Match List-I with List-II regarding the missing term ' x ' in...

The ideal gas equation can be expressed in various forms.

In the macroscopic form involving mass density $\rho$, the equation is $P = \rho \dfrac{RT}{M_0}$. Thus, in (A), $x$ represents mass density (II).

In the microscopic form, the equation is $P = n_v k_B T$, where $n_v$ is the number density (number of molecules per unit volume). Thus, in (B), $x$ represents number density (I).

The standard molar form is $PV = nRT$, where $n$ is the number of moles. Thus, in (C), $x$ represents the number of moles (IV).

The number of moles $n$ can be written as the ratio of total mass $m$ to molar mass $M_0$, giving $PV = \left(\dfrac{m}{M_0}\right)RT$. Thus, in (D), $x$ represents molar mass (III).

The correct matching is (A)-(II), (B)-(I), (C)-(IV), (D)-(III).

Answer: (A)-(II), (B)-(I), (C)-(IV), (D)-(III)