Perfect Gas/ Ideal Gas and Deviation of Real Gases from Ideality

 

Perfect Gas/ Ideal Gas and Deviation of real gases from ideality

 

Definition of ideal gas

ideal gas is an imaginary gas whose behaviour can be predicted precisely on the basis of kinetic molecular theory and gas laws.

OR

It is a hypothetical gas which strictly obeys gas laws (Boyle’s law, Charles’s law etc.) or ideal gas equation (PV = nRT as gas laws contained in it) for all conditions of temperature and pressure behaving according to the kinetic molecular theory and does not show deviation from gas laws. It is an imaginary gas and has no real existence.

OR

Ideal gas is a model gas for which ratio of PV/nRT called compressibility factor (z) is equal to 1.

 

In other words,

 

ideal gas is a reference gas for which graph between P on x-axis and PV/nRT on y-axis would be a horizontal line parallel to x-axis.

 

It is an imaginary gas and has no real existence. Actually there is no gas which is perfectly ideal. Actually, none of the known gases exactly follows the ideal gas laws and called as real gases. Some gases such as H₂, N₂, O₂ do not deviate greatly from the ideal behaviour at moderate temperatures and pressures because of their smaller size of molecules and weak forces of attraction between their molecules. Thus, an ideal gas can only exist at low pressure and high temperature.  Among all real gases helium acts most likely as an ideal gas at room temperature

 

Real gases shows deviation from gas laws particularly at high pressure and low temperature. Therefore, at low temperature, the attractive forces become significant, eventually the gas liquefies. This property of real gases cause deviates them from ideal behaviour.

 

Ideality Sequence

He > H₂ > N₂ > CO₂ > Nh₃ > SO₂

 

Conditions for Ideality

1.         High temperature

2.         Low pressure

 

Properties of an Ideal Gas in the light of KMT

1. Their molecules occupy no space or occupy negligible volume and have point mass.

2. Their molecules exert no forces one another.

3. Their molecules undergo elastic collisions.

4. It cannot be liquefied due to lack of attractive forces between the molecules.

 

Graphical Explanation of Deviation of Real Gases

To understand the attitude of real gases graphically and their deviation from ideal behaviour is expressed by introducing a factor known as compressibility factor ‘z’ in the ideal gas equation which is modified as should

 

PV = z (nRT) or z = PV/nRT

 

In case of ideal gas, PV = nRT or  z = 1

In case of real gas, PV ≠ nRt or z ≠ 1 (less or more than unity)

Thus in case of real gases z can be < 1 or > 1  

 

compressibility factor is a ratio of PV and nRT.

In other word,

The ratio of volume of real gas, V_real to the ideal volume of that gas, V_perfect calculated by ideal gas equation is known as compressibility factor. 

 

z = PV_real/nRT

 

But from ideal gas equation: 

 

PV_perfect = nRT            Or        V_perfect = nRT/P

 

Therefore

 

z = PV_real/nRT = V_real/V_perfect

 

It is clear from above graphs that the volume of real gas is more than or less than expected in certain cases.

The graph plotted between z and P at constant temperature is not a straight line for real gases. There is a significant deviation from the ideal behaviour. The extent of deviation of real gases from ideality is based on pressure, temperature and the nature of gases.

 

Two types of curves are seen. In the curves for hydrogen and helium, as the pressure increases the value of pV also increases. The second type of plot is seen in the case of other gases like carbon monoxide and methane. In these plots, first there is a negative deviation from ideal behaviour, the pV value decreases with increase in pressure and reaches to a minimum value characteristic of a gas. After that, pV value starts increasing. The curve then crosses the line for ideal gas and after that shows positive deviation continuously. It is thus, found that real gases do not follow ideal gas equation perfectly under all conditions.

 

The graph plotted between z and P for an ideal gas and various real gases provides the following information:

 

Case-I : If Z=1 

All gases reaches a value of z =1 , when the pressure approached to zero. This reveals that all gases tend to act like ideal gas at very low pressure.

 

Case-II : If z>1 

When Z > 1, it is a positive deviation.

V_real > V_ideal 

 

It shows that the gas is less compressible than expected from ideal behaviour. 

 

The repulsion forces become more significant than the attractive forces. 

 

The gas cannot be compressed easily. 

 

Usually the z > 1 for so called permanent gases like He, H₂ etc. 

 

Case-III: If z < 1 

When Z < 1, it is a negative deviation.

V_real < V_ideal 

 

It shows that the gas is more compressible than expected from ideal behaviour.  

 

The attractive forces are more significant than the repulsive forces. 

 

The gas can be liquefied easily. 

