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 $CO_{2}$ co-exist in equilibrium?
$(b)$ What is the effect of decrease of pressure on the fusion and boiling point of $CO_{2}$?
$(c)$ What are the critical temperature and pressure for $CO_{2}$? What is their significance?
$(d)$ Is $CO_{2}$ solid,liquid or gas at $(i)$ $-70^{\circ}C$ under $1\;atm$,$(ii)$ $-60^{\circ}C$ under $10\;atm$,$(iii)$ $15^{\circ}C$ under $56\;atm$?

(N/A) The $P-T$ phase diagram for $CO_{2}$ is shown in the provided figure.
$(a)$ Point $C$ is the triple point of the $CO_{2}$ phase diagram. At this point,the temperature is $-56.6^{\circ}C$ and the pressure is $5.11\;atm$. At these conditions,the solid,liquid,and vapour phases of $CO_{2}$ co-exist in equilibrium.
$(b)$ The fusion and boiling points of $CO_{2}$ decrease with a decrease in pressure.
$(c)$ The critical temperature and critical pressure of $CO_{2}$ are $31.1^{\circ}C$ and $73\;atm$ respectively. The significance is that $CO_{2}$ cannot be liquefied above the critical temperature,regardless of how much pressure is applied.
$(d)$ Based on the $P-T$ phase diagram:
$(i)$ At $-70^{\circ}C$ and $1\;atm$,$CO_{2}$ is in the vapour (gas) phase.
$(ii)$ At $-60^{\circ}C$ and $10\;atm$,$CO_{2}$ is in the solid phase.
$(iii)$ At $15^{\circ}C$ and $56\;atm$,$CO_{2}$ is in the liquid phase.