[smghz]

I read that CT is the temperature above which a liquid cannot exist, i.e. only exists as supercritical fluid. I also learned that critical pressure is the minimum pressure that can be applied at the CT to liquefy it.

All cool, right?

Well, see these proliferated and confusing statements online:

"The critical temperature of a substance is the temperature at and above which vapor of the substance cannot be liquefied, no matter how much pressure is applied."

"The critical pressure of a substance is the pressure required to liquefy a gas at its critical temperature. Some examples are shown below."

"Make sure that you understand the critical temperature correctly; liquefaction can occur only below the critical temperature if sufficient pressure has been applied to the gas."

How is this possible? I am getting legitimately confused. On one hand, I read that you can apply critical pressure at CT and still be able to liquefy a gas; on another, I read that, "No, you better have the gas below the CT or else it won't liquefy even if you put the pressure of the entire universe into it". Why so confusing??

[AWK]

At critical point the liquid and its vapor become indistinguishable. So you cannot liquefy a gas at these conditions

[Borek]

I see how it can be confusing.

Would it help to think about the transition between liquid and supercritical liquid as of a phase transition, like boiling or melting (when two phases coexist at a specific temperature)?

[smghz]

But are there any clear-cut answers, instead of just a confusing jumble of "at" and "below" I understand phase transitions, just not whether the substance can actually be liquefied at CT if the critical pressure was applied.

[AWK]

But are there any clear-cut answers

I disagree. Critical point is the first point when only one phase (superciritical fluid) exists.

[smghz]

So, say we have CO2 (which has CT of 31C). If I applied enough critical pressure for CO2 at its CT, would it liquefy or not liquefy (remain as a supercritical fluid)? B/c I learnt that a substance becomes a supercritical fluid only once it is above the CT. thanks

[Borek]

I disagree. Critical point is the first point when only one phase (superciritical fluid) exists.

Is it? Critical point (or critical state) is defined as the end point of a phase equilibrium curve. If the curve exist at a point, gas and liquid should exist as well. What you propose seems to be suggesting critical point is the first temperature higher than the one at which separate gas and liquid existed - but I don't see how to define what this "first temperature above" is without using infinitesimals.

[AWK]

At critical point density of liquid is equal to density of compressed gas. Then at this point two phases cannot exist.
Moreover, we do not know an exact parameters of critical point since it is measured.

[mjc123]

The confusion seems to be due to regarding the P-T diagram as having three regions: "below", "at" and "above" the critical temperature (or pressure), and asking what happens in the region "at". But this "region" has zero area on the diagram. "At" is simply the boundary (of zero width) between the "below" and "above" regions. Below you can have two phases in equilibrium, above you can only have one. Thus I don't really think the statements quoted by smghz are contradictory; I don't think it's meaningful to ask what happens at exactly Tc.
To put it more mathematically, for any ε, however small, a temperature range T1 - T2 (where T2 = T1+ε) can be defined such that at T1 two phases can exist in equilibrium and at T2 only one can. The smallest value you can reliably determine for ε defines the uncertainty of your knowledge of Tc. Practically ε always > 0.