 

Usually the z < 1 for gases like NH₃, CO₂, SO₂ etc.

Detailed Explanation

1.         If z = 1 then line would be parallel to x-axis.

 

2.    If z < 1 then the line obtained will below the line of an ideal gas, which means that there is larger decrease in volume of the gas than predicted by general gas equation due to the appearance of attractive forces present among the molecules.

 

3.         If z > 1 then the line obtained will above the line of an ideal gas, which means that there is less decrease in the volume of the gas than predicted by general gas equation due to the appearance of repulsive forces present among the molecules.

 

Upto what pressure a gas will follow the ideal gas law, depends upon nature of the gas and its temperature. The temperature at which a real gas obeys ideal gas law over an appreciable range of pressure is called Boyle temperature or Boyle point. Boyle point of a gas depends upon its nature.

 

Above their Boyle point, real gases show positive deviations from ideality and z values are greater than one. The forces of attraction between the molecules are very feeble. Below Boyle temperature real gases first show decrease in z value with increasing pressure, which reaches a minimum value. On further increase in pressure, the value of z increases continuously. Above explanation shows that at low pressure and high temperature gases show ideal behaviour. These conditions are different for different gases.

Definition of real gas

The gases which do not obey gas laws strictly at all temperatures and pressures and show deviation from ideal behaviour under all or certain conditions of temperatures and pressures is called Real or Non-Ideal Gas. It exists in the universe e.g. CO₂, SO₂, Cl₂, F₂ etc.

 

Conditions for Ideality for Real Gases

Real gases follow the ideal gas equation of state only at sufficiently low densities. At atmospheric pressure, the ideal gas law is quite well satisfied for most gases, but for some (e.g. water vapours, ammonia, SO₂ etc.) there are deviations of 1 to 2%. e.g.

 

a).  Boyle’s law (PV = K),   is no longer satisfied at high pressure.

b). Charle’s law (V/T = K), begins to break down at low temperature

c).  Avogadro’s law (V/n = K), does not hold strictly for real gases at moderate pressure.

Deviation of Real Gases from Ideal Behaviour

A Real Gas is one, which do not obey gas laws strictly and show deviation from ideal behaviour under all or certain conditions of temperature and pressure.

 

Conditions of Deviation of Real Gases from Ideal Behaviour/Conditions for Non-Ideality

Real gases show considerable deviations from their ideal behaviour at very high pressure and at very low temperature. Thus, there are two conditions under which real gases show considerable deviation from their ideal behaviour:

 

1.         At very high pressure.

2.         At very low temperature.

Causes of Deviation

To analyze why real gases deviate from ideal behaviour, we should know the basics of formulation of the ideal gas equation, which was obtained from certain faulty assumptions of kinetic molecular theory. The deviation of real gases from the ideality is due to following to erroneous assumptions of kinetic molecular theory:

1.   Actual volume of gas molecules is negligibly small as compared to total volume of gas.

2.   Gas Molecules have neither attractive nor repulsive forces.

 

Contrary to these faulty assumptions, molecules of all gases do exert some attractive force on one another and they do occupy some space in the total volume of gas. The assumption 1 is valid at low pressure while assumption 2 is effective at high temperature. The postulate 1 is responsible for deviation at very high pressure and postulate 2 for the deviation at low temperature.

 

The reason is that the attractive forces diminish rapidly as the distance between molecules increases. Thus at high pressure and low temperature intermolecular forces becomes significant because molecules tend to be close together.

 

The main reason of deviation of real gases from ideality is the presence of intermolecular forces and un-negligible volume of gas molecules.

 

Reason of deviation at high pressure

At high pressure, the gas volume decreases and gas molecules come closer (thereby decreasing the empty spaces among molecules) due to which volume occupied by the actual gas molecule does not remain negligible as compared to total volume of gas. Moreover, attractive forces also arise among molecules at high pressure.  Hence at high pressure gases deviate from ideal behaviour.

 

Reason of deviation at low temperature

At low temperature, the kinetic energy of gas molecules decreases and intermolecular attractive forces become more effective. Hence at low temperature, gases deviate from ideal behaviour. There are two types of intermolecular forces.

 

1. van der Waal’s Forces

It is the force between gaseous molecules arising due to transit or temporary polarity due to unsymmetrical distribution of electronic charge cloud around the nucleus. e.g. London dispersion forces.

 

2. Dipole-Dipole Interaction

It is the force between gaseous molecules arising due to permanent polarity because of unequal distribution of electronic charge cloud around the nucleus e.g. Hydrogen bonding; H–Cl, NH₃, H₂S etc.

Ideal Vs Real Gas