Question

Derive ideal gas equation and explain the terms in it

Answer 1

the ideal gas equation can be proved using the gas laws

BOYLE'S LAW states that the volume of a gas is inversely proportional to its pressure.
V ∝ 1/P

CHARLES'S LAW states that the volume of a gas is directly proportional to its Kelvin temperature.
V ∝ T

AVAGADRO'S LAW states the volume of a gas is directly proportional to the number of moles.
V ∝ n

If we combine these laws, we get
V ∝ nT/P

We covert the proportionality to an equality
V = RnT/P
here

R is known asuniversal gas constant
and we get

V = nRT/P

This can be rearranged to give the IDEAL GAS LAW

PV = nRT

Answer 2

$\huge\textbf{Ideal Gas Equation :}$

A gas that follows Boyles law, Charles law, Avogadro law is called an Ideal gas law. 

At constant T and n, 

V is inversally proportional to P [Boyles law] ...(1)

At constant P and n,

V is directly proportional to T [Charles law] ...(2)

At constant P and T,

V is directly proportional to n [Avogadro law] ...(3)

By combination of equation (1), (2) and (3) we get;

$V$ $\alpha$ $\frac{nR}{T}$

$V\:=\:R$ $\frac{nT}{P}$

$\textbf{PV = nRT}$

(Ideal Gas Equation)

In this;

P = Pressure of gas

V = Volume of gas