Under all temperature & pressure.
No gas is ideal but they are real gases which obeys ideal gas eq. at low pressure & high temperature.

Ideal gas is characterised by following postulates:

(1) Ideal gas cannot be liquefied.

(2) There is no force of attraction b/w gas molecule.

(3) Volume of ideal gas molecule is negligible as compared to containce

For ideal gas

Compressibility factor z = 1

For real gas z1. 

z > 1 (Volume of gas is relatively more dominant)

It shows +ve deviation. This implies gas is less compressible.

z < 1 (Force of attraction of gas molecule is relatively more dominant)

It shows -ve deviation. This implies gas is more compressible.z =................................................ (i)

If gas shows ideal behaviourPv_ideal= nRT    v_ideal=Substituting in (i)

z =into account, force of attraction among molecule as nell as volume of gaseous molecule.

Derivation

:Correction for volume

: Suppose volume occupied by gas molecules is v. When molecules are moving their effective is 4 times factual volume i.e. 4v.b = 4v (excluded volume)

 corrected volume = (v - nb) for n moles

Dumb Question

: Why effective volume is 4 times of actual volume ?

Ans:

Excluded volume of 2 molecules is sphere of radius of 2R where R radius of ...Excluded volume for two molecule    

 Excluded volume for one molecule ?

Constant 'a'measures force of attraction. Greater value 'a', higher intermolecular force of attraction.

Dumb Question

: How unit of 'a' = atm L mol ?

Ans: P =

a = atm²L mol^-2Units of 'b' = L mol^-1

Different forms of Vander Waal Equation

:

(i)At very low pressure

: v is very large. Hence, correction term a/v²is negligible correction term 'b' is also negligible. Now Equation reduced to

That's why real gas behave like ideal gas at very low pressure.

(ii)At mederate pressure

:V decreases. Hence a/v²

increases & cannot neglected but b is negligible because volume is still high. 

  v = RT (for 1 mole)

(iii)At high pressure

: v is so small so b cannot be neglected. Factor a/v²is no doubt large but as P is very high, a/v²can be neglected.

(iv)At high temperature

: v is very large (at constant pressure). So, that both correction factors are negligible. (a/v²& b)

 So, at high temperature, real gases behave like ideal gas.

*Tip

: Gases tend to behave ideally at high temperature and low pressure and non ideally at low temperature and high pressure.

Illustration: Calculate pressure exerted by 110g of CO₂ in vessel of 2L at 27⁰C. Given that Vander Waal's constants are a = 3.59 L² atm mol^-2 & b = 0.0427 L mol^-1.
Ans: According to Vander Waal's Equation

n == 2.5 mol.

P =

P =

  = (33.61 - 5.61) atm

   = 28 atm

Shows ideal gas behaviour.

Mathematically defined.

= 0
= 0
(v - b) = RT (For 1 mole)
P =
Pv =