What are ideal gases? In what way real gases differ from ideal gases.

1. Gas Laws:

(i) Boyle’s law: Temperature remaining constant, volume of a given mass of a gas is inversely proportional to its pressure, i.e., $\mathrm{V} \propto 1/\mathrm{P}$ at constant T or PV = constant, i.e., ${\mathrm{P}}_{\mathrm{1}}{\mathrm{V}}_{\mathrm{1}}= {\mathrm{P}}_{\mathrm{2}}{\mathrm{V}}_{\mathrm{2}}$.

(ii) Charles law: Pressure remaining constant, volume of a fixed mass of a gas is directly proportional to its absolute temperature.

$\frac{{\mathrm{V}}_{\mathrm{1}}}{{\mathrm{T}}_{\mathrm{1}}}=\frac{{\mathrm{V}}_{\mathrm{2}}}{{\mathrm{T}}_{\mathrm{2}}}$

(iii) Gay Lussac’s law: At constant volume, pressure of a fixed amount of a gas varies directly with the temperature.

$\frac{{\mathrm{P}}_{\mathrm{1}}}{{\mathrm{T}}_{\mathrm{1}}}=\frac{{\mathrm{P}}_{\mathrm{2}}}{{\mathrm{T}}_{\mathrm{2}}}$

(iv) Avogadro’s law: Under similar conditions of temperature and pressure, equal volumes of all gases contain equal number of molecules. Avogadro’s number $(6·022 \times {10}^{23})$.

2. Ideal gas equation:

(i) It represents simultaneous effect of temperature and pressure on the volume of a gas.

(ii) The equation is $\frac{{\mathrm{P}}_1{\mathrm{V}}_1}{{\mathrm{T}}_1}=\frac{{\mathrm{P}}_2{\mathrm{V}}_2}{{\mathrm{T}}_2} \mathrm{o}\mathrm{r} \frac{\mathrm{P}\mathrm{V}}{\mathrm{T}}=$ constant $= \mathrm{R}$, gas constant. Thus, $\mathrm{PV} = \mathrm{RT}$ for $1$ mole of the gas or $\mathrm{PV} = \mathrm{nRT}$ for n moles of the gas.

3. Dalton’s law of partial pressures:

If two or more gases which do not react chemically with each other are enclosed in a vessel, then total pressure exerted by the gaseous mixture is the sum of their partial pressures, i.e., $\mathrm{P} = {\mathrm{p}}_1 + {\mathrm{p}}_2 + \dots \dots$

4. Graham’s law of diffusion/effusion:

Under similar conditions of temperature and pressure, rates of diffusion/effusion of different gases are inversely proportional to the square root of their densities, i.e., r1r2=d2d1=M2M1

5. Molecular speeds:

(i) Root mean square speed: It is the square root of the mean of the squares of the speeds of different molecules.

(ii) Average speed: It is the arithmetic mean of the speeds of different molecules.

(iii) Most probable speed: It is the speed possessed by maximum number of molecules of the gas.

6. Behaviour of real gases:

(i) A gas which obeys ideal gas equation under all conditions of temperature and pressure is called an ideal gas. But, the concept of ideal gas is only hypothetical. The gases obey gas laws only if pressure is low or temperature is high. Such gases are called real gases.

(ii) Compressibility factor (Z): The extent of deviation of a real gas from ideal behaviour is expressed in terms of compressibility factor (Z).

$\mathrm{Z}=\frac{\mathrm{PV}}{\mathrm{nRT}}.$

(iii) The temperature at which a real gas behaves like an ideal gas over an appreciable pressure range is called Boyle temperature.

7. Van der Waals equation:

Equation of state for real gases (van der Waals equation): Applying correction to pressure and volume, equation obtained is

$\left(\mathrm{P}+\frac{\mathrm{a}}{{\mathrm{V}}^2}\right)\left(\mathrm{V}-\mathrm{b}\right)=\mathrm{RT}\mathrm{ }\mathrm{for}\mathrm{ }1\mathrm{ }\mathrm{mole}\mathrm{ }\mathrm{or}\left(\mathrm{P}+\frac{{\mathrm{an}}^2}{{\mathrm{V}}^2}\right)\left(\mathrm{V}-\mathrm{nb}\right)=\mathrm{n}\mathrm{ }\mathrm{RT}\mathrm{ }\mathrm{for}\mathrm{ }\mathrm{n}\mathrm{ }\mathrm{moles}$

where ‘a’ and ‘b’ are called van der Waals constants.

8. Liquefaction of gases:

(i) A gas can be liquefied by cooling the gas or applying pressure on the gas or the combined effect of both.

(ii) However, for every gas, there is a particular temperature above which a gas cannot be liquefied howsoever high pressure we may apply on the gas. This temperature is called critical temperature $\left({\mathrm{T}}_{\mathrm{c}}\right)$. The corresponding pressure and volume are called critical pressure $\left({\mathrm{P}}_{\mathrm{c}}\right)$ and critical volume $\left({\mathrm{V}}_{\mathrm{c}}\right)$.