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6. Deviations from Ideal Behaviour

An ideal gas is one which obeys the gas laws of the gas equation PV = RT at all pressure and temperatures. However, no gas in nature is ideal. Almost all gases show significant deviations from the ideal behaviour. Thus the gases H2, N2 and CO2 which fail to obey the ideal-gas equation are termed as non-ideal or real gases.

Compressibility Factor : The extent to which a real gas departs from the ideal behaviour may be depicted in terms of a new function called the compressibility factor, denoted by Z. It is defined as

Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET

The deviations from ideality may be shown by a plot of the compressibility factor Z, against P.

For an ideal gas, Z = 1 and it is independent of temperature and pressure.

The deviations from ideal behaviour of a real gas will be determined by the value of Z being greater or less than 1.

The difference between unity and the value of the compressibility factor of a gas is a measure of the degree of non-ideality of the gas.

For a real gas, the deviations from ideal behaviour depends on :

(i) pressure; and (ii) temperature.

This will be illustrated by examining the compressibility curves of some gases discussed below with the variation of pressure and temperature.


Effect of Pressure Variation on Deviations: 

Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET


Effect of Temperature on Deviations: 

Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET


From the above curves we can conclude that:

1. At low pressure and fairly high temperatures, real gases show nearly ideal behaviour and the ideal-gas equation is obeyed.

2. At low temperatures and sufficiently high pressures, a real gas deviates significantly from ideality and the ideal-gas equation is no longer valid.

3. The closer the gas is to the liquefaction point, the larger will be the deviation from the ideal behaviour.

Greater is the departure of Z from unity, more is the deviation from ideal behaviour.

(i) When Z < 1, this implies that gas is more compressible.

(ii) When Z > 1, this means that gas is less compressible.

(iii) When Z = 1, the gas is ideal.


Vander Waals Equation of State for a Real Gas: The equation of state generated by Vander Waals in 1873 reproduces the observed behaviour with moderate accuracy. For n moles of gas, the Vander Waals equation is


Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET(V - nb) = nRT


where and b are constants characteristic of a gas. This equation can be derived by considering a real gas and converting it to an ideal gas.


Volume Correction : We know that for an ideal gas P x V = nRT. Now in a real gas the molecular volume cannot be ignored and therefore let us assume that `b' is the volume excluded (out of the volume of container) for the moving gas molecules per mole of a gas. Therefore due to n moles of a gas the volume excluded would be nb.

∴ a real gas in a container of volume V has only available volume of (V - nb) and this can be thought of, as an ideal gas in a container of volume (V - nb)

Pressure Correction: Let us assume that the real gas exerts a pressure P. The molecules that exert the force on the container will get attracted by molecules of the immediate layer which are not assumed to be exerting pressure.

It can be seen that pressure the real gas exerts would be less than the pressure an ideal gas would have exerted. Therefore if a real gas exerts a pressure P, then an ideal gas would exert a pressure equal to P p(p is the pressure lost by the gas molecules due to attractions). This small pressure p would be directly proportional to the extent of attraction between the molecules which are hitting the container wall and the molecules which are attracting these.

Therefore Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET (concentration of molecules which are hitting the container's wall)

Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET (concentration of molecules which are attracting these molecules ) Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEETBehaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET

Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET

where a is the constant of proportionality which depends on the nature of gas. Higher value of `a' reflects the increased attraction between gas molecules.

The Vander Waals constant b (the excluded volume) is actually 4 times the volume of a single molecule. i.e. b = 4 NAwhere NA xx Avogadro number.

Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET b = 4 x 6.023 x 1023Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET, where  r  is the radius of a molecule.


The constant a and b: Vander Waals constant for attraction (A) and volume (B) are characteristic for a given gas. Some salient features of `a' and `b' are:

(i) For a given gas Vander Waal's constant of attraction `a' is always greater than Vander Waals constant of volume (B).

(ii) The gas having higher value of `a' can be liquified easily and therefore H2 and He are not liquified easily.

(iii) The units of a = litre2 atm mole-2 and that of b = litre mole-1

(iv) The numerical values of a and b are in the order of 10-1 to 10-2 to 10-4 respectively.

(v) Higher is the value of `a' for a given gas, easier is the liquefaction.


Explanation of deviation by Van der Waals equation

(i) At lower pressure : `V' is large and `b' is negligible in comparison with V.

