The critical point of \(\mathrm{NH}_{3}\) is \(132^{\circ} \mathrm{C}\) and \(111 \mathrm{~atm}\), and the critical point of \(\mathrm{N}_{2}\) is \(-147^{\circ} \mathrm{C}\) and \(34 \mathrm{~atm}\). Which of these substances cannot be liquefied at room temperature no matter how much pressure is applied? Explain.

Liquefaction of gases is a process that transforms a gas into a liquid state. This conversion is a common industrial procedure and an interesting scientific phenomenon, both governed by physical laws relating to temperature and pressure.

For a gas to liquefy, it must be cooled below its boiling point or compressed to a high enough pressure while being below its critical temperature. If the gas's temperature is below the critical temperature, increasing the pressure would lead to liquefaction. This concept is important in many applications, ranging from the storage and transport of natural gas to refrigeration and air conditioning systems.

Let's consider ammonia (NH₃) as an example. With a critical temperature of 132°C, it remains a candidate for liquefaction at room temperature by applying pressure. In contrast, nitrogen (N₂), with a critical temperature of -147°C, cannot be liquefied at room temperature; it needs to be cooled below this temperature before pressurization can take effect.

The concept of critical temperature is pivotal when discussing the states of matter under different conditions. It is the highest temperature at which a gas can be converted to a liquid, regardless of the pressure applied. Above this temperature, the gas cannot condense because the kinetic energy of the molecules is too great, preventing them from being held together in a liquid state.

In the context of our exercise, ammonia has a higher critical temperature than room temperature, implying that it may be converted to liquid form through compression. On the other hand, nitrogen's critical temperature is significantly below room temperature, signalling that no achievable compression at that temperature can compel it into a liquid state. This indicates why nitrogen gas cannot be liquefied by pressurization alone at room temperature.

A phase diagram is a graphical representation of the phases of a substance as a function of temperature and pressure. It delineates boundaries that distinguish between the solid, liquid, and gas states, as well as conditions for sublimation and the critical point beyond which distinct liquid and gas phases do not exist.

Critical points are particularly relevant as they define the conditions at which the substance exhibits properties of both liquid and gas without distinction. For students looking at the ammonia and nitrogen comparison, analyzing a phase diagram facilitates understanding why nitrogen cannot be liquefied at room temperature. It would show that increasing pressure above the critical point does not result in a transition from gas to liquid, reinforcing the theoretical explanation with a visual context.