Question

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.

Short answer

\(\mathrm{N}_{2}\) cannot be liquefied at room temperature, no matter how much pressure is applied. This is because its critical temperature is \(-147^{\circ} \mathrm{C}\), which is lower than room temperature. On the other hand, \(\mathrm{NH}_{3}\) can be liquefied at room temperature by applying sufficient pressure, as its critical temperature is higher than room temperature.

Step-by-step solution

Understand the Critical Points of NH3 and N2

We are given that the critical point of \(\mathrm{NH}_{3}\) is \(132^{\circ} \mathrm{C}\) and \(111 \mathrm{atm}\). This means that NH\(_3\) can be liquefied by applying pressure if the temperature is below 132 degrees Celsius. Similarly, the critical point of \(\mathrm{N}_{2}\) is \(-147^{\circ} \mathrm{C}\) and \(34 \mathrm{atm}\). This means that N\(_2\) can be liquefied by applying pressure if the temperature is below -147 degrees Celsius.

Compare Critical Points to Room Temperature

Room temperature is generally around \(20^{\circ} \mathrm{C}\). Now, let's compare this temperature to the critical temperatures of both substances: For NH\(_3\): The critical temperature is \(132^{\circ} \mathrm{C}\), which is higher than room temperature. This implies that we can liquefy NH\(_3\) by applying sufficient pressure at room temperature. For N\(_2\): The critical temperature is \(-147^{\circ} \mathrm{C}\), which is lower than room temperature. This implies that no matter how much pressure we apply at room temperature, we cannot liquefy N\(_2\).

Determine Which Substance Cannot Be Liquefied at Room Temperature

Based on the comparison in Step 2, we can conclude that \(\mathrm{N}_{2}\) cannot be liquefied at room temperature, regardless of the pressure applied. This is because its critical temperature is lower than room temperature. On the other hand, NH\(_3\) can be liquefied at room temperature by applying sufficient pressure, as its critical temperature is higher than room temperature.

Key concepts

Liquefaction

Liquefaction is the process of converting a substance from a gas to a liquid. For gases, this typically means reducing the temperature or increasing the pressure until the gas transitions into a liquid state. Each substance has a specific 'critical point' that determines whether it can be liquefied. The critical point refers to a specific temperature and pressure at which a substance cannot exist as a liquid regardless of pressure once it's above this temperature.- A substance below its critical temperature can potentially be liquefied if enough pressure is applied.- Above the critical temperature, no amount of pressure will result in liquefaction.In our example, ammonia (NH\(_3\)) can be liquefied at room temperature because its critical point temperature is above the typical room temperature. Nitrogen (N\(_2\)), however, cannot be liquefied at room temperature, regardless of the pressure applied, since its critical temperature is much lower than what is considered as room temperature.Understanding these concepts is crucial in industrial applications, such as gas storage and transportation.

Pressure

Pressure plays a vital role in the process of liquefaction. It can be thought of as a force that can push molecules closer together, making it easier for them to transition into a liquid state. When a gas is below its critical temperature, increasing the pressure can cause it to liquefy. This is because higher pressure forces gas molecules closer together, overcoming the energy that keeps them in a gaseous state.- Increasing pressure is key to achieving liquefaction below the critical temperature.- Above the critical temperature, pressure alone cannot achieve liquefaction.For instance, with ammonia (NH\(_3\)), at room temperature—a temperature below its critical temperature—you can increase pressure to achieve liquefaction. However, with nitrogen (N\(_2\)) at room temperature, the temperature itself is too high for liquefaction to occur, regardless of the pressure applied.When designing systems for gas storage, safety and efficiency, these pressure concepts are integrated to ensure safe liquefaction and containment of gases.

Temperature

Temperature is a measure of how much thermal energy or heat a system contains. It directly influences the movement and energy of molecules within a substance. Critical temperature is a pivotal factor in determining the ability to achieve liquefaction for gases.- When a gas is above its critical temperature, it cannot be converted into a liquid by any amount of pressure.- Below the critical temperature, it becomes possible to convert the gas to a liquid by altering the pressure.In the context of our problem, the critical temperature for ammonia (NH\(_3\)) is 132°C, while for nitrogen (N\(_2\)) it is -147°C. This means that if NH\(_3\) is at room temperature (around 20°C), it is below its critical temperature, hence can be liquefied by increasing pressure. Conversely, nitrogen at room temperature is well above its critical temperature, meaning it remains gaseous even under high pressure.Recognizing how temperature relates to a gas's critical point helps in optimizing processes for effective gas handling and transformation.