Problem 83 - A Complete Resource Book in Chemistry for JEE Main

Question

An ideal gas obeying kinetic gas equation can be liquefied if (a) it cannot be liquefi ed at any value of \(\mathrm{P}\) and \(\mathrm{T}\) (b) its temperature is more than Boyle's temperature (c) its temperature is more than critical temperature (d) its pressure is more than critical pressure

Step-by-Step Solution

Answer

The gas cannot be liquefied if its temperature is more than the critical temperature.

Step 1: Identify Key Concepts

To solve this problem, we need to utilize the concepts of critical temperature and pressure. An ideal gas can be liquefied if its temperature is below a certain threshold called the 'critical temperature'. Similarly, the pressure also plays a role where it must be above the critical pressure for liquefaction to occur.

Step 2: Conceptual Understanding of Critical Temperature

The critical temperature is the maximum temperature at which a substance can exist as a liquid, regardless of the pressure applied. If the temperature of the gas is more than the critical temperature, it will not liquefy no matter how much pressure is applied.

Step 3: Evaluate Each Option

Let's evaluate given options: - (a) is incorrect because a gas above critical temperature is not liquefiable at any ,P and ,T . - (b) Boyle's temperature relates to the ideality of gas, not liquefaction, making it irrelevant here. - (c) is correct because if the gas temperature is more than the critical temperature, it cannot be liquefied. - (d) is sometimes true but it is not the definitive criteria; the temperature condition in (c) is the deciding factor.

Key Concepts

Critical Temperature

The critical temperature of a gas is a key concept when discussing the liquefaction of gases. It is the maximum temperature at which a gas can remain in a liquid state. If a gas is at or below this temperature, it can potentially be turned into a liquid with the application of the right amount of pressure. However, if its temperature exceeds the critical temperature, no amount of pressure will be able to convert the gas into a liquid. Understanding the critical temperature helps us realize why some gases in their natural state remain gases under our everyday conditions on Earth. Important notes about critical temperature include:

• It varies for different substances. Each gas has its own unique critical temperature.
• It represents a physical property of a substance, defining a boundary between gaseous and liquid states.
• Beyond this temperature point, the gas molecules have too much kinetic energy to be compressed into a liquid.

Thus, knowing the critical temperature is crucial in industrial applications where the liquefaction of gases is necessary for storage and transport.

Critical Pressure

Critical pressure is closely linked to critical temperature and is vital for the process of liquefying gases. It is defined as the minimum pressure needed to liquefy a gas at its critical temperature. Above this pressure level, a gas can be compressed into a liquid, as long as its temperature does not exceed the critical temperature. Here are some useful insights regarding critical pressure:

• It helps determine the specific conditions necessary for transitioning from a gas to a liquid state.
• Like critical temperature, critical pressure is unique for each gas, based on its molecular structure.
• When conducting experiments or commercial applications involving gases, knowing the critical pressure assists in designing equipment that can handle the required pressures for safety and efficiency.

The understanding of critical pressure is essential in fields like chemical engineering and the production of liquefied natural gases (LNG). It helps determine the efficacy and safety of compressing gases into a liquid form.

Boyle's Temperature

Boyle's temperature is a unique concept that examines the behavior of real gases. Unlike critical temperature and pressure, which focus on liquefaction, Boyle's temperature relates more to the behavior of gases under various conditions. At this temperature, the real gas obeys Boyle's Law over a wider range of pressures, meaning it behaves in a way that more closely resembles an ideal gas. A few points about Boyle's temperature include:

• It indicates the temperature where pressure and volume are inversely related for a real gas, as described by Boyle's Law.
• It is unique for each gas, determined by the specific intermolecular forces present.
• This temperature gives insight into deviations between real and ideal gas laws, particularly useful in understanding gas behavior in different conditions.

While not directly involved in the process of liquefaction, understanding Boyle’s temperature is crucial for scientists and engineers looking to predict gas behaviors under varying conditions, which directly impacts calculations for practical uses.