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Chapter 10: Problem 126

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 atm. Which of these substances cannot be liquefied at room temperature no matter how much pressure is applied? Explain.

Short Answer

Expert verified
Nitrogen (N2) cannot be liquefied at room temperature, no matter how much pressure is applied. This is because its critical temperature (\(T_{c_{N2}}\) = 126.15 K) is lower than room temperature (298 K). On the other hand, ammonia (NH3) can be liquefied at room temperature since its critical temperature (\(T_{c_{NH3}}\) = 405.15 K) is higher than room temperature.

Step by step solution

01

Identify the critical points of NH3 and N2.

The critical point of ammonia (NH3) is given as 132°C and 111 atm. The critical point of nitrogen (N2) is given as -147°C and 34 atm.
02

Convert the critical temperatures to Kelvin.

We need to convert the critical temperatures from Celsius to Kelvin to facilitate the comparison with room temperature (298 K). To convert from Celsius to Kelvin, add 273.15 to the Celsius temperature. For NH3: \(T_{c_{NH3}}\) = 132°C + 273.15 = 405.15 K For N2: \(T_{c_{N2}}\) = -147° + 273.15 = 126.15 K
03

Compare the critical temperatures with room temperature.

If the critical temperature of a substance is below room temperature (298 K), it cannot be liquefied at room temperature, regardless of the pressure applied. For NH3: \(T_{c_{NH3}}\) = 405.15 K > 298 K, so NH3 can be liquefied at room temperature. For N2: \(T_{c_{N2}}\) = 126.15 K < 298 K, so N2 cannot be liquefied at room temperature, no matter how much pressure is applied.
04

State the conclusion.

Based on the comparison of the critical temperatures with room temperature, it is clear that nitrogen (N2) cannot be liquefied at room temperature, regardless of the pressure applied.

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