# Is there a pressure dependent function for freezing points of water and carbon dioxide?

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.

• 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. – Martin - マーチン Jan 20 '15 at 2:06
• 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. – anarchy8 Jan 20 '15 at 6:55
• Sorry about that. Maybe this helps for CO2 and this might help for water – Martin - マーチン Jan 20 '15 at 7:15
• Diagrams on en.wikipedia.org/wiki/Carbon_dioxide – Mithoron Jan 20 '15 at 12:32
• @Martin That link does not load.@Mithoron that's the first place I looked. Not detailed enough. – anarchy8 Jan 20 '15 at 16:28

For ice I melting pressure as a function of temperature:

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

where

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

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

For carbon dioxide:

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

Where:

$T$ 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).

• 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? – anarchy8 Jan 23 '15 at 0:06
• I'm not a Chemist, and unfortunately beyond Wolfram Alpha I don't know how to use these equations. – anarchy8 Jan 23 '15 at 0:15
• @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. – DavePhD Jan 23 '15 at 1:30