Real Gases vs Ideal Gases

In the study of gases and gas laws, it is important to distinguish between real gases and ideal gases. The concept of ideal gases is derived from some simplifying assumptions that allow us to predict and understand gas behavior using mathematical models. On the other hand, real gases deviate from these models in certain situations. Let us look at these concepts in detail.

Understanding ideal gases

An ideal gas is a theoretical gas composed of many randomly moving point particles that interact only through elastic collisions. The concept of an ideal gas helps simplify the study of gases by assuming the following:

• Gas particles are in constant, random motion.
• There is no force of attraction or repulsion between the particles.
• The volume of the gas particles is negligible compared to the volume of the container.
• Collisions between gas particles and between particles and the walls of the container are perfectly elastic, that is, no energy is lost in the collision.

The behavior of an ideal gas can be completely described by the ideal gas law:

PV = nRT

Where:

• P = pressure of the gas
• V = volume of the gas
• n = amount of substance (in moles)
• R = ideal gas constant (about 8.314 J/(mol K))
• T = temperature of the gas (in Kelvin)

Characteristics of ideal gas behaviour

An ideal gas behaves predictably and uniformly under all conditions of temperature and pressure. When plotted on a PV diagram, the relationship between pressure and volume is linear, assuming a constant temperature. This simplicity allows us to predict the behavior of gases with a high degree of accuracy under many situations. However, it is important to remember that real gases only approximate ideal gas behavior under certain conditions.

Example: Calculating volume from the ideal gas law

Suppose you have 2 moles of an ideal gas at a temperature of 273 Kelvin (0 degrees Celsius) and a pressure of 101.3 kPa. You can calculate the volume of the gas using the ideal gas law formula:

PV = nRT

Substituting the values:

V = (nRT)/P = (2 moles × 8.314 J/(mol·K) × 273 K) / 101.3 kPa = 44.8 liters

Assuming ideal gas behaviour, the calculated volume for the given conditions is 44.8 litres.

Understanding real gases

Unlike ideal gases, real gases have physical contact between particles and occupy space. These deviations become significant under conditions of high pressure or low temperature, where gas molecules are close to each other. Real gases deviate from ideal gas behavior because:

• Gas molecules occupy space and they also have volume.
• There are attractive or repulsive forces between particles, especially when they are close to each other.

Characteristics of real gas behaviour

Real gases do not always follow the ideal gas law exactly. They can show deviations that are especially noticeable when gases are compressed or close to condensing. These deviations are often corrected for in calculations using the van der Waals equation, which accounts for molecular volume and attractive forces:

(P + a(n/V)^2) (V - nb) = nRT

where a and b are specific constants for each gas, (n/V) is the molar concentration of the gas particles, and (P + a(n/V)^2) accounts for intermolecular forces.

Example: Calculating pressure with the van der Waals equation

Suppose you have 1 mole of carbon dioxide (CO₂) at 300 Kelvin in a 10-liter container. The constants for CO₂ are a = 3.592 L²·atm/mol² and b = 0.0427 L/mol. Calculate the pressure using the van der Waals equation:

(P + a(n/V)^2) (V - nb) = nRT

Substitute the values:

(P + (3.592 atm L²/mol² × (1 mol / 10 L)²) (10 L - 0.0427 L/mol × 1 mol) = 1 mol × 0.0821 L atm/(mol K) × 300 K

On simplifying the equation:

(P + 0.03592 atm) (9.9573 L) = 24.63 L atm

Finally, solve for P:

P = (24.63 L atm / 9.9573 L) - 0.03592 atm = 2.439 atm

The calculated pressure for CO₂ under these actual conditions is 2.439 atm.

Visual explanations

To visually understand the differences, consider two identical containers filled with gases at the same temperature and volume conditions, one containing an ideal gas and the other containing a real gas:

In these examples:

• The blue circles in the ideal gas container represent gas particles moving without interacting with each other, fully obeying the assumptions of the ideal gas law.
• The red circles in the real gas container represent gas particles that have attractive forces between them, represented by connecting lines. This shows a more realistic interaction between particles, which leads to deviations from the ideal gas model.

Conditions affecting the behaviour of a gas

The deviation between real and ideal gases is more pronounced in certain situations:

• High Pressure: Under high pressure, gas molecules come closer to each other. The volume occupied by gas molecules becomes significant, and intermolecular forces are more pronounced.
• Low Temperatures: At low temperatures, gas molecules move slower, which increases the effect of attractive forces as they come closer to each other.

Example scenario: Oxygen gas in a scuba tank

Imagine a scuba diver's tank filled with oxygen gas at high pressure and low temperature under the sea. Under these conditions, the gas in the tank will behave like a real gas rather than an ideal gas. This understanding is important for engineers and manufacturers who design equipment that must operate safely under varying environmental conditions.

The main differences in a nutshell

Let us summarize the main differences between real gases and ideal gases:

Aspect	Ideal gas	Real gas
Particle volume	Insignificant	Important at high pressure
Intermolecular forces	Ignored	Considerable and important at low temperatures
Applicable terms	High temperature, low pressure	Variable; requires adjustment for high pressure and low temperatures

Conclusion

Understanding the difference between real gases and ideal gases is important for accurately predicting the behavior of gases in practical applications. While the ideal gas law provides a useful framework for understanding gas behavior in many situations, it is the acknowledgement of real gas behavior through equations such as van der Waals that allows for more accurate calculations in engineering, chemistry, and environmental science.

In conclusion, while the concept of an ideal gas provides simplicity and ease of understanding, real gases exhibit complex interactions that occur at the microscopic level. By recognizing these differences and knowing how to account for them in calculations, we gain a deeper understanding of how gases behave in the real world.

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