Question

The cause of deviation from ideal behaviour is
(A) Low pressure
(B) High temperature
(C) Both low pressure and high temperature
(D) None of the above

Answer 1

Hint: Certain assumptions were made before evaluating the formula for the behaviour of ideal gases. The real gases which exist practically did not follow the gas laws and their deviation increased further with the variations in pressure, volume and temperature of the gas.

Complete step by step solution:
-The formula derived for ideal gases is ${{\left( PV \right)}_{ideal}}=nRT$ which is called the gas law. Real gases do not follow this law. The deviation of real gases is studied by compressibility factor (Z) which can be represented as
$\begin{align}
& Z=\dfrac{{{\left( PV \right)}_{real}}}{{{\left( PV \right)}_{ideal}}} \\
& Z=\dfrac{PV}{nRT}=\dfrac{P{{V}_{m}}}{RT} \\
\end{align}$
where ${{V}_{m}}$ is the molar volume or volume of 1 mole of gas.
-Real gases do not obey the ideal gas laws due to the assumptions of the ideal gases which are
1. Real gas molecules have a finite volume.
2. We cannot neglect the intermolecular attractive forces between real gas molecules which are considered zero for ideal gases.
-A real gas behaves more like an ideal gas when the temperature is high and pressure is low. This is because, under such conditions, the potential energy of the gas becomes less compared to kinetic energy because of the decrease in the intermolecular force of attraction between the gas molecules. Also, the molecule size becomes negligible compared to the volume of the gas.
-The gas law for real gases made after correction is
$\left( P+\dfrac{a{{n}^{2}}}{{{V}^{2}}} \right)\left( V-nb \right)=nRT$
Where a and b are correction factors.
a is the van der waal constant of attraction and b is van der waal constant of volume.
Unit of a is ${{L}^{2}}atm\text{ mo}{{\text{l}}^{-2}}$ and unit of b is $Lmo{{l}^{-1}}$
-At low pressure, the equation reduces to $\left( P+\dfrac{a}{{{V}^{2}}} \right)V=RT$
At high pressure, the equation reduces to P(V-b)=RT
At very low pressure, the equation becomes that of ideal gas law which is PV=RT
Therefore, the real gases follow the ideal gas law at low pressure and high temperature.

Thus, the correct option is D. None of the above

Note: The ideal gas law also does not take into account the chemical reactions that might occur in the gases ultimately resulting in a change of the characteristics of the gas like its pressure, volume and temperature. Also, the real molar volume at STP is 22.7L.