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

Real gases behave like ideal gases under high temperature and low pressure (option a).

Step 1: Understanding Ideal Gas Behavior

Ideal gas behavior assumes that gas molecules have no volume and no intermolecular interactions. This is usually true under conditions where intermolecular forces are minimized and molecular volume is negligible.

Step 2: Analyzing Conditions for High Temperature

At high temperatures, the kinetic energy of gas molecules is large compared to potential energy from intermolecular forces. This minimizes the impact of these forces, allowing the gas to behave more like an ideal gas.

Step 3: Analyzing Conditions for Low Pressure

At low pressures, gas molecules are far apart, which reduces the effect of intermolecular forces and volume occupancy by individual gas molecules. This makes real gases behave more like ideal gases.

Step 4: Combining Conditions

The combination of high temperature and low pressure reduces both molecular volume effects and intermolecular forces, making real gases behave like ideal gases.

Key Concepts

Ideal gas behavior

Ideal gas behavior is a theoretical concept where gas molecules are considered to be point particles with no volume. Additionally, they do not exert any attractive or repulsive forces on each other. This model simplifies calculations and helps to predict how gases will behave under different conditions. The Ideal Gas Law, given by the equation \( PV = nRT \), describes this concept, where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin. However, in reality, gases do not perfectly align with this model because:

• Gases have finite molecular volumes.
• Intermolecular forces do exist, especially at high pressures or low temperatures.

This is why real gases deviate from ideal gas behavior. However, under certain conditions like high temperatures and low pressures, gases can nearly achieve ideal gas behavior, as these conditions minimize the deviations from these assumptions.

High temperature effect

High temperatures play a critical role in encouraging gases to behave more like an ideal gas. At high temperatures, the molecules of a gas have significantly greater kinetic energy. When kinetic energy is high:

• The molecules move faster, diminishing the effect of intermolecular attractions or repulsions. Thus, they act more like ideal gases.
• Potential energy due to attractive forces becomes negligible compared to the kinetic energy of molecules.

As a result, gases at high temperatures tend to have minimal intermolecular interactions, making them more likely to follow the Ideal Gas Law assumptions better than at lower temperatures. This high kinetic energy overpowers all forces that might usually cause deviations from ideality.

Low pressure effect

When gas is at low pressure, it is likely to behave more like an ideal gas. Low pressure means there is a reduced number of gas molecules in a given volume. This is important because:

• With molecules spread far apart, the influence of intermolecular forces is reduced, which means such forces hardly affect the gas's behavior.
• The volume occupied by the gas molecules themselves becomes insignificant compared to the volume of the container.

Thus, with minimal force interactions and negligible molecular volume, low-pressure conditions present the ideal setting for a gas to adhere closely to the ideal gas model. Therefore, at low pressures, gases can closely follow the laws and equations applicable to ideal gases, making low pressure a key condition for approaching ideal behavior.