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Chapter 10: Problem 130

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

Expert verified
\(\mathrm{N}_{2}\) 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

01

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.
02

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\(_2\).
03

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.

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