Ideal gas equation

Introduction

An ideal gas is an imaginary entity that does not exist in reality. Almost all gasses are real, and they only approach perfect gas behavior under particular circumstances. Here The concept of an ideal gas, the ideal gas law, and the ideal gas equation are explained briefly. It also describes the limitations of ideal gas law.

Ideal gas law is a well-defined explanation of the behavior of several gasses under various situations in thermodynamics. The Ideal gas equation is a mathematical formula that combines empirical laws such as Charle’s law, Boyle’s law, and Avogadro’s law.

What is Ideal Gas?

An ideal gas is a hypothetical gas developed to simplify calculations of a gas molecule’s temperature and pressure. The concept of an ideal gas is that it is made up of molecules that can travel in all directions at random. The collision between the particles is thought to be fully elastic, meaning that there is no loss of kinetic energy of the particles due to the collision.

In actuality, Ideal gas does not exist. It is a theoretical concept. When the density is low, the gas molecules are too far apart to interact with each other, that is why all gasses are real and tend to behave like ideal gasses . An ideal gas should follow a few rules which are-

• The molecules of an ideal gas neither attract nor repel each other.
• Elastic collisions between perfect gas molecules cause them to interact.
• These molecules have no volume on their own.
• The molecules in an ideal gas are moving point particles with no volume of their own.

 As a result, the ideal gas notion helps us in studying real gases.The ideal gas notion is advantageous because it adheres to the ideal gas law. In this section, we will look at the Ideal Gas Law. 

The Ideal Gas Law/Equation

The purpose of creating Ideal gas law was to show the relationship between pressure, volume, moles of gas, and temperature. It is a hypothetical or speculative equation for an ideal gas. Pressure and volume have an inverse relationship; however, the temperature has a direct relationship. The equation for the Ideal Gas Law is:

P × V = n × R × T

Where,

‘P’ denotes the ideal gas pressure. ‘V’ denotes the volume of the ideal gas. ‘n’ represents the quantity of ideal gas measured in moles. ‘R’ is the proportionality constant or the gas constant and ‘T’ stands for the ideal gas temperature.

Derivation of Ideal Gas Equation

The Ideal gas law is synthesized with the help of three basic gas laws, i.e., Avogadro’s law, Boyle’s law, and Charles’s law.

 The ideal gas law is now derived:

1. i) Avogadro’s law: This law indicates that the volume of a gas is proportional to the number of moles. 

V∝n—————(1)

1. ii) Boyle’s law indicates that a gas’s pressure is inversely proportional to its volume.

 V∝1/P—————(2)

 iii) Charles’ law says that the volume of a gas is proportional to its Kelvin temperature.

 V∝T—————–(3)

 When we combine all three equations for Ideal gas law, we obtain

 V∝n×T/P

 We apply the universal gas constant R to convert proportionality to equality. We get,

 V=n×R×T/P

 As a result, the equation for the Ideal gas equation  is stated as

 P x V = n x R x T

Units of Ideal Gas Equation

The Ideal gas equation has four parameters and one proportionality constant. These quantities are measured in the following units:

Terms Symbol Units

Pressure P Pascal or N/mol

Volume V m3

Amount of substances/number of moles n Mole

Ideal gas constant R =8.314JK–1mol–1

Temperature T K or ∘C

 Limitations of Ideal Gas

Although the ideal gas equation helps solve problems numerically, it has numerous limitations. These are-

• The ideal gas model fails at lower temperatures or greater pressures when intermolecular forces and molecular size become important. 
• It also fails for heavy gasses, such as many refrigerants and gasses with high intermolecular forces, especially water vapor.

For example-

• Assume you’re condensing an ideal gas. Because ideal gas particles have no volume, the gas should be condensed to a volume of zero. Let’s face it: Real gas particles occupy space. Gas will be condensed into a liquid with volume. Because the material is no longer a gas, the gas law no longer applies! 
• The same thing happened. We suppose that the particles of gas are not attracted to one another. Let’s face it: Genuine gas particles are attracted to one another. As the kinetic energy of gas particles declines, they finally travel slowly enough that their attractive forces induce them to condense. Because the material is no longer a gas, the gas law no longer applies!

Conclusion

The equation characterizing the states of hypothetical gasses stated mathematically by combinations of empirical and physical constants is known as the Ideal Gas Equation. It’s also known as the general gas equation. It is defined as follows:

“The ideal gas law is the equation of state for a fictitious ideal gas.” Although it has significant drawbacks, it provides a decent approximation of the behavior of various gasses under many situations.”