Then Vander Waals equation reduces to :

Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET ⇒ Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET

Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET ⇒ z = Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET = 1 - Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET

or PV < RT  at low pressure (below Boyle temperature)

this accounts for the dip in PV  vs  P isotherm at low pressure.


(ii)  At fairly high pressures :Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET may be neglected in comparison with P.

The Vander Waals equation becomes

P ( V-b) = RT ⇒ PV - Pb = RT

PV = RT Pb ⇒ z = Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET = 1 Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET

or PV > RT at higher pressure (above Boyle temperature)

This accounts for the rising parts of the PV vs P isotherm at high pressures.



(iii) At very low pressure :  V becomes so large that both b and become negligible and the Vander Waals equation reduces to PV = RT 

Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET At extremely low pressure (at Boyle temperature)

This shows why gases approach ideal behaviour at very low pressures.


(iv) Hydrogen and Helium : These are two lightest gases known. Their molecules have very small masses. The attractive forces between such molecules will be extensively small. So Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET is negligible even at ordinary temperatures. Thus PV > RT. 

Dieterici Equation : 

P (V - nb) = n R T ea/VRT (for `n' mole of a gas)

Berthelot Equation :

Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET (V - nb) = n R T


Virial Equation Of State For 1 Mole Of Gas : 

z = Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET = 1 B Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET C Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET D Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET ..............

B = second virial co-efficient , temperature dependent = b -

C = third virial co - efficient, temperature dependent = b2


Illustration 16 : The compressibility factor for 1 mole of a van der Waals gas at 0xC and 100 atm pressure is found to be 0.5. Assuming that the volume of a gas molecule is negligible, calculate the van der Waals constant, a.  

Solution: For 1 mole of the gas,

Z = Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET ⇒ 0.5 = Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET; V = 0.112 L

Neglecting  b, van der Waals equation reduces to  Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET

or pV  + Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET = RT

or 100 x 0.112 + Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET = .0821 x 273

a = 1.25 L2atm mol-2

The document Behaviour of Real Gases Deviation from Ideal Gas | Physics Class 11 - NEET is a part of the NEET Course Physics Class 11.
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FAQs on Behaviour of Real Gases Deviation from Ideal Gas - Physics Class 11 - NEET

1. What is the ideal gas law and how does it relate to real gases?
Ans. The ideal gas law is a mathematical equation that describes the behavior of an ideal gas. It states that the pressure, volume, and temperature of a gas are related by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature. Real gases deviate from ideal behavior due to factors such as intermolecular interactions and finite molecular size.
2. How do real gases deviate from ideal behavior?
Ans. Real gases deviate from ideal behavior primarily due to two factors: intermolecular interactions and finite molecular size. In real gases, molecules interact with each other through attractive and repulsive forces, which can cause deviations from the ideal gas behavior. Additionally, the volume occupied by the gas molecules themselves becomes significant at high pressures and low temperatures, leading to deviations from ideal gas behavior.
3. What is the compressibility factor and how does it indicate the deviation of a gas from ideal behavior?
Ans. The compressibility factor, denoted by Z, is a dimensionless quantity that indicates the deviation of a gas from ideal behavior. For an ideal gas, Z is equal to 1. If Z is greater than 1, it suggests that the gas has a greater volume than expected due to intermolecular interactions. Conversely, if Z is less than 1, it indicates that the gas occupies less volume than expected, possibly due to molecular size effects. The compressibility factor provides a measure of how much a gas deviates from ideal gas behavior.
4. How do intermolecular forces affect the behavior of real gases?
Ans. Intermolecular forces, such as van der Waals forces and hydrogen bonding, play a significant role in the behavior of real gases. These forces attract or repel gas molecules, causing deviations from ideal gas behavior. Attractive forces between molecules can lead to a decrease in pressure and an increase in volume compared to ideal gas behavior. On the other hand, repulsive forces can cause an increase in pressure and a decrease in volume. These intermolecular forces become more significant at lower temperatures and higher pressures.
5. Can real gases ever exhibit ideal gas behavior?
Ans. Real gases can approach ideal gas behavior under certain conditions. At high temperatures and low pressures, the intermolecular forces become less significant, and the gas molecules behave more like ideal gas particles. Additionally, gases composed of non-polar molecules with weak intermolecular forces tend to exhibit behavior closer to that of an ideal gas. However, it is important to note that no gas is truly ideal, and deviations from ideal behavior can still occur even under these conditions.
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