Ideal gas: A gas that follows Boyle's law, Charles' law and Avogadro law strictly is called an ideal gas. It is assumed that intermolecular forces are not present between the molecules of an ideal gas.
Real gases: Gases which deviate from ideal gas behaviour are known as real gases. NH₃ is expected to show more deviation. Since NH₃ is polar in nature and it can be liquefied easily.

The temperature below which a gas obeys Joule - Thomson effect is called inversion temperature (T_i). This value is given using van der waals constants a and b.,
\(T_i=\frac{2a}{Rb}\)

When diffusing gases are at different pressures (P_A,P_B),
\(\frac{r_A}{r_B}=\frac{P_A}{P_B}\sqrt{\frac{M_B}{M_A}}\)
Where r_A and r_B are the rates of diffusion of A and B and the M_A and M_B are their respective molecular masses.

Charles law: According to Charles law ,gases expand on heating. Since mass of gas is unchanged, increase in volume decreases density. Thus hot air is less dense than cold air. This causes hot air balloon to rise displacing the cooler air of the atmosphere.

For every 10 m of depth, a diver experiences an additional 1 atm of pressure due to the weight of water surrounding him so the most important rule in diving is never hold breath. Divers must ascend slowly and breathe continuously allowing the regulator to bring the air pressure in their lungs to 1atm by the time they reach the surface.

Mass of oxygen = 4.25 g
No. of moles of oxygen = \(\frac { 4.25 }{ 32 } =0.1328\) moles
Pressure P = 1.21 atm, volume V = 2.15 dm³
According to ideal gas equation
PV = nRT
\(T=\frac { PV }{ nR } =\frac { 1.21\times 2.15 }{ 0.1328\times 0.0821 } \)
\(\because\) R is the gas constant
R = 0.0821 L atm K mol^-1
\(=\frac { 2.6015 }{ 0.0109 } =238\quad K\)

Pressure of a gas at ground level P₁ = 0.965 atm
Volume of the gas at ground level V₁ = 10.0 m³
Volume of the gas at an altitude of 5300m V₂  = 20.0 m³
Pressure of the gas at an altitude of 5300 P₂ = ?
According to Boyle's law = T₁ V₁ = P₂ V₂
0.0965 \(\times\) 10 = P₂ \(\times\) 20.0
\({ P }_{ 2 }=\frac { 0.0965\times 10.0 }{ 20.0 } \)
= 0.04825 atm
Pressure of the gas at an altitude of 5300m
P₂  = 0.04825 atm

a = 3.67 atm lit² mol^-2
b = 0.0408 lit mol^-1
R = 0.0821 atm lit K^-1 mol^-1
(i) \({ T }_{ c }=\frac { 8a }{ 27Rb } \)
\(=\frac { 8\times 3.67 }{ 27\times 0.082\times 0.0408 } =324.7\quad K\)
T_c = 324.7 K
(ii) \({ P }_{ c }=\frac { a }{ 27{ b }^{ 2 } } \)
\(=\frac { 3.67 }{ 27\times { (0.0408) }^{ 2 } } =81.6\)
P_c = 81.6 atm.

n = 5; V = 2 Iitre;T= 27 + 273 = 300 K
\(P=\frac { nRT }{ V } [\because PV=nRT]\)
\(P=\frac { 5\times 8.314\times 300 }{ 2 } =62.355\quad bar\)
\(\therefore\) The pressure of CI₂ gas will be 62.355 bar.

(i) Over a range of low pressures, the real gases can behave ideally at a particular temperature called as Boyle temperature or Boyle point.
(ii) The Boyle point varies with the nature of the gas.
(iii) Above the Boyle point, the compression point Z > 1 for real gases i.e. real gases show positive deviation.
(iv) Below the Boyle point, the real gases first show a decrease for Z, reaches a minimum and then increase with increase in pressure. So, it is clear that at low pressure and at high temperature, the real gases behave as ideal gases.
(v) Hence, \(Z=\frac{PV_{real}}{nRT}\)
\(PV_{ideal}=\frac{nRT}{P}\)
So, \(Z=\frac{V_{real}}{V_{ideal}}\)

Avogadro's hypothesis states that equal volumes of all gases under the same conditions of temperature and pressure contain equal number of molecules.
\(V\propto n\)
\(\frac{V_1}{n_1}=\frac{V_2}{n_2}\) = Constant
Where V₁ and n₁ are the volume and number of moles of a gas and V₂ and n₂ are the different set of values of volume and number of moles of the same gas.
A better example to illustrate Avogadro's hypothesis is to observe the effect of pumping more gas into a balloon. When more gas molecules (particularly CO₂) are passed, the volume of the balloon increases. The pressure and temperature stay constant as the balloon inflates, so the increase in volume is due to the increase in the quantity of gas inside the balloon.

P_Ne = X_Ne P_Total
\(X_{Ne}=\frac{n_{Ne}}{n_{Ne}+n_{Ar}+n_{Xe}}\)
\(=\frac{4.76}{4.76+0.74+2.5}=0.595\)
\(X_{Ar}=\frac{n_{Ar}}{n_{Ne}+n_{Ar}+n_{Xe}}\)
 \(=\frac{0.74}{4.76+0.74+2.5}=0.0093\)
\(X_{Xe}=\frac{n_{Xe}}{n_{Ne}+n_{Ar}+n_{Xe}}\)
\(=\frac{2.5}{4.76+0.74+2.5}=0.312\)
P_Ne = X_Ne P_Total = 0.595 x 2
= 1.19 atm.
P_Ar = X_Ar P_Total = 0.093 x 2
= 0.186 atm.
P_Xe = X_Xe P_Total = 0.312 x 2
= 0.624 atm.

\(Z=\frac { { PV }_{ real } }{ nRT } \) ......(1)
\({ V }_{ ideal }=\frac { nRT }{ P } \)  ......(2)
Substituting (2) in (1)
\(Z=\frac { { V }_{ real } }{ { V }_{ ideal } } \)
Where V_real is the molar volume of the real gas and ideal is the molar volume of it when it behaves ideal. i.e. compressibility is the ratio of real volume of the. gas to ideal volume of any gas.

(i) Boyle's point is the temperature at which, real gases behave ideally over a range of low pressures.
(ii) The Boyle point varies with the nature of the gas.
(iii) Above the Boyle point, Z > 1 for real gases. i.e., they show positive deviation.
(iv) Below the Boyle point, the real gases first show a decrease for Z, reaches a minimum and then increase with increase in pressure.