Conceptual Mishap Clustering

In retrospect,

$\cfrac{V}{n}=\cfrac{1}{\rho_n}\ne \cfrac{dn_s}{df}$

of is it?

Not,

$PV=nRT$

but,

$PV=[T_{boom}]R$

$n=1$

where for any instance of $T_{boom}$ as part of a distribution,

$\cfrac{E_a}{kT_{boom}}=\cfrac{1}{m}$

$T_{boom}$ is associated with each particle and with

$mT_a=T_{boom}$

where $T_a$ is associated with each particle without aggregation.  Energy states is separately accounted for by $m$, such that,

$\cfrac{E_a}{kT_{boom}}=\cfrac{1}{m}$

but,

$\cfrac{E_a}{kT_a}=\cfrac{1}{m}m=1$

please refer to the post "An Old Friend For New Reasons" 17 Nov 2017.  With $E[m]=n_{\small{E}}$

$PV=n_{\small{E}}T_a.R$

the number of mole, $n=1$.  $T_a$ measures the kinetic energy of a single, not clustered particle.

OK?