Problem 11 - A Complete Resource Book in Chemistry for JEE Main

Question

Van der Waals real gas, act as an ideal gas, at which condition? (a) high temperature, low pressure (b) low temperature, high pressure (c) high temperature, high pressure (d) low temperature, low pressure

Step-by-Step Solution

Answer

The correct condition is (a) high temperature, low pressure.

Step 1: Understanding Ideal Gas Conditions

An ideal gas is defined by its particles having negligible volume and no interactions. Real gases best approximate ideal gas behavior when the particles are far apart and moving quickly.

Step 2: Analyzing High Temperature

At a high temperature, particles in a gas gain kinetic energy and move more rapidly. This rapid motion minimizes the interactions (or attractive forces) between gas particles.

Step 3: Analyzing Low Pressure

At low pressure, the volume of the gas increases as there is less force compressing the gas particles together. This makes the individual volumes of the gas particles negligible relative to the total volume.

Step 4: Conclusion

Combining these analyses, when a gas is at high temperature, the kinetic energy is high, and at low pressure, there is minimal compression. Therefore, under these conditions, the gas behaves most like an ideal gas as particle interactions and sizes are negligible.

Key Concepts

Ideal Gas Behavior

Ideal gas behavior is a specific model used in chemistry and physics to describe how gases behave under certain conditions. In this model, gases are assumed to have particles that:

• Have negligible volume.
• Exert no forces on each other, meaning they do not attract or repel one another.
• Move in random, straight paths and undergo perfectly elastic collisions.

Under these simplified conditions, gases follow the Ideal Gas Law, which is expressed as \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is temperature.

However, real gases often deviate from ideal behavior, particularly at low temperatures and high pressures. The Van der Waals equation helps account for these deviations by considering the volume of gas particles and the interactions between them. Despite these complexities, conditions like high temperatures and low pressures can make real gases behave very closely to this ideal model.

High Temperature Conditions

High temperature conditions play a crucial role in bringing real gases closer to ideal gas behavior. With an increase in temperature:

• Gas particles gain more kinetic energy.
• The speed of particle movement increases, reducing the impact of any intermolecular forces.

This high-speed movement means particles collide with each other less frequently and at greater impact, mimicking the conditions described in the ideal gas law. The energy provided by heat is sufficient to overcome any weak attractive forces present among particles of a real gas. In essence, at high temperatures, the assumptions about negligible interactions in ideal gases becomes more valid. Consequently, real gases behave more similarly to ideal gases, because increased kinetic energy allows particles to act independently.

Low Pressure Effects

Low pressure conditions also help real gases behave more like ideal gases. Here's why:

• At low pressures, gases occupy larger volumes.
• This decreases the density of gas particles because they are spread out over a larger area.
• When particles are further apart, the actual volume each particle occupies becomes negligible, aligning with the ideal gas assumption of zero volume particles.

The greater distance between particles at low pressure significantly reduces the likelihood of intermolecular attractions. This condition helps to minimize interactions between particles, making real gases easier to model as ideal gases. The Van der Waals equation modifies typical gas laws to account for molecular size and interactions, but under low pressure conditions, these modifications become less necessary, as gases naturally exhibit more ideal behavior.