Question

Assume that you have samples of the following three gases at \(25{ }^{\circ} \mathrm{C}\). Which of the three can be liquefied by applying pressure, and which cannot? Explain. Ammonia: \(T_{c}=132.5^{\circ} \mathrm{C}\) and \(P_{c}=112.5\) atm Methane: \(T_{c}=-82.1^{\circ} \mathrm{C}\) and \(P_{\mathrm{c}}=45.8 \mathrm{~atm}\) Sulfur dioxide: \(T_{c}=157.8^{\circ} \mathrm{C}\) and \(P_{c}=77.7\) atm

Short answer

Ammonia and sulfur dioxide can be liquefied at 25°C; methane cannot.

Step-by-step solution

Understand Critical Temperature

The critical temperature \(T_c\) is the highest temperature at which a gas can be liquefied by pressure alone. Above this temperature, no amount of pressure will liquefy the gas.

Compare Given Temperature with Critical Temperatures

Our given temperature is \(25^{\circ}C\). We compare this with the critical temperatures of each gas:- Ammonia: \(T_c = 132.5^{\circ}C\)- Methane: \(T_c = -82.1^{\circ}C\)- Sulfur dioxide: \(T_c = 157.8^{\circ}C\)

Determine Liquefiability for Each Gas

- Ammonia (\(132.5^{\circ}C\) is greater than \(25^{\circ}C\)): Can be liquefied because \(25^{\circ}C\) is below its critical temperature.- Methane (\(-82.1^{\circ}C\) is less than \(25^{\circ}C\)): Cannot be liquefied because \(25^{\circ}C\) is above its critical temperature.- Sulfur dioxide (\(157.8^{\circ}C\) is greater than \(25^{\circ}C\)): Can be liquefied because \(25^{\circ}C\) is below its critical temperature.

Formulate Conclusion

Ammonia and sulfur dioxide can be liquefied by applying pressure at \(25^{\circ}C\), but methane cannot.

Key concepts

Understanding Critical Temperature

The critical temperature of a gas is a fundamental concept in understanding gas liquefaction.It's defined as the maximum temperature at which a gas can transition into a liquid state by applying pressure. When the temperature is higher than the critical temperature, even with increased pressure, the gas remains in its gaseous form.

For instance, if we look at ammonia in our exercise, its critical temperature is given as \(132.5^{\circ}C\). This means that ammonia can be liquefied at any temperature below \(132.5^{\circ}C\) with enough pressure applied.On the other hand, methane with a critical temperature of \(-82.1^{\circ}C\) cannot be liquefied at \(25^{\circ}C\) because this temperature exceeds its critical threshold.

• Critical temperature sets the "cooling limit" for liquefaction.
• It varies uniquely from gas to gas depending on intermolecular forces.
• Assessing whether a certain gas can be liquefied involves comparing the environmental temperature to its critical temperature.

Understanding this concept helps to comprehend why and how different gases behave when subjected to external pressures at given temperatures.

Role of Pressure Application

Pressure plays a vital role in the process of gas liquefaction.By compressing a gas, you force the molecules closer together, increasing the likelihood of them adhering to each other and transforming into a liquid. However, pressure alone cannot achieve liquefaction if the temperature is above the critical temperature.

In our exercise, because ammonia and sulfur dioxide are below their critical temperatures at \(25^{\circ}C\), applying enough pressure will push the molecules closer, allowing them to condense into a liquid form. Conversely, methane cannot be liquefied by pressure at \(25^{\circ}C\) because its molecules possess too much kinetic energy above their threshold temperature to come together even under high pressure.

• Pressure must be paired with temperature conditions conducive to liquefaction, i.e., below the critical temperature.
• It effectively 'squeezes' molecules, but is ineffective once critical temperature is surpassed.
• Every gas has its own pressure requirement for liquefaction which is influenced by molecular interactions and structure.

This concept emphasizes why gases with different properties and conditions react distinctively when pressure is applied.

Exploring Gas Properties

Different gases have unique properties that influence their ability to be liquefied. These properties include critical temperature and the nature of intermolecular forces at play.

In the exercise, ammonia, methane, and sulfur dioxide each have specific critical temperatures and pressures. These parameters are pivotal in determining their behavior under pressure. For instance, ammonia's higher critical temperature compared to methane indicates that it can be liquefied at a higher ambient temperature.

• Gas properties such as molecular weight and type of intermolecular forces (e.g., hydrogen bonding in ammonia) affect critical temperature and pressure.
• The intermolecular forces between gas molecules dictate how easily these molecules can come together to form a liquid.
• Understanding the inherent properties of a gas allows for better prediction and control over its phase changes.

Thus, studying gas properties offers insights into understanding the conditions required for converting gases from one state to another effectively.