Arenowned laboratory reports quadruple-point coordinates of 10.2 mbar and 24.1°c for four-phase equilibrium of allotropic solid forms of the exotic chemical β-miasmone. is the claim valid or not?

Explanation:

We should have an invariant point condition (The degree of freedom F=0 as per phase rule) for a quadruple point to occur and to test whether this argument is valid or not we must implement phase rule in a given case.

So, as per the Phase Principle F= C-P+2 Here in this situation all types are allotropic implying they consist of the same chemical compound, i.e. each have the same chemical composition.

Then constituents C=1,  P= 4 (because they have 4 phases) Also no parameters for the given system are 2, Pressure and Temperature, these are found by including 2 in the formula of phase rule

Therefore,  F= 1-4+ 2=-1 is certainly not equal to 0 and therefore the claim that they found a quadruple point is counterfeit.