Problem 12 - A Complete Resource Book in Chemistry for JEE Main

Question

The compressibility factor of an ideal gas is (a) 1 (b) 2 (c) 4 (d) 0

Step-by-Step Solution

Answer

The compressibility factor of an ideal gas is 1.

Step 1: Understanding the Compressibility Factor

The compressibility factor (Z) is a measure of how much a real gas deviates from ideal gas behavior. For ideal gases, the compressibility factor is used to describe the relation, but it is usually '1' because ideal gases perfectly follow the ideal gas law without any deviation.

Step 2: Identifying the Ideal Gas Behavior

For an ideal gas, the equation is given by the ideal gas law: \[ PV = nRT \]where P is pressure, V is volume, n is number of moles, R is the gas constant, and T is temperature. Ideal gases are assumed to have no intermolecular forces and occupy no volume, so deviations from these assumptions for real gases are measured by the compressibility factor.

Step 3: Evaluating the Choice for Ideal Gas

The compressibility factor for an ideal gas is always '1', meaning there is no deviation from ideal behavior. This means, given the options, the correct choice where Z equals for an ideal gas is (a) 1.

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental principle in chemistry and physics that explains how gases behave under different conditions. It is expressed through the equation \( PV = nRT \). Here's what each symbol means:

• \( P \) stands for pressure, which is the force exerted by the gas particles against the container walls.
• \( V \) represents volume, the space available for the gas particles to move around.
• \( n \) denotes the number of moles, essentially counting the particles in the gas.
• \( R \) is the gas constant, a fixed number that makes the math work out just right.
• \( T \) is temperature, measured in Kelvin, indicating how fast the particles are moving.

The Ideal Gas Law assumes that gas particles occupy no space and have no intermolecular forces. This means they behave perfectly according to these ideal conditions.
Under these assumptions, the compressibility factor, which measures how real gases deviate from ideal gases, is 1 for an ideal gas. Real gases often deviate slightly from this, except at high temperatures and low pressures where they behave more ideally.

Real Gas Behavior

Real gases often don't follow the Ideal Gas Law perfectly. This is because, unlike ideal gases, real gases have particles that interact with each other and have their own volume. These interactions and small volumes cause real gases to behave differently under various conditions.
One key measure of this deviation is the compressibility factor or \( Z \). For a real gas,

• If \( Z > 1 \), it means the particles are moving away from each other due to high pressures or low temperatures, resulting in a greater-than-ideal volume.
• If \( Z < 1 \), it indicates that the particles are more attracted to each other, causing them to pack closer together than in an ideal gas.

In general, real gases behave more like ideal gases at high temperatures and low pressures. These conditions reduce the impact of intermolecular forces and the volume of gas particles, making them behave more ideally.

Intermolecular Forces

Intermolecular forces are the attractive forces between molecules in a gas. These forces can greatly influence the behavior of gases, especially when they start to deviate from ideal behavior.
There are several types of intermolecular forces at play:

• **Van der Waals forces**, which include dipole-dipole interactions and London dispersion forces. These are weak forces that occur between neutral molecules.
• **Dipole-dipole forces** occur between molecules that have permanent dipole moments.
• **Hydrogen bonds**, which are strong dipole-dipole attractions that occur under specific conditions, such as with molecules containing H bonded to O, N, or F.

In gases, stronger intermolecular forces can cause the gas particles to be more attracted to each other. This results in deviations from ideal gas behavior, observable through the compressibility factor. Real gases with significant intermolecular forces will have compressibility factors different from 1, showing deviations from ideal conditions.