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Lee and Kesler developed a three-parameter corresponding-states correlation for pure, nonpolar, nonhydrogen-bonding fluids—especially, hydrocarbons. Values are provided for

  • acentric factor
  • vapor pressure
  • molar volume
  • residual enthalpy
  • residual entropy
  • fugacity coefficient
Brief Description of Method

The correlation is based on the Benedict-Webb-Rubin equation of state. For the equation of state, the Lee-Kesler correlation expresses the compressibility factor Z as a linear function of the acentric factor ω:

Z = Z0 + ω Z1

where Z0 is the compressibility factor for simple fluids, ω is Pitzer's acentric factor, and Z1 corrects Z for the effects of nonspherical intermolecular forces (primarily dