Engineering & Science
Redlich-Kwong Real-Gas Equation of State (Pressure & Deviation From Ideal)
Calculate real-gas cylinder & pipeline pressure P = (R*T)/(V_m - b) - a/(SQRT(T)*V_m*(V_m + b)) in MPa using Otto Redlich and Joseph Kwong’s temperature-dependent attractive term.
Why Redlich & Kwong’s 1 / SQRT(T) cohesion term revolutionized chemical process simulation!
Van der Waals’s 1873 equation treated intermolecular attraction a / V_m^2 as completely independent of temperature—badly over-predicting liquid/supercritical pressures in high-pressure CO2, ethylene, and natural-gas compressors! Otto Redlich and Joseph Neng Shun Kwong (1949) introduced two surgical upgrades without adding a third parameter: scaling attraction inversely with SQRT(T) and replacing V_m^2 with V_m * (V_m + b): P = (R * T) / (V_m - b) - a / (SQRT(T) * V_m * (V_m + b))!
Look at supercritical Carbon Dioxide (CO2: a = 6.46 Pa*m^6*K^0.5/mol^2, covolume b = 0.0000297 m^3/mol) compressed to molar volume V_m = 0.00050 m^3/mol (500 cm^3/mol) at T = 350 K: the Ideal Gas Law P_ideal = R * T / V_m predicts 5.820 MPa, whereas Redlich-Kwong accounts for excluded molecular volume (+0.369 MPa) and strong CO2 quadrupole attraction (-1.305 MPa) to predict the realistic 4.884 MPa (compressibility factor Z = P * V_m / (R * T) = 0.8391, a 16.1% non-ideal pressure drop)!
| CO2 Compression State at T = 350 K (a = 6.46, b = 2.97e-5) | Ideal Pressure RT / Vm (MPa) | Redlich-Kwong Pressure (MPa) | Compressibility Factor Z |
|---|---|---|---|
| Supercritical Dense CO2 (Vm = 0.0005 m^3/mol) | 5.820 MPa | 4.884 MPa | 0.8391 (-16.1% Non-Ideal) |
| Moderate Pipeline Gas (Vm = 0.0050 m^3/mol) | 0.582 MPa | 0.572 MPa | 0.9830 (Near-Ideal) |
| Unphysical Compression (Vm <= b) | Hard-Sphere Singularity | "Molar Volume <= Covolume b" | Excluded-Volume Guard |
Redlich-Kwong Real-Gas Pressure P (MPa)
Evaluates ((8.31446 * T) / (V_m - b) - a / (SQRT(T) * V_m * (V_m + b))) / 1,000,000 while guarding against V_m <= b.
=IF(OR(B2 <= 0, B3 <= B5, B4 < 0, B5 < 0), "Molar Volume <= Covolume b", ROUND((((8.31446 * B2) / (B3 - B5)) - (B4 / (SQRT(B2) * B3 * (B3 + B5)))) / 1000000, 3))Dimensionless Real-Gas Compressibility Factor Z = (P * V_m) / (R * T)
Measures fractional departure from Z = 1.0000 ideal-gas behavior.
=IF(OR(B2 <= 0, B3 <= B5, B4 < 0, B5 < 0), "Molar Volume <= Covolume b", ROUND(((((8.31446 * B2) / (B3 - B5)) - (B4 / (SQRT(B2) * B3 * (B3 + B5)))) * B3) / (8.31446 * B2), 4))Try the example
Use the original values or change them to test your understanding.