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Since there is no liquid state of carbon dioxide, what will carbon dioxide turn into when exposed to high pressure?

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There is a liquid state for carbon dioxide. Borrowing the $\ce{CO2}$ phase diagram from Wikipedia, we can see that $\ce{CO2}$ will condense at a few atmospheres, dependent on temperature. At still higher pressures, the liquid will solidify. Below the triple point temperature, the gas will transition directly to solid.

enter image description here

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  • $\begingroup$ just to add a little bit of cultural reference to @Richard Terret's already great answer, solid carbon dioxide is what most of us know more commonly as dry ice. $\endgroup$ – insaner Mar 10 '14 at 7:54
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Carbon dioxide phase diagram,

enter image description here

This is extremely important. $Trillion cumulative carbon sequestration demands deep "burial" of captured power plant carbon dioxide. All proposed reservoirs are above 31 C. Above its critical temperature, CO2 is an astoundingly effective penetrant (right through thick solid concrete for a one-day accelerated cure). You can pump it down there, but it will come back up. (Also note, PV = energy, 101.325 J/liter-atm. Capturing, compressing, and pumping emitted carbon dioxide must consume at least 30% of a fossil fuel power plant's output.)

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