These gases which obey the Boyle’s law, Charles’s law or general gas equation are said to be ideal. In order to check the ideality of a gas, we can plot a graph between “n = = Z”, and thepressure of the gas for one mole of gas. In the case of ideal gas, a straight line is expected parallel to the pressure axis showing that for one mole of a gas the compressibility factor (Z) should be one.

Anyhow, it has been observed that the most common gases like H_{2}, N_{2}, He, CO_{2} etc., do not follow the straight line. It means that the product of P and V docs not remain constant, at constant temperature.

The graphs of the gases at 17C, show more deviations from ideal behavior than at 100C. Moreover, the extent of deviation of these gases are more prominent at high pressures. Wedraw the important conclusion from the above graphs.

(i) The gases are comparatively ideal at high temperature and low pressures.

(ii) The gases become non-ideal at low temperature and high pressures.

**Causes for Deviation from Ideality**

Kinetic theory is the foundation stone of all the gas laws and the general gas equation. There are two faulty assumptions in the kinetic theory of gases.

Let us recall these faulty assumptions and then try to find the remedy for them.

(i) Actual volume of gas molecules is negligible as compared to the volume of the vessel.

(ii) There are no forces of attractions among the molecules of gases.

Both these postulates arc correct, at low pressures and high temperatures and these postulates become wrong at low temperatures and high pressures.

Actually, low temperature and high pressure become responsible for creation of forces of attractions and moreover, actual volume does not remain negligible. It is necessary to account for the actual volume and mutual attractions of molecules. This job was done by Van der Waal.

**Van der Waal’s Equation**

Van der Waal modified the general gas equation and performed the corrections i.e., volume correction and pressure correction.

**Volume Correction**

Van der Waal thought that some of the volume of the vessel is occupied by the molecules the gas and that volume is not available for the free movement of the molecules, Actually, we need the free volume of the gas and that is obtained when we subtract the volume of molecules from the volume of the vessel.

V_{free} = V_{vessel}– V_{molecule}

Let ‘V’_{free}is ‘V’_{molecule}is ‘b’for one mole of a real gas.

So, V = V_{vessel}– b (1)

This ‘b’ is called effective volume of gas molecules. Keep it in mind that ‘b’ is not the actual volume of gas molecules, but is roughly equal to 4 times their molar volumes. If we have one mole of a gas, then

b = 4V_{m}

V_{m}= actual volume of gas molecules for one mole of the gas.

**Pressure Correction**

The pressure which is exerted on the walls of the vessel is due to collisions. Since thereare forces of attraction, so the molecules cannot hit the walls of the vessel with that much force, with which they should have been in the absence of attractive forces.

It means that the pressure being observed on the walls of the vessel is a little bit less than the ideal pressure.

P_{observed} = P_{ideal}– P_{lessened}

The pressure which is being lessened is denoted by P’

Let us say that P_{observed} = P and P_{lessened}is denoted by P’

P = P_{i}– P

The value of P’ given by Van der Waal is.

P’ =

In order to estimate the value of P’ which is lessened pressure, we proceed as follows. Suppose we have two types of molecules A and B. Let the concentrations of A and B type molecules are C_{A} and C_{B}. The force of attraction between A and B is proportional to C_{A} and C_{B}.

So,

P’ C_{A}C_{B}

Now suppose that “n” is the number of moles of A and B separately. Hencenumber of moles dm^{-3}of A and B separately:”V” is the volume of the vessel containing the gas

So,

P’ .

P’

P’ =

Where a = constant of proportionality

If the number of moles of gas is unity, then n = 1

P’ =

Pressure of the ideal gas P_{i}= P + P’

So, P_{i}= P’ = (2)

‘a’ is the co-efficient of attraction. In other words, it is attraction per unit volume and is a constant for a particular real gas.

Introducing these corrections, the general gas equation is modified.

(P + ) (V – b) = R (3)

For ‘n’ moles of a gas,

(P + ) (V – nb) = nRT (4)

) (v nb)

– nRT

‘a’ and ‘b’ are called Van der Waal’s constants.