Core Concept

In chemistry, gases are often assumed to behave ideally, meaning they follow the Ideal Gas Law under all conditions. However, real gases deviate from ideal behavior, especially under certain conditions. This study guide covers the assumptions of ideal gases, the reasons for deviations, and how real gases behave differently.

Key Assumptions for Ideal Gases:

1. Gas Particles Have No Volume:

   • The particles themselves are assumed to occupy no space.

2. No Intermolecular Forces:

   • There are no attractive or repulsive forces between gas particles.

3. Elastic Collisions:

   • Collisions between gas particles are perfectly elastic, meaning there is no loss of kinetic energy.

4. Continuous, Random Motion:

   • Particles move in constant, random motion, colliding with container walls to exert pressure.

5. Average Kinetic Energy Proportional to Temperature:

   • The kinetic energy of gas particles depends only on the temperature, not on the identity of the gas.

These assumptions hold true under low pressure and high temperature, where gas particles are far apart and moving quickly.

Real Gas Behavior

Real Gases:

• Real gases deviate from ideal behavior under conditions of high pressure and low temperature.

• At high pressures, gas particles are closer together, and the assumptions of no volume and no intermolecular forces no longer hold.

Reasons for Deviations:

1. Finite Particle Volume:

   • At high pressures, the volume occupied by the gas particles themselves becomes significant, causing the actual volume to be greater than predicted by the Ideal Gas Law.

2. Intermolecular Forces:

   • At low temperatures, particles have lower kinetic energy and are more affected by intermolecular attractions (van der Waals forces), causing them to stick together temporarily and reducing the actual pressure exerted by the gas.

Conditions Affecting Real Gas Behavior

1. High Pressure:

   • Particles are pushed closer together, making their finite volume significant.

   • The actual volume of the gas is greater than the volume predicted by the Ideal Gas Law.

2. Low Temperature:

   • Particles move slower, allowing intermolecular attractions to have a greater effect.

   • This reduces the collisions with container walls, leading to lower pressure than expected by the Ideal Gas Law.

van der Waals Equation for Real Gases

The van der Waals equation adjusts the Ideal Gas Law to account for particle volume and intermolecular forces:

$\left( P + \frac{a}{V^2} \right)(V - b) = nRT$

Where:

• P = Observed pressure of the gas

• V = Observed volume of the gas

• a = Correction factor for intermolecular attractions (varies by gas)

• b = Correction factor for the finite volume of gas particles (varies by gas)

• n = Number of moles of gas

• R = Ideal gas constant

• T = Temperature in Kelvin

Explanation of Corrections:

• a: Accounts for attractions between particles. The greater the value of aaa, the stronger the intermolecular forces.

• b: Accounts for the volume occupied by the gas particles themselves.

The van der Waals equation gives a more accurate representation of real gas behavior than the Ideal Gas Law, especially at high pressures and low temperatures.

Graphical Representation: Ideal vs. Real Gas Behavior

1. PV/RT vs. P Graph:

   • For an ideal gas, PV/RT should equal 1 at all pressures (a horizontal line).

   • For real gases:

     • At high pressure: PV/R rises above 1 because of particle volume.

     • At low temperature: PV/RT falls below 1 initially due to attractive forces and then rises at very high pressures due to particle volume.

2. Compression Factor (Z):

   • The compression factor $Z = \frac{PV}{nRT}$ indicates how much a real gas deviates from ideal behavior.

   • Z = 1 for an ideal gas.

   • Z < 1 when intermolecular forces dominate (low temperatures).

   • Z > 1 when particle volume dominates (high pressures).