# Fluids with critical point at ordinary temperature and pressure

Are there any fluids with critical point near STP or that are supercritical at STP?

If not would it be feasible to design a molecule for a substance with critical point near STP using theoretical/computational methods?

## Update

@Diracology and @Floris's great answers helped me find large carbon chain molecules, particularly those with large numbers of fluoride atom, that $P_c < 10\, atm$ and $T_c < 1000K$. That is within the reach of a good bicycle pump and a burner. In particular:

Given @Diracology and @Floris's answer, that suggests that something like $C_{100}F_{202}$ could be critical at around ordinary pressure and an easily achievable temperature, ie it might be possible to get a critical fluid by heating some goop in an open saucepan.

Unfortunately this is ignoring the availability, cost and safe handling of such a substance, but otherwise it could make one hell of a Youtube video :).

It is going to be a tough call awarding the bounty which has already been well earned by both @Diracology and @Floris.

• If it makes your decision easier, award the bounty to @Diracology's answer. Without that answer, I would not have explored the design space in the way I did - in particular I would not have remembered that there are expressions (idealized but useful) that capture the relationships between Van der Waals forces and $P_c, T_c$ – Floris Jul 28 '16 at 11:33
• chemistry.stackexchange.com/questions/41345/… – Mithoron Jul 30 '16 at 23:33
• Nice question and answers. You could accept one answer and give the bounty to the other.... Do the molecules you mentioned exist? – Arnold Neumaier Aug 2 '16 at 11:19
• @ArnoldNeumaier I think they exist, I found them in the chemical databases that they are linked to in the question. – Daniel Mahler Aug 2 '16 at 15:41
• @DanielMahler: If I click on your chemical formulas I only get a pop-up menu for mathjax information, not a link to a database entry. – Arnold Neumaier Aug 2 '16 at 18:08

## 3 Answers

Whether an answer exists depends on your definition of "near" compared to STP.

There are a few fluids that have their critical point at a temperature close to STP, but higher pressure. For example, (see http://www.engineeringtoolbox.com/critical-point-d_997.html)

  material   Tc(K)    Pc(atm)
acetylene    309.5     61.6
ethylene     283.1     50.5
ethane       305.5     48.2


All these are non-polar molecules with a very modest atomic mass. As soon as you add oxygen, the critical temperature increases by a lot, while the pressure comes down only slightly:

acetone       508       48
acetaldehyde  466       55


The problem is that for a critical point to exist near atmospheric pressure, your liquid needs to have a density close to that of the vapor at atmospheric pressure. And that would require an extremely low-density liquid. Or a high-density gas.

UPDATE

It is possible (as shown by @Diracology) to estimate the Van der Waals coefficients of the substance that would have the desired properties. Following those calculations (for which a derivation can be found here, I computed the Van der Waals coefficients $a$ and $b$ for a few small molecules. Plotting the volume (computed from critical parameters) against number of atoms in these molecules gives a "reasonable straight line". When I extrapolate that line (which is NOT a reasonable thing to do), I find that the X molecule would contain about 300 atoms:

(note - while I show pressure in atm in the table, I convert to Pa for the calculation).

As you can see - the hard thing is to get a molecule with such high intermolecular attraction (a=25; the most polar molecule in the list, acetone, has a=1.6 so you are about 15x off your target); but if you want to play with your computer model to create such a molecule, I think it could be fun.

Just to help with the optimization, here is a graph showing the behavior of $a$ and $b$ and their effect of $T_c$ and $P_c$ (source code to generate this shown below).

And the source code:

#critical point calcs
import numpy as np
import matplotlib.pyplot as plt
from math import pi

# constants
R=8.31
Na=6.02E23
#number of lines for a,b
N1=5
N2=5

def pc(a,b):
return a/(27.0*b*b)

def tc(a,b):
return 8*a/(27*b*R)

# range of values for a,b:
a = np.logspace(-0.5,1.5,N1)
b = np.logspace(-4,-2,N2)

T = np.zeros((N1,N2))
P = np.zeros((N1,N2))

for ii in range(N2):
for jj in range(N1):
T[jj,ii]=tc(a[jj],b[ii])
P[jj,ii]=pc(a[jj],b[ii])

Tc = 293
Pc = 1e5
plt.figure()
plt.loglog(T,P,'b')
plt.loglog(T.T,P.T,'r')
plt.loglog([Tc,Tc],[1e2,Pc],'g')
plt.loglog([1,Tc],[Pc,Pc],'g')
plt.xlabel('Tc')
plt.ylabel('Pc')
plt.title('critical point for different a and b')
plt.xlim((1e1,1e4))
plt.ylim((1e3,1e8))

bc = R*Tc/(8*Pc)
ac = 27*bc*bc*Pc
vc = bc/(4*Na)
rc = np.power(3*vc/(4*pi),1./3.)
t = '  a=%.1f, b=%.4f; r=%.2e'%(ac,bc,rc)
plt.annotate(t, xy=(Tc,Pc), verticalalignment='top')
plt.annotate('increasing b', xy=(0.4, 0.1), xycoords='axes fraction',
xytext=(0.2, 0.6), textcoords='axes fraction',
arrowprops=dict(facecolor='blue', edgecolor='none', shrink=0.05),
horizontalalignment='right', verticalalignment='top',
)
plt.annotate('increasing a', xy=(0.8, 0.6), xycoords='axes fraction',
xytext=(0.3, 0.7), textcoords='axes fraction',
arrowprops=dict(facecolor='red', edgecolor='none', shrink=0.05),
horizontalalignment='right', verticalalignment='top',
)
plt.show()

