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Oct 18, 2018

Comparison Between Ideal and Real Gases

Comparison Between Ideal and Real Gases:

Simply one equation can be used to distinguish between ideal gas from real gas and this is,
PV = nRT
The gas which obeys this equation under all conditions of temperature and pressure is called ideal gas and the gas which does not obey this equation under all conditions of temperature and pressure is called real gasesA number of points can be discussed to compare the two types of gases.

Ideal Gas : 

(i) The Ideal Gas can not be liquefied since it has no inter-molecular attraction and so that molecule will not condense.
(ii) The coefficient of thermal expansion(𝛂) depends on temperature(T) and does not depends on the nature of the gas.
Show that coefficient of thermal expansion of Ideal Gas depends on the temperature of the gas.
Coefficient of thermal expansion(𝛂) is defined as 𝛂 = (1/V)(dV/dT)P.
Ideal Gas Equation for 1 mole gas is PV = RT.
Hence (dV/dT)p = R/P.
Thus 𝛂 = (1/V) × (R/P) = (R/PV) = 1/T.
This means all the gases have the same coefficient of thermal expansion.
(iii) The coefficient of compressibility(β) similarly depends on the Pressure(P) of the gas and will be same for all gases.
Show that coefficient of Compressibility of Ideal Gas depends on the Pressure of the gas.
Coefficient of Compressibility(β) is defined as β = - (1/V)(dV/dP)T.
Ideal Gas Equation for 1 mole gas is PV = RT.
Hence (dV/dP)T = - (RT/P²).
Thus β = (1/V) × (RT/P²) = (RT/P²V) = (RT/PV) × (1/P) = (1/P).
This means coefficient of Compressibility depends on the Pressure(P) of the gas. 
(iv) When P is plotted against V, at constant temperature(T) a rectangular hyperbola curve is obtained as demanded by Boyle's Low PV = Constant. 
Comparison Between Ideal and Real Gases.
P vs V Plot
The hyperbola Curve at each temperature is called one isotherm and at different tempera-ture we have different isotherms. Two isotherms will never intersect.
(v) When PV is plotted against P, at constant T a straight line parallel to P-axis is obtained. At different temperature there will be different parallel lines.
Comparison Between Ideal and Real Gases.
PV vs P Plot

(vi) When an ideal gas passes through a porous plug from higher pressure to lower pressure within insulated enclosure, there will be no change of temperature of the gas . This confirms that the ideal gas has no inter-molecular attraction. 

Real Gas :

(i) This gas could be liquefied since it has inter molecular attraction which helps to coalesce the gas molecules.
(ii) The coefficient of thermal expansion (α) is found to vary from gas to gas that is α depends on the nature of the gas.
(iii) The coefficient of compressibility (β) also is found to depend on the nature of the gas.
(iv) When P is plotted against V, a rectangular hyperbola is obtained only at high temperature (above the critical temperature).

What is the Real Gases?
P vs V Plot for Real Gas
But a temperature below the critical temperature(C), the gas is liquefied after certain pressure depends on temperature. The point C is the critical point where he liquid and gas can be indistinguishable.
(v)  When PV is plotted against P for real gas, following plots, called Amagat Curve are obtained.

Amagat Curve:

What is the Ideal and Real Gas?
Amagat Curves for different gases
at a given Temperate(0°C)
It shows that for most gases, value of PV decreases, attain minimum and then increases with the increase of P
Only Hydrogen(H₂) and Helium(He) baffle this trend and the curve rises with increase of Pressure(P) from the very beginning.
Comparison Between Ideal and Real Gases
Amagat Curves for a gas (CO₂)
at different temperature 
This shows that for CO₂ gas the depth of the minimum shifts towards the PV-axis with the increase of temperature (T). 
At T₃ temperature PV runs parallel to the P-axis up to certain range of P at low pressure region (P0).

Boyle Temperature(TB):

In the above Curve T₃ is called Boyle Temperature(TB) at which real gas obeys Boyle’s Law up to certain range of pressure at the low pressure region. 
The minimum coincides with the PV-axis. The mathematical condition for the calculation of Boyle Temperature(TB) is give by, [d(PV)/dP]T = 0 when P 0.
The curves obtained for Hydrogen(H₂) and Helium(He) at 0°C is above their Boyle Temperature and so with increase of P, values of PV increases from the beginning.

Compressibility Factor(Z):

An important single parameter, called Compressibility factor (Z) is used to measure the extent of deviation of the real gases from ideal behavior. 
It is defined as, Z = PV/RT where V is the molar volume.
When Z=1, the gas is ideal or there is no deviation from ideal behavior. 
When Z ≠ 1, the gas is non-ideal and departure of the value of Z from unity is measure of the extent of non-ideality of the gas.
When Zく1, the gas is more compressible then ideal gas and When Z 〉1, the gas is less compressible then ideal gas.
(vi) When real gases pass through porous plug from higher pressure to lower pressure within insulated enclosure, there occurs a change of temperature. This is due to the fact that real gases have inter-molecular attraction and when the gas expands, the molecules have to spend energy to overcome inter-molecular attraction and so the temperature of the gas drops down.

At 273 K and under pressure of 100 atm the compressibility factor of O₂ is 0.97. Calculate the mass of O₂ necessary to fill a gas cylinder of 108.5 lit capacity under the given conditions.
From the given data, we have 
T = 273 K, Z = 0.97 and P = 100 atm.
From the definition of compressibility factor Z = PV/RT where V is the molar Volume.
Thus the molar volume of O₂ is
Vm = ZRT/P = (0.97) × (0.082 lit atm mol⁻¹ K⁻¹) × (273 K)/(100 atm) = 2.17 lit mol⁻¹
The mass of this molar volume will be equal to the molar mass of oxygen, that is 2.17 lit of oxygen equal to 32 gm.
Thus the mass of oxygen required to fill the gas cylinder 108.5 lit under the given condition
= {(32 gm)/(2.17 lit)} × (108.5 lit)
= 1600 gm = 1.6 Kg