Thanks Ramboacid
Interesting.  It seems to me that as temperature is essentially just a molecular speedometer, that ΔHvap is perhaps the truer reflection of the energy required to overcome the intermolecular forces and it does relate energy to amount ie kJ to mol.  Therefore this suggests the forces of attraction between ethanol molecules are stronger (despite less H-bonding) possibly due to greater total temporary dipole forces.  We could then say that because ΔSvap ethanol is higher, that more disorder has to be created as part of spontaneous ethanol boiling, compared to water boiling, which makes sense from the H-bonded structure of water … a lot of order exists in water vapour relative to the liquid, or vice versa.  So finally this suggests that boiling point is simply the measure of enthalpy required per mole per unit of disorder created in vapourisation … if you can visualise this??!
OR, alternatively, that temperature is the better indicator of energy needed to overcome intermolecular forces, as it is a measure of molecular (kinetic) energy, and that at the boiling point, all IMF’s in the liquid state have been broken.  What then has to happen is vapourisation, a second process, requiring a huge increase in entropy, and a greater increase for ethanol than water considering their different structures.
In the former scenario, temperature is the consequence of the necessary ΔH and ΔS, in the latter, ΔH is the consequence of the necessary boiling point and ΔS – which one do you prefer … if either?!

[ramboacid]

I hadn't thought of the relationship between  :delta: H_vap and intermolecular forces much before reading your post, and at first I was also baffled.

I approached your question at first by trying to explain all why the enthalpy changes were the way they were assuming that nothing else (the entropy changes and the boiling points) could be changed. In retrospect, I guess that approach points to the fact that enthalpy is dependent on entropy and temperature. The enthalpy of vaporization is a victim in this approach, as its fate is solely decided by the boiling point and entropy of vaporization.

That is the way I prefer to think about it. While both interpretations are perfectly correct, I like to think of it as a balancing act; the enthalpy change is only there to compensate for the entropy change.

However, one difficulty that might arise from the first interpretation is that the enthalpy of vaporization doesn't necessarily reflect the intermolecular forces as well as the temperature, because the enthalpy change is dependent on the enthalpies of liquid and gas phases while the temperature is more of an absolute value. The relativeness comes because, although we like to think of gases as ideal gases in which there are no intermolecular forces, those IMFs still persist. For example, when hydrogen fluoride vaporizes, it still forms chains up to 5 or 6 molecules long in the gas phase. So not all of the enthalpy of vaporization contributed to disrupting the strong intermolecular forces. Similarly, the entropy change is much less than expected because of the dimerization of the HF molecules.

Temperature can be more directly compared to kinetic energy, and since the kinetic energy of the molecules is related to the phase of the molecules, I would think it is more indicative of the strength of intermolecular forces because strong intermolecular forces would have to hold molecules in place at higher temperatures.

[Miffymycat]

Yep - I agree and am now an official enthalpy-is-a-victim supporter!  Temperature-entropy rules OK!

[Enthalpy]

You can find a not too bad relationship between intermolecular forces and the critical temperature. For instance, cryogenic gases need little heat to boil.

A relation with the vaporization enthalpy and the boiling temperature isn't as simple:
- The vaporization enthalpy depends fundamentally on how far you're from the critical temperature. It's zero at the critical temperature.
- The vaporization enthalpy depends on the difference of heat capacity between the liquid and the gas (just integrate it between the critical temperature and your boiling temperature)
- The boiling temperature depends on the pressure...

In an idealized mental image, a liquid molecule would store internal energy in as many translations, rotations, vibrations as the gas, corrected by the liquid's intermolecular forces and the gas' PV. The boiling temperature would just overcome this difference, with the help of low pressure accounted by the entropy.

Intermolecular forces weaken as temperature expands the liquid, explaining the difference in heat capacity - or the liquid expands as temperature overcomes intermolecular forces. Water for instance weighs only 1/4 t/m³ at +373°C, its critical point. Useful to reduce the reactivity of a slow neutrons uranium reactor when it gets hot.