Question

Select the incorrect statements:
(A) The fraction of molecules having velocities u to $\left( {u + du} \right)$ of a gas of molar mass m at temperature T is the same as that of molar mass 2m at temperature T/2.
(B) It is possible to liquefy an ideal gas
(C) Vapour phase of a liquid exist above its critical temperature
(D) The excluded volume b is four times the actual volume occupied by the molecules.

Answer 1

The difference between an ideal and a real gas is that there exists intermolecular force of attraction or repulsion between the molecules of ideal gases and also the volume of the gas molecule is not negligible as compared to the volume of the real gas.

Complete step by step solution:
First of all, The Maxwell-Boltzmann distribution is used to determine the number of molecules present in the velocity range of u to $\left( {u + du} \right)$ according to the formula: $\dfrac{{{\text{dN}}}}{{\text{N}}}{\text{ = }}{\left( {\dfrac{{\text{m}}}{{{\text{2\pi }}{{\text{k}}_{\text{B}}}{\text{T}}}}} \right)^{\dfrac{{\text{1}}}{{\text{2}}}}}{{\text{e}}^{{\text{ - }}\dfrac{{{\text{m}}{{\text{v}}^{\text{2}}}}}{{{\text{2}}{{\text{k}}_{\text{B}}}{\text{T}}}}}}{\text{dv}}$
Where m is the mass of the molecules and T is the absolute temperature in the Kelvin scale. As long as the ratio of $\dfrac{{\text{m}}}{{\text{T}}}$ remains constant, the number of molecules having velocities in the range of u to $\left( {u + du} \right)$ will be constant. Hence this statement is correct.
Gases can be liquefied to convert them to liquids by applying pressure and reducing the temperature so that the speed of the molecules is reduced and the intermolecular force of attraction between them grows. But in case of an ideal gas there is no force of attraction between the molecules and hence ideal gases cannot be liquefied. This statement is false.
The critical temperature is that temperature is that point at which there will be an equilibrium between the liquid vapour and gaseous phases the liquid will change to gaseous state beyond the critical temperature. Hence Vapour phase of a liquid exists below the critical temperature. This statement is false.
The excluded volume b is four times the proper volume of the gas molecules. This statement is true.

Note:
The kinetic molecular theory of gases is used to determine the motion of a molecule of an ideal gas under a set of conditions. However, for a mole of an ideal gas, it is impossible to measure the velocity of each molecule at each instant of time.