List of top Physical Chemistry Questions on Gaseous State

In the van der Waals equation of state, the volume correction factor (b) arises from the repulsive interactions between the gas moleculesConsidering the molecules to behave as hard spheres of radius r, b = Y $\times$ V$_{\text{molecule}}$ $\times$ N$_A$The value of Y is _ _ _.

For an ideal gas, the isothermal compressibility $k_T = -\frac{1}{V}\left(\frac{\partial V}{\partial P}\right)_T$ is _ _ _.

The Lennard-Jones (LJ) potential of interaction between two molecules as a function of distance ($r$), is given by $V_{LJ}(r) = 4\epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6 \right]$, where $\epsilon$ and $\sigma$ are constantsThe expression of $r$ at which $V_{LJ}(r)$ reaches minimum is _ _ _.

For one mole of an ideal gas, the correct statement(s) is/are
[𝑈=internal energy; 𝑉= volume; 𝑇=temperature; 𝑃=pressure]

If nitrogen and oxygen gases are at the same temperature, the correct statement according to the kinetic theory of gases is

Equal number of gas molecules A (mass 𝑚 and radius 𝑟) and B (mass 2𝑚 and radius 2𝑟) are placed in two separate containers of equal volume. At a given temperature, the ratio of the collision frequency of B to that of A is
(Assume the gas molecules as hard spheres)

The Maxwell-Boltzmann distribution $f(v_x)$ of one-dimensional velocities $v_x$ at temperature T is [Given: A is a normalization constant such that $ \int_{-\infty}^{\infty} f(v_x) dv_x = 1$, and $k_B$ is the Boltzmann constant]

The Boyle temperature (\(T_B\)) is defined as the temperature at which the properties of a real gas coincide with those of an ideal gas in the low pressure limit. The graph that shows the pressure dependence of the compression factor (Z) for a real gas at \(T_B\) is

Assuming ideal gas behavior, the density of \( \text{O}_2 \) gas at 300 K and 1.0 atm is ......... g L\(^{-1}\) (rounded up to two decimal places).