• The comex deep dives subjected people to these pressures, so it may be possible to swim in supercritical fluids. – Kevin Kostlan Jul 26 '16 at 19:42
• I am after something that allows very low tech demonstration of criticality. I would probably take something with ordinary pressure and vary the temperature. Say something that goes critical by heating in a saucepan or chucking some (dry) ice in. – Daniel Mahler Jul 26 '16 at 20:31
• I recall being shown a demo with a liquid in a strong glass container (yes I suppose it was probably over 60 atm inside). Quite feasible, but maybe not as low tech as you are looking for. – Floris Jul 26 '16 at 21:21
• @DanielMahler , does your demo require a pure component, or would a mixture also suffice? If you can tolerate a mixture, you should have a LOT more degrees of freedom regarding the physical properties that can be achieved. – David White Jul 27 '16 at 0:29
• Yes but 700 K should be achievable with minimal tech requirements. Many fuels burn at several times that. This shows that you and @Diracology pointed me in the right direction in a direction. Just by looking around for substances with a high $a$ and $b$ known substances that are a lot closer then what I was previously aware of. Makes me thing that actually designing such a molecule could be feasible. – Daniel Mahler Jul 28 '16 at 6:57

The critical pressure is given by $$P_c=\frac{a}{27b^2},$$ while the critical temperature is $$T_c=\frac{8a}{27bR}=\frac{8bP_c}{R}.$$ The parameter $b$ is related to to the effective volume occupied by the molecules, $$b=4N_0V_0,$$ where $V_0$ is the volume of the molecule and $N_0$ is the Avogadro number.

So at least theoretically you can chose $P_c=1\, \mathrm{atm}\approx 10^5\, \mathrm{Pa}$ and $T_c=273\, \mathrm{K}$ and then solve it for $b$, $$b=\frac{RT_c}{8P_c}\approx 2.7\cdot 10^{-3},$$ which means a molecule radius of $6.4\cdot 10^{-10}\, \mathrm{m}$, which is reasonable. If you want just to make a model, you can fix $T_c=273\, \mathrm{K}$ and $a\sim 10^0$ (which is the highest value I have seen) and then solve for $P_c$ and $b$. Then you will find how far from $1\, \mathrm{atm}$ and a tipical radius $10^{-10}$ the solution is.

• The parameter $a$ characterizes the strength of the attractive intermolecular interaction and it has a quite large range of values for different molecules. However since it appears equally in the expression for $P_c$ and $T_c$ we can eliminate it with those expressions. – Diracology Jul 26 '16 at 20:00
• Nice analysis - but now that you have $b$, you need to calculate $a$ as well - the other Van der Waals coefficient. Using your numbers, I get $a=20$ - that seems an order of magnitude too large for any known materials. Thoughts? – Floris Jul 26 '16 at 20:04
• @Floris Thanks for pointing this out. It is correct, this is way above a realistic value for $a$ which in the table I have at hands is of order $10^{-3}-10^{-1}$. I think that is where your answer comes in. We can play with the relations for $P_c$ and $T_c$ but we can't get exactly the STP conditions. How near we get is, as you said, a matter of definition. – Diracology Jul 26 '16 at 20:11
• @DanielMahler $a$ relates to the attractive forces between the molecules; $b$ is a proxy for their volume. They are independent; but it is hard to imagine a large molecule with a sufficiently large $a$ (I suppose a crazy surface of alternating electrophilic and electrophobic atoms would be needed). – Floris Jul 26 '16 at 21:17
• Incidentally this link gives a very accessible derivation of the expressions used here. – Floris Jul 26 '16 at 23:12

Candidate substances can also be found using group contribution methods such as the Klincewicz and Joback methods, which predict substance properties by taking weighted counts of atomic groups within the molecule. Bothe of the above named methods predict $T_c$ and $P_c$. These methods are only heuristic though and it is not clear what their domain of validity is. In particular they can not distinguish beween isomers of a molecule which have significant effects on $T_c$ and $P_c$.

It is still interesting to see what insights these methods can provide. Inspecting the formula and tables of these methods shows that the dominant trend is that $P_c$ decreases with increasing number of atoms and molecular weight while $T_c$ with the specifics of the molecule providing corrections to the rate of this effect. This is consistent with the relationship between $T_c$, $P_c$ and Van der Waals $b$ in @Floris and @Diracology's answers as well as my finding of low $P_c$ substances among large flourocarbons.

The need for large molecules implies a carbon backbone. The remaining constituents can the be chosen to try and minimize the associated rise in $T_c$. According to the Joback method. Fluorine does appear to be one of the best constituents for this purpose.