(a) What is the significance of the critical point in a phase diagram? (b) Why does the line that separates the gas and liquid phases end at the critical point?

A phase diagram is a graphical representation of the equilibrium states of a substance under varying conditions of temperature and pressure. It shows the boundaries between different phases (e.g., solid, liquid, and gas) and indicates the required conditions for a substance to exist in a specific state. Phase diagrams help in understanding the behavior of a substance under diverse conditions and aid in the prediction of its phase transitions.

The critical point is a particular state at which the liquid and gas phases of a substance become indistinguishable from each other. In other words, at the critical point, the properties of the liquid and gas phases become identical, and the substance is referred to as a supercritical fluid. The critical point can be described by the critical temperature (\(T_c\)) and the critical pressure (\(P_c\)), which are specific to each substance.

The critical point plays a significant role in understanding the behavior of a substance as it marks the boundary beyond which the transition between liquid and gas phases is continuous and no phase boundaries exist. Moreover, when a substance is heated or pressurized beyond its critical point, it exhibits unique properties, such as a high density like a liquid and low viscosity like a gas, which makes it suitable for various industrial applications, such as supercritical fluid extraction, enhanced oil recovery, and power generation.

The line that separates the gas and liquid phases in a phase diagram is called the phase boundary or equilibrium line. This line marks the conditions at which a substance undergoes a phase transition between liquid and gas states. However, when approaching the critical point, the distinction between the liquid and gas phases fades as their properties converge, and they effectively become the same phase. At the critical point, the substance exists as a supercritical fluid, and the phase boundary ends since the concept of liquid and gas phases is no longer applicable. Consequently, beyond the critical point, the substance does not have a separate liquid or gas phase, and only a single supercritical fluid phase exists. Thus, the line that separates the gas and liquid phases ends at the critical point, denoting the boundary where the two phases become indistinguishable.