Derivation of Ideal gas equation

Introduction

What is an ideal gas? 

There are millions of gases that collide and interact with each other. It is hard to explain natural gas’s behavior. Scientists created the concept of an ideal gas. Ideal gas helps us to predict the behaviour of a gas. 

The ideal gas equation combines four variables: volume, pressure, temperature, and several moles in a gas. In the Ideal gas equation, we’ll combine Boyle’s Law, Charles’s Law, and Avogadro’s Law.  

The ideal gases follow some rules which are:- 

1. Ideal gases molecules do not attract each other or repel each other. The only collision will be an elastic collision with the wall of the container.  
2. Ideal gases do not take any volume.

Molar form of an ideal gas. 

PV=nRT is considered an ideal gas equation to teach the behaviour of a gas. It’s also called the General equation of gas or constant gases.  

         PV=nRT 

Where  ∝ P is the pressure of the that is the volume of the gas 

T is the temperature of the gas, R is the gas constant, n is the number of moles of the gas  

Ideal Gas Equation Derivation 

Boyle’s Law says that the volume of a system is inversely proportional to the system’s pressure in which the number of mole and temperature remains constant. Boyle studied changes in the volume of gas by varying the pressure of a certain amount of gas at a constant temperature. He trapped some air in the tube and kept adding more mercury to the tube, which eventually increased the gas pressure and reduced the amount of gas. 

 V ∝ 1/p    (n and t are constant……….equation1)

Charles studied the effect of temperature on gases volume at a constant pressure.  

Charle’s Law says that the system’s volume is directly proportional to the temperature.  

 V ∝ T       (n and p are constant……….equation2)

 Avogadro formulated a formula for calculating molecules existing at constant pressure and temperature.  

Avogadro’s Law says that the system’s volume is directly proportional to the temperature. 

 V ∝ n        (P and T are constant………..equation3)

 By combining all three laws, we get the ideal gas equation.  

 V ∝ n T/P

 V = R nT/P

 PV=nRT

R:Gas constant

 This equation is ideal for only ideal gases. An ideal gas is a hypothetical situation where there is no intermolecular force. 

Value of Gas constant R 

In the equation PV=nRT, P is indicated in the atmosphere (arm), T in Kelvin(K) and n is the number of moles.            

PV is a unit of energy together, so the unit of R will be expressed in J/K.mol       R= 8.314  

With the help of this equation, we can find any variable if the other four are given. 

Limitations of an ideal gas. 

1. An ideal gas is a hypothetical situation. In reality, it doesn’t exist. But it is a helpful way to understand the behaviour of a certain gas. 
2. Gases at the given condition such as low density, low pressure and high-temperature act as an ideal gas. 
3. Ideal gas law doesn’t apply where the density is low, the temperature is high, and pressure is high because, in this situation, intermolecular forces matter. 
4. It doesn’t apply to dense gases and gases in which intermolecular forces are strong. 

   Conclusion

The ideal gas equation combines four variables and is derived from 3 laws: Boyle’s Law, Charle’s Law, and Avogadro’s Law. An ideal gas is a hypothetical situation. It is helped to understand the behaviour of the gas. Ideal gas doesn’t work in low-temperature, high density and high pressures. 

Ideal gas doesn’t apply to heavy gases.