Notes on Ideal and Real Gases, Deviation, and Applications

Ideal Gas

• Definition: An ideal gas is a hypothetical gas that perfectly follows all gas laws under all conditions.

• Characteristics:

  • Composed of tiny particles that have negligible size and mass compared to the distances between them.

  • Collisions between ideal gas particles are perfectly elastic, meaning no energy is lost in the collision.

  • There are no attractive forces between ideal gas particles, allowing them to move freely.

  • Ideal gases obey the ideal gas law: $PV = nRT$ directly.

  • When the value of $nRT/PV$ equals 1 for a gas, it is considered an ideal gas.

Real Gases

• Real Gas Behavior:

  • Real gases consist of particles with size and mass.

  • Under high pressure and low temperature, they behave more like real gases due to increased inter-particle forces.

  • Ideal gas equations can only approximate the behavior of real gases under certain conditions (low pressure, high temperature).

Deviation from Ideal Gas Behavior

• Real Gases under Changing Conditions:

  • At high pressures, real gas behavior deviates due to the volume occupied by particles and the effects of intermolecular forces.

  • At low temperatures, intermolecular forces become significant, leading to a decrease in the kinetic energy and causing clustering of gas particles.

Deviations due to Intermolecular Forces

• Real gases exhibit deviations from ideal behavior because:

  1. Attractive Forces: Unlike ideal gases, real gases have intermolecular forces (like Van der Waals forces), leading to lower pressure measures than expected.

  2. Particle Volume: The actual volume occupied by gas particles leads to noticeable deviations in property predictions under high pressure conditions.

Van der Waals Equation

• Developed by Johannes Diderik van der Waals to account for real gas behavior, taking into account the volume of particles (b) and the attractive forces between them (a).

• The equation is: $\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT$ Where:

  • $P$ = pressure,

  • $V$ = volume,

  • $n$ = moles of gas,

  • $R$ = gas constant,

  • $a$ and $b$ are the Van der Waals constants specific to each gas.

Liquefaction of Gases

• Liquefaction involves converting a gas to liquid by applying high pressure and low temperature, where the intermolecular forces are sufficient to hold particles together.

• This typically occurs with:

  • Low temperatures leading to reduced kinetic energy of particles.

  • High pressures bringing particles closer, enhancing the intermolecular attractions.

Critical Temperature and Pressure

• Critical Temperature (Tc): The highest temperature at which a substance can exist as a liquid regardless of the pressure applied.

• Critical Pressure (Pc): The minimum pressure needed to liquify a gas at its critical temperature.

• If additional pressure is applied above the critical pressure, the gas can be liquified, provided it is below the critical temperature.

Applications of Liquefied Gases

• Used extensively in industry for various processes, including:

  1. Efficient cooling and purifying gases in refrigeration.

  2. Extraction of elements from liquefied air, such as oxygen and nitrogen.

  3. For chemical reactions requiring reactive gases in liquid form.

Real Life Applications of Gas Laws

• Various gas laws are utilized practically:

  • Aerosol sprays: Utilize Boyle's Law, where gas expands upon release.

  • Diving: Understanding gas compression and expansion as divers ascend or descend to avoid health issues.

  • Airbags: Use nitrogen from chemical reactions to inflate rapidly and protect vehicle occupants upon collision.