I'm trying to determine whether or not certain compounds form solid ice at certain atmospheric pressures. These pressures vary significantly, from 0.001 atm to 800 atm. I understand that there is no equation relating the freezing points of all elements, but is there one or two that relate to carbon dioxide and water?

Ideally I'd like a Python function (or library) or equation where the input is atmospheric pressure or kPa.

Or, failing that, if someone could point me in the direction of a phase diagram for both compounds where I can input specific atmospheric pressure values and read a specific temperature for freezing point, that would be helpful as well.

  • $\begingroup$ Welcome to chemistry.se! If you have questions about how to beautify your posts, have a look at the help center. Do you want to know more about this site, please take the tour.|| I do not have the time to do more research, but maybe this page can help. $\endgroup$ Jan 20, 2015 at 2:06
  • $\begingroup$ I did a lot of research already but I couldn't find a very detailed phase diagram. The link you posted's phase diagram for CO2 is broken. $\endgroup$
    – anarchy8
    Jan 20, 2015 at 6:55
  • $\begingroup$ Sorry about that. Maybe this helps for CO2 and this might help for water $\endgroup$ Jan 20, 2015 at 7:15
  • 1
    $\begingroup$ Diagrams on en.wikipedia.org/wiki/Carbon_dioxide $\endgroup$
    – Mithoron
    Jan 20, 2015 at 12:32
  • $\begingroup$ @Martin That link does not load.@Mithoron that's the first place I looked. Not detailed enough. $\endgroup$
    – anarchy8
    Jan 20, 2015 at 16:28

1 Answer 1


For ice I melting pressure as a function of temperature:

$$\pi = 1- 0.626000 \times 10^6 (1- \theta^{-3}) + 0.197135 \times 10^6 (1- \theta^{21.2})$$


$\pi =$ (pressure in MPa)/0.000611657 MPa

$\theta =$ (temperature in kelvins)/273.16K

Source is International Equation of the Pressure along the Melting and along the Sublimation Curve of Ordinary Water substance (no paywall).

For carbon dioxide:

$$\frac{p_m}{p_n} = 1 + a_1 (\frac{T}{T_t}) + a_2 (\frac{T}{T_t})^2$$


$T$ is temperature in kelvins

$T_t =$ 216.592K

$p_m$ is the melting pressure in MPa

$p_n =$ 0.51795 MPa

$a_1 =$ 1955.5390

$a_2 =$ 2055.4593

Source is A New Equation of State for Carbon Dioxide... (no paywall)

Check original sources before using equations in case I made typo(s).

  • $\begingroup$ Thanks! What exactly is P_sub_n? If I had an atmosphere of 0.006 atm or 0.00060795 MPa, would P_sub_n be 0.00060795? If I solve for T, would that give the temperature that C02 freezes at at at that pressure? $\endgroup$
    – anarchy8
    Jan 23, 2015 at 0:06
  • $\begingroup$ I'm not a Chemist, and unfortunately beyond Wolfram Alpha I don't know how to use these equations. $\endgroup$
    – anarchy8
    Jan 23, 2015 at 0:15
  • $\begingroup$ @anarchy8 p_n is the triple point pressure, the pressure at which gas, liquid and solid are in equilibrium. P_m is the melting point pressure, so 0.00060795 in your example. The co2 equation you could solve for t/t_t using the quadratic formula or a program like wolfram, or you could construct a table of values and interpolate the table. $\endgroup$
    – DavePhD
    Jan 23, 2015 at 1:30

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