Deviation of Real Gases from Ideal Behaviour
Ideal gas➠
• An ideal gas is that gas which obeys the gas equation (PV = nRT) at all temperatures and pressures.
• In actual practice, most of the gases obey gas equation and other gas laws at low pressures and high temperatures.
Real gas➠
• The gases which do not obey the gas equation or other gas laws at all temperatures and pressures are called non-ideal gases (or real gases).
Some Important Facts:
• In reality, no ideal gas exists. But some gases behave like ideal gases under certain conditions, i.e.,(In fact, no gas is found to be perfectly ideal. )
• No real gas is ideal gas. But some real gases like \(H_2, O_2, N_2, He_2\) behaves like ideal gas under certain conditions.
What are these certain conditions under which some real gases behave like ideal gas?
• At low temperature & high pressure the molecules of real gas (say H_{2}) are at maximum distance and behaves like ideal gas, i.e,
• when the pressure becomes high or temperature is decreased then the deviations from ideal behaviour are observed.
Distinction between Ideal gas and Real gas
Ideal Gas | Real Gas |
No intermolecular forces of attraction between the molecules | Having Intermolecular forces |
Volume of gas molecules is negligible as compared to total volume occupied by the gas | Volume is well known. |
Collision is perfectly elastic; i.e., No energy loss when molecules collides | Collision is perfectly non-elastic; i.e., energy loss occurs after collision. |
Ideal gases follow gas equation, PV=nRT | Real gases do not follow gas equation. They obey vanderwaals equation. |
It is hypothetical | All gases are real |
Deviation of Real Gases from Ideal Behaviour
Explanation
1. The volume occupied by the gas molecules themselves is negligibly small as compared to total volume occupied by the gas.
2. The forces of attraction between the gas molecules are negligible because under conditions of low pressure or high temperature, the molecules lie far apart from each other.
Note that:
• above two statements from the postulates of KTG are valid for extreme conditions of low pressure and high temperature only.
• These postulates do not appear to hold good under all conditions (i.e., not valid at high pressures and low temperatures )
The equation of state PV = nRT derived from the postulates of the kinetic theory, is valid for an ideal gas only.
Real gases obey this equation only approximately and that too under conditions of low pressure and high temperature.
• The higher the pressure and the lower the temperature, the greater are the deviations from the ideal behaviour.
• In general, the most easily liquefiable and highly soluble gases show larger deviations. Thus, gases like carbon dioxide(CO_{2}), sulphur dioxide(SO_{2}) and ammonia(NH_{3}) show much larger deviations than hydrogen(H2), oxygen (O_{2}), nitrogen(N_{2}), etc.
The deviations from ideal behaviour are best represented in terms of the compressibility factor (compression factor), Z.
compressibility factor is defined as
\( \fbox{\(Z= \frac{PV} {(PV)_{ideal}}\) = \(\frac{PV}{nRT}\) = \(\frac{PV_m}{RT}\)} \)
where \(V_m = \frac{V}{n}\) is the molar volume, i.e., the volume occupied by one mole of the gas.
For an ideal gas, z = 1 under all conditions of temperature and pressure.
• The deviation of Z from unity is, thus, a measure of the imperfection of the gas under consideration.
Graph of compressibility factor (z) vs Pressure in atmosphere (at constant temp., 0°C) showing deviations of real gases from ideal behaviour :
• At extremely low pressures, all the gases are known to have z≈1 which means that the gases behave almost ideally.
• At very high pressures, all the gases have Z>1 ; indicating that the gases are less compressible than an ideal gas.This is due to the fact that at high pressures, the molecular repulsive forces are dominant.
Graph shows that:
For z=1 Ideal gas
PV = nRT
For z<1 (Negative deviation)
⇒PV < PV ideal
⇒PV < nRT
⇒PVm < RT
• At moderately low pressures, the Long range attractive forces are dominant and favour compression. Therefore,at moderately low pressures, carbon monoxide, methane and ammonia are more compressible than an ideal gas, i.e., PV is less than (PV) ideal so that z < 1
For z>1 (Positive deviation)
⇒PV > PV ideal
⇒PV > nRT
⇒PVm > RT
• The compressibility factor Z goes on decreasing with increase in pressure, passes through a minimum at a certain stage and then begins to increase with increase in pressure
• At high pressure, the gases become less compressible than an ideal gas, i.e., PV is more than (PV) ideal so that z > 1
Note: From graph it can be clearly seen that :
• carbon monoxide and methane exhibit marked deviations from ideal behaviour only at high pressures.
• Ammoniashows large deviations even at low pressures.
• At 0°C, Hydrogen and helium are seen to be less compressible than the ideal gas ar all pressures, i.e., z > 1• At sufficiently low temperature (H➤ -48°C , He➤ – 242°C) H & He also give the same type of Z-P plots as are shown by ammonia, carbon monoxide and methane at 0°C
• At sufficiently high temperature , the Z – P plots of ammonia, carbon monoxide and methane will be similar to those of hydrogen and helium at 0°C i.e., the value of Z will increase continuously with increase in pressure.
Effect of Temperature on Deviations from Ideal Behaviour
Consider the Z vs P plots of nitrogen at different temperatures varying between – 70°C and 50 °C
• The graph shows that as the temperature is raised, the dip in the curve becomes smaller and smaller.
At 50°C the curve is almost horizontal for an appreciable range of pressure (0➠100 atm),
⇒Z ≈ 1 under these conditions.
In other words, PV = constant and thus Boyle’s law is obeyed within this range of pressure at 50°C.
• This temperature is called the Boyle point or Boyle temperature.
• Boyle’s temperature is that temperature at which a real gas obeys the ideal gas law over an appreciable range of pressure.
• Below Boyle’s temperature, the value of Z is firstly decreases, approaches a minimum and then increases continuously with increase in the pressure.
• Above Boyle’s temperature (above 50°C) ,the value of compressibility factor (z) shows a continuous rise with increase in pressure.
Note :
The Boyle’s temperature is different for different gases.
for He ➤ -250.4 °C (Boyle’s temp.)
• At T= -250.4 °C helium obeys Boyle’s law for an appreciable range of pressure
• At T< -250.4 °C ,the plot of z vs P first shows a fall and then a rise as pressure is increased continuously.
• At T > -250.4 °C ,Z shows a continuous rise with increase in pressure