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

Short answer

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

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.

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

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.

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.

Key concepts

Ammonia (NH3)

Ammonia, or \( ext{NH}_3\), is a colorless gas with a pungent smell that is composed of nitrogen and hydrogen. It is commonly used in various industrial applications, including fertilizers, cleaning products, and refrigeration systems. Ammonia has a relatively high critical temperature of 132°C (405.15 K), \(
\)allowing it to be easily condensed into a liquid at room temperature. This characteristic makes \( ext{NH}_3\) very useful for cooling and other applications involving phase changes. \(
\)Understanding its critical point is essential to efficiently employ it in systems where precise temperature control is needed.

Nitrogen (N2)

Nitrogen, or \( ext{N}_2\), constitutes about 78% of the Earth's atmosphere by volume. It is a diatomic molecule that plays a critical role in supporting life through the nitrogen cycle. The critical point of nitrogen is quite low, at \(-147°C\) or 126.15 K. \(
\)This low critical temperature means at higher temperatures, such as room temperature, \( ext{N}_2\) remains gaseous regardless of the pressure applied. \(
\)It is important to note that nitrogen remains stable and non-reactive under most conditions, which contributes to its wide range of applications from cryogenics to serving as an inert atmosphere for chemical reactions.

Liquefaction

Liquefaction is the process of converting a gas into its liquid form. This process involves changing the temperature and pressure conditions to bring the gas below its critical temperature and above its critical pressure. \(
\)For a gas to liquefy, the temperature must be below its critical temperature. If it is above, like the case with nitrogen at room temperature, \( ext{N}_2\) cannot be compressed into a liquid. \(
\)The practical implications of liquefaction are significant in many industries. By liquefying gases, we can store and transport them more efficiently, especially for gases, such as natural gas and ammonia.

Pressure

Pressure is a fundamental concept in physics that describes the force exerted per unit area. It plays a crucial role in determining the state of a substance (gas, liquid, or solid) under various conditions. \(
\)In the context of liquefaction, pressure is combined with temperature to examine a substance’s critical point. \(
\)If the pressure is increased above the critical pressure while at a temperature below the critical temperature, a gas will turn into a liquid. Thus, by manipulating pressure, substances like ammonia can be liquefied efficiently at room temperature.

Temperature Conversion

Temperature conversion, especially between Celsius and Kelvin, is essential for scientific calculations involving thermal systems. Kelvin is the SI unit for temperature, which starts at absolute zero, the point at which molecular motion stops. \(
\)To convert Celsius to Kelvin, 273.15 is added to the Celsius value. This conversion allows for consistent scientific communication and comparison. \(
\)Understanding these conversions is vital in identifying conditions like critical points where phase changes occur, as seen in the comparison of ammonia and nitrogen critical temperatures to room temperature.