Phenomenological Equations of State (EOS) for fluids near their critical point have been obtained using literature compression factor data, Zc = Pc Vc/(n R Tc) = 0.40 to 0.10 in Table I (Pc, Vc/n, Tc are the pressure, volume per n mole, and the absolute temperature of the fluid at the critical point). The objective is to explain the deviations from the van der Waals value, Zc(vdW) = 3/8 (-70 % for molten Se and alkali metals up to 6 % for molten Pb, Hg, and In) by including in the commonly used phenomenological thermodynamic relations a term which explicitly describes the Heisenberg spin exchange interactions, in order to understand electron transfer reactions in solvents near their critical point. Literature data near the critical point indicate that the 199,201Hg (Zc  0.4) Knight shift plummets to zero while the alkali metals and Se (Zc = 0.2 to 0.1) are paramagnetic fluids, and that the enhanced rates for free radical electron exchange reactions (in CO2, n-C2H6 and CHF3 with intermediate Zc) are correlated to Zc. The difference between the solvent behavior for electron spin exchange reactions near its critical point is ascribed to spin interactions. The analysis shows that the solvated electron osmotic pressure in metal ammonia solutions versus the solvent density r,NH3 = Vc/V goes through a maximum where enhanced rates of electron exchange also attain a maximum. This can be applied to choose the best solvents, near their critical point, for the syntheses of new materials and metal oxide extraction.