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 _ _ _.