# Important Differences Between Ideal Gas and Real Gas

Ideal Gas

An ideal gas is a theoretical model used in physics and chemistry to describe the behavior of gases under specific conditions. It is an imaginary gas that perfectly follows the ideal gas law, which relates its pressure, volume, and temperature. According to this law, an ideal gas is characterized by several key assumptions:

• Negligible Volume:

The volume occupied by the gas molecules themselves is considered negligible compared to the volume of the container they occupy.

• Negligible Intermolecular Forces:

Ideal gases are assumed to have no intermolecular forces or interactions between particles.

• Random Motion:

The gas particles are in constant, random motion and move independently of one another.

• Elastic Collisions:

Collisions between gas particles and with the container walls are perfectly elastic, meaning there is no loss of kinetic energy.

• Continuous Energy Distribution:

The energy of gas molecules is continuously distributed among translational, rotational, and vibrational modes.

• No Molecular Volume:

The volume occupied by gas molecules is considered zero.

Ideal Gas Equation

The ideal gas equation, also known as the ideal gas law, is a fundamental principle in thermodynamics and describes the behavior of an ideal gas under various conditions. It is expressed mathematically as:

PV = nRT

Where:

• P is the pressure of the gas (in Pascals, Pa)
• V is the volume of the gas (in cubic meters, m³)
• n is the number of moles of the gas
• R is the universal gas constant (8.314 J mol−1K−1)
• T is the absolute temperature of the gas (in Kelvin, K)

Ideal Gas Limitations

• Neglects Molecular Volume:

The ideal gas law assumes that gas particles have zero volume, which is not true for real gases. At high pressures or low temperatures, the volume occupied by gas molecules becomes significant, leading to deviations from ideal behavior.

• Neglects Intermolecular Forces:

Real gases experience intermolecular forces, such as Van der Waals forces, which are ignored in the ideal gas law. These forces become significant at high pressures or low temperatures, causing deviations from ideal behavior.

• Assumes Elastic Collisions:

While real gas collisions are generally elastic, at very high pressures or low temperatures, some energy may be lost in collisions, violating this assumption.

• Assumes Continuous Energy Distribution:

The ideal gas law assumes that energy is evenly distributed among translational, rotational, and vibrational modes. At very low temperatures, not all modes may be equally accessible, leading to deviations.

• Limited Applicability at Extreme Conditions:

The ideal gas law is less accurate under extreme conditions of high pressure or low temperature, where the assumptions underlying the law may not hold.

• Not Suitable for High Pressure or Low Temperature:

At very high pressures or very low temperatures, real gases can deviate significantly from ideal behavior due to the molecular interactions and finite molecular volume.

• Doesn’t Consider Quantum Effects:

At very low temperatures, quantum effects become important, and the classical treatment of gases breaks down. The ideal gas law does not account for quantum mechanical behavior.

• Not Applicable to Condensed Phases:

The ideal gas law is only valid for gases and does not apply to liquids or solids.

Real Gas

A real gas is a physical substance composed of molecules or atoms that possess both volume and intermolecular forces. Unlike an ideal gas, which is a theoretical model, a real gas does not perfectly adhere to the ideal gas law at all conditions. Real gases deviate from ideal behavior under certain circumstances, such as at high pressures or low temperatures. These deviations arise due to the finite size of gas molecules and the presence of intermolecular forces. Real gases can also undergo phase transitions, like condensation and liquefaction, which are not accounted for in the ideal gas law. Understanding the behavior of real gases is crucial in various scientific and industrial applications, particularly in scenarios where gases approach conditions where they behave less ideally.

Real Gas Equation

The real gas equation, also known as the Van der Waals equation, is a modification of the ideal gas law that accounts for the finite size of gas molecules and the existence of intermolecular forces. It is expressed as:

Examples of Real Gases

• Water Vapor (H₂O):

Water vapor exhibits non-ideal behavior, especially at high pressures and low temperatures. It undergoes condensation to form liquid water.

• Carbon Dioxide (CO₂):

Carbon dioxide shows deviations from ideal gas behavior, particularly at high pressures. It can undergo phase transitions to form dry ice (solid CO₂).

• Ammonia (NH₃):

Ammonia behaves as a real gas, especially at high pressures or low temperatures. It can undergo liquefaction.

• Chlorine (Cl₂):

Chlorine exhibits non-ideal behavior, particularly at high pressures. It can liquefy under certain conditions.

• Methane (CH₄):

Methane deviates from ideal gas behavior, especially at high pressures. It can undergo liquefaction and form a liquid.

• Hydrogen Chloride (HCl):

Hydrogen chloride is another example of a real gas, particularly at high pressures. It can condense to form a liquid.

• Nitrogen (N₂):

Nitrogen shows deviations from ideal behavior, particularly at very low temperatures where it can be liquefied.

• Oxygen (O₂):

Oxygen is a real gas, especially at low temperatures where it can be liquefied.

• Sulfur Hexafluoride (SF₆):

SF₆ deviates from ideal behavior, especially at high pressures. It is used as an electrical insulator in high-voltage equipment.

• Argon (Ar):

Argon behaves as a real gas, particularly at low temperatures where it can be liquefied.

Important Differences Between Ideal Gas and Real Gas

 Basis of Comparison Ideal Gas Real Gas Molecular Volume Negligible (Point particles) Significant (Finite molecular size) Intermolecular Forces Absent Present Pressure-Volume PV = nRT (Always holds) PV = nRT + an²/V² (Modified by Van der Waals) Deviations None (Follows ideal gas law exactly) Deviates at high pressure, low temp Volume Changes Perfectly elastic (No volume changes) Elastic, but some volume changes possible Phase Transitions No phase transitions Can undergo condensation, liquefaction Applicability Ideal for low pressure, high temp conditions Applicable across a wider range of conditions Density Density is calculated with ideal behavior Density may differ due to molecular volume Compressibility Infinitely compressible Finite compressibility Equations of State Simple (PV = nRT) Complex (Van der Waals equation) Assumptions Point-like particles, no interactions Finite molecular size, intermolecular forces Molecular Structure Assumes no molecular size or forces Recognizes molecular size and forces Predictive Accuracy Approximate More accurate, especially at extremes Real-World Example None (Theoretical concept) Actual gases with physical properties

Important Similarities Between Ideal Gas and Real Gas

 Basis of Comparison Ideal Gas Real Gas Molecular Motion Follows kinetic theory of gases Follows kinetic theory of gases Boyle’s Law Follows Boyle’s law (P₁V₁ = P₂V₂) Follows Boyle’s law (P₁V₁ = P₂V₂) Charles’s Law Follows Charles’s law (V₁/T₁ = V₂/T₂) Follows Charles’s law (V₁/T₁ = V₂/T₂) Avogadro’s Principle Follows Avogadro’s principle Follows Avogadro’s principle Combined Gas Law Follows the combined gas law Follows the combined gas law Ideal Gas Constant R is a constant for all ideal gases R is a constant for all real gases Universal Gas Law Follows the universal gas law (PV = nRT) Follows the universal gas law (PV = nRT) Pressure-Volume P and V are inversely proportional P and V are inversely proportional Temperature-Volume V and T are directly proportional V and T are directly proportional Gas Behavior Exhibits predictable behavior Exhibits behavior within limits of real gases State Equations Follows state equations for ideal gases Follows state equations for real gases

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