Answer the following questions based on the P-T phase diagram of carbon dioxide:
(a) At what temperature and pressure can the solid, liquid and vapour phases of $C O_{2}$ co-exits in equilibrium ?
(b) What is the effect of decrease of pressure on the fusion and boiling point of $C O_{2}$ ?
(c) What are the critical temperature and pressure for $C O_{2}$ ? what is their significance ?
(d) Is $C O_{2}$ solid, liquid or gas at (a) $- 70^{o} C$ under 1 atm, (b) $- 60^{o} C$ under 10 atm, (c) $15^{o} C$ under 56 atm ?

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Solution

The P-T phase diagram for CO2 is shown in the attached figure.
(a) The three phases can coexist at triple point. From the graph, it is at $- {56.6}^{o} C$ and 5.11 atm.
(b) With the decrease in pressure, both the fusion and boiling point of carbon dioxide will decrease.
(c) For carbon dioxide, the critical temperature is ${31.1}^{o} C$ and critical pressure is 73.0 atm. If the temperature of carbon dioxide is more than ${31.1}^{o} C$ , it can not be liquefied, however large pressure we may apply.
(d) Carbon dioxide will be (a) a vapour, at $= 70^{o} C$ under 1 atm. (b) a solid, at $- 6^{o} C$ under 10 atm (c) a liquid, at $15^{o} C$ under 56 atm.

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