Riedel Parameter (αc): Critical Vapor-Pressure Slope & dPsat/dT at Tc

Anchoring high-pressure vapor-pressure equations right at the critical point!

Simple three-constant Antoine equations extrapolate poorly near the critical point because they fail to match the thermodynamic slope where the vapor-liquid coexistence curve terminates into the critical isochore! L. Riedel (Chemie Ingenieur Technik, 1954) introduced the fundamental dimensionless critical vapor-pressure slope parameter α_c = (d ln P_r^sat / d ln T_r)|_(T_r = 1), linked directly to Pitzer’s acentric factor ω by α_c = 5.808 + 4.93 * ω!

Multiplying α_c by (P_c / T_c) immediately yields the exact physical saturation curve slope right at the critical point: (dP_sat / dT)|_Tc = α_c * P_c / T_c! For propane (ω = 0.152, T_c = 369.8 K, P_c = 42.48 bar), Riedel α_c = 6.557 and critical slope = 0.7533 bar/K; for strongly hydrogen-bonded water (ω = 0.344, T_c = 647.1 K, P_c = 220.64 bar), α_c = 7.504 and critical pressure rises at a steep 2.5586 bar/K!

Riedel Dimensionless Critical Slope Parameter α_c = 5.808 + 4.93 * ω

Evaluates Riedel’s parameter from Pitzer acentric factor B2 (valid including slightly negative quantum fluids like H_2 down to ω > -0.5).

=IF(B2 <= -0.5, "Invalid Acentric Factor", ROUND(5.808 + 4.93 * B2, 3))

Dimensional Critical Coexistence Slope (dP_sat / dT)|_Tc (bar/K)

Multiplies α_c by critical pressure B4 (bar) over critical temperature B3 (K), matching the critical isometric slope by Plank-Riedel theorem.

=IF(OR(B2 <= -0.5, B3 <= 0, B4 <= 0), "Invalid Critical Inputs", ROUND((5.808 + 4.93 * B2) * B4 / B3, 4))

Further reading

• Microsoft Support — ROUND function