Chemistry · Ch 10 — States of Matter
Liquefaction of gases and critical constant
Liquefaction of gases and critical constant
Most gases behave close to ideally at high temperature -- for instance, carbon dioxide's pressure-volume curve at °C closely follows the ideal Boyle's-law curve. As temperature is progressively lowered, the -- curve increasingly departs from ideal behaviour, and at some sufficiently low temperature the gas can be liquefied by compressing it to a high enough pressure -- CO2, for example, liquefies at °C and atmospheres. The highest temperature at which a substance can still be liquefied by pressure alone is called its critical temperature (); above , no matter how great the applied pressure, the substance can exist only as a gas. The pressure needed to liquefy the gas exactly at its critical temperature is the critical pressure (), and the molar volume at that point is the critical volume (). Everyday gases like N2 and O2 have critical temperatures far below room temperature (roughly K and K respectively) with relatively high critical pressures, which is why liquefying air requires substantial compression combined with cooling; by contrast, water has an unusually high ( K) and ( bar), which is why it exists as a liquid, not a gas, under ordinary room conditions, while CO2's ( K) is close to room temperature but its ( bar) is high, so CO2 is normally a gas at room temperature and pressure. The liquid state and gaseous state are not always sharply separated -- above the critical temperature a substance is more properly called a fluid, since there is a continuity between gas and liquid with no distinct phase boundary, whereas below the two states can genuinely coexist and be told apart. When a liquid exposed to the atmosphere is heated, its vapour pressure rises until it equals the surrounding atmospheric pressure -- the temperature at which this happens is the liquid's boiling point; a higher surrounding pressure raises the boiling point (as in a sealed pressure cooker), and a lower surrounding pressure lowers it (as in a partially evacuated vessel or at high altitude, where atmosphe …
Substance | Tc (K) | Pc (bar) | Vc (dm3 mol-1)
H2 | 33.2 | 12.97 | 0.0650
He | 5.3 | 2.29 | 0.0577
N2 | 126.0 | 33.9 | 0.0900
O2 | 154.3 | 50.4 | 0.0744
CO2 | 304.10 | 73.9 | 0.0956
H2O | 647.1 | 220.6 | 0.0450
NH3 | 405.5 | 113.0 | 0.0723 …
What this figure shows. A pressure-volume graph showing several curves ('isotherms'), one for each of a series of different fixed temperatures, for carbon dioxide gas. At higher temperatures the curve looks like a smooth ideal-gas hyperbola with no flat region. As temperature is lowered, each successive isotherm develops a horizontal flat plateau over a certain range of volume -- this plateau is where liquid and gas CO2 coexist together at a fixed pressure while the volume changes as more gas condenses to liquid; the plateau shrinks and finally vanishes exactly at the critical isotherm (30.98 C for CO2), above which no flat/coexistence region appears at any pressure and CO2 can …
Worked out. Water has Tc = 647.1 K and Pc = 220.6 bar; what does this imply about water's state under ordinary conditions? Since water's Tc and Pc are both very high compared to typical room temperature (around 298 K) and atmospheric pressure (around 1 atm/1.013 bar), water is far below its critical point under everyday conditions, and consequently it exists as a liquid (not a gas) under ordinary temperature and pressure. [Note: the source PDF labels this 'Problem 10.5' a second time, a duplicate of the Dalton's-law worked example already numbered Problem 10.5 in section 10.5.6 -- both are transcribed here exactly as printed, since they …
Worked out. CO2 has Tc = 38.98 C and Pc = 73 atm; how many phases of CO2 coexist at (i) 50 C and 73 atm, and (ii) 20 C and 50 atm? (i) 50 C is above CO2's critical temperature of 38.98 C, so regardless of how high the pressure is, CO2 cannot exist as a distinct liquid there -- it exists as a single (gaseous/fluid) phase only. (ii) 20 C is below the critical temperature, so under these conditions liquid CO2 and gaseous CO2 can coexist toget …
Worked out. In which of the following will water have the highest and lowest boiling point: (a) an open vessel, (b) a pressure cooker, (c) an evacuated vessel? The boiling point of a liquid rises as the surrounding pressure on its surface rises, and falls as that surrounding pressure falls. A pressure cooker traps steam and raises the pressure above the water well beyond normal atmospheric pressure, so water boils at its HIGHEST temperature in the pressure cooker (option b). An evacuated vessel has the surrounding pressure pumped down far below atmospheric, so water boils at its LOWEST temperature there (option c), lower even than in an open vessel at ordinary atmospheric pressure ( …