The critical temperature
Andrew Usher
good index of cohesion in molecular liquids. This is incorrect; the
critical temperature is the right index. The cohesion per unit volume
has units of energy of temperature (~a/b in terms of van der Waals
constants), not pressure. The critical pressure, then, is basically
the ratio of this to the molecular volume.
This explains, for example, why liquid nitrogen is miscible with
liquid methane, but not with higher hydrocarbons, at all temperatures
where both are liquid. The critical pressure is not very different
between methane, ethane, and propane, but the critical temperature
changes sharply. And, in fact, the van der Waals formula and other
equations of state, when used to predict critical behavior, predict
that the phase behavior of simllar liquids should essentially depend
on the ratio of their critical temperatures (not pressures).
In the paraffins (or any other homologous series), therefore, the
critical temperature should approach a finite limit while the pressure
goes to zero. This seems to be the case from what experimental data do
exist; the limit is probably around 900 K. The perfluorinated
paraffins may be around 100 K lower, and are surely the lowest of any
such series.
Again this limiting temperature reflects the cohesive energy per unit
volume, which is lower for the fluorinated compounds.
Heavier atoms generally have higher dispersion forces, which is why
critical temperatures go up if an atom is replaced by a homolog of a
higher period, unless hydrogen-bonding is involved. The pressure does,
too, but not so much as the volume is also larger. For example:
MeOH 512 K 81 bar Me2O 400 K 54 bar
MeSH 470 K 72 bar Me2S 503 K 55 bar
Or:
F2 144 K 52 bar HF 461 K 65 bar
Cl2 417 K 80 bar HCl 325 K 83 bar
Br2 588 K 103 bar HBr 363 K 86 bar
I2 819 K ??? bar HI 424 K 83 bar
The pressure for I2 is not given, but is likely the highest of all.
The pressure for HF is anomalously low because its association in the
vapor phase causes it to effectively have a larger molecular volume
than HCl. In fact the critical pressure of HF seems to be the lowest
of all the Group V, VI, and VII hydrides. (The Group IV hydrides are
considerably lower as they are non-polar and their tetrahedral
structures do not admit of interactions between the central atoms.)
It is interesting that though the strength of covalent bonds decreases
generally toward heavier elements (in the main groups anyway), that of
inter-molecular interactions increases, but not parasoxical.
Water has the highest critical pressure of all molecular substances,
but that does not truly say it has the highest cohesive forces, but
the highest in proportion to its size. Water is a small molecule (the
smallest of any with more than 2 atoms), explaining also its strangely
high density - although HF and HCN don't have the same high density, I
suppose the linear polymerisation they have causes more voids?
Of all molecular substances, that are molecular around the critical
point, bismuth iodide surely has the highest critical temperature
(1300 K or so). Its pyramidal structure allows substantial interaction
between bismuth atoms, and both bismuth and iodine are among the
heaviest atoms.
Andrew Usher
Andrew Usher
> In the paraffins (or any other homologous series), therefore, the
> critical temperature should approach a finite limit while the pressure
> goes to zero. This seems to be the case from what experimental data do
> exist; the limit is probably around 900 K. The perfluorinated
> paraffins may be around 100 K lower, and are surely the lowest of any
> such series.
I have realised that the critical density must also go to 0, and the
data on the paraffins do show it decreasing. This is because the heat
of vaporisation goes to infinity; and the evaporation equation shows
that, with the heat of evaporation rising without limit while the
temperature is bounded (by the limiting critical temperature), the
vapor pressure curve becomes infinitely steep. Thus, the limit will
have the vapor density zero at all temperatures below the critical,
and the critical density must then be zero to avoid discontinuity.
The liquid density can approach 0 with the normal critical
exponent. Having a liquid state at arbitrarily low densities is
consistent with the fact that the molecular speed goes to
zero, meaning that the ratio of cohesive energy to kinetic
energy goes to zero at fixed density. Turning that around,
the minimum density for a given cohesive ratio falls without
limit, which also supports the limiting critical density being
zero.
Andrew Usher
John Park
> On Sep 29, 3:50 am, Andrew Usher <k_over_hb...@yahoo.com> wrote:
>
>> In the paraffins (or any other homologous series), therefore, the
>> critical temperature should approach a finite limit while the pressure
>> goes to zero. This seems to be the case from what experimental data do
>> exist; the limit is probably around 900 K. The perfluorinated
>> paraffins may be around 100 K lower, and are surely the lowest of any
>> such series.
>
> I have realised that the critical density must also go to 0, and the
> data on the paraffins do show it decreasing. This is because the heat
> of vaporisation goes to infinity; and the evaporation equation shows
> that, with the heat of evaporation rising without limit while the
> temperature is bounded (by the limiting critical temperature), the
> vapor pressure curve becomes infinitely steep. Thus, the limit will
> have the vapor density zero at all temperatures below the critical,
> and the critical density must then be zero to avoid discontinuity.
>
> The liquid density can approach 0 with the normal critical
> exponent. Having a liquid state at arbitrarily low densities is
> consistent with the fact that the molecular speed goes to
> zero, meaning that the ratio of cohesive energy to kinetic
What about the equipartition theorem?
--John Park
Andrew Usher
> > Having a liquid state at arbitrarily low densities is
> > consistent with the fact that the molecular speed goes to
> > zero, meaning that the ratio of cohesive energy to kinetic
>
> ^^^^^
> What about the equipartition theorem?
Yes, that says that the kinetic energy per molecule is
independent of the size of the molecule. The cohesive
energy per molecule, at constant density, is roughly
proportional to the size of the molecule. Therefore the
ratio has a limit of zero.
Andrew Usher
Andrew Usher
are isomorphic to the critical solution temperature of that substance
with a solvent.
And what we observe in polymer solutions is indeed that the critical
temperature approaches a maximum as a chain length goes to
infinity, while the solubility at the consolute point goes to 0 (by
weight or volume, not just by number). This verifies experimentally
my conjectures, which can't be investigated directly as all suitable
substances decompose before their critical temperatures.
Andrew Usher
Uncle Al
Waste of flesh.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
Andrew Usher
> Andrew Usher wrote:
>
> > It's occurred to me that the critical properties of a single substance
> > are isomorphic to the critical solution temperature of that substance
> > with a solvent.
>
> > And what we observe in polymer solutions is indeed that the critical
> > temperature approaches a maximum as a chain length goes to
> > infinity, while the solubility at the consolute point goes to 0 (by
> > weight or volume, not just by number). This verifies experimentally
> > my conjectures, which can't be investigated directly as all suitable
> > substances decompose before their critical temperatures.
>
> > Andrew Usher
>
> Waste of flesh.
????
Andrew Usher
Uncle Al
Tch, tch.
Andrew Usher
> "which can't be investigated directly as all suitable substances
> decompose before their critical temperatures."
>
> Tch, tch.
If you think it's wrong, name a counter-example. Name a high
polymer that does not decompose before its critical
temperature.
Andrew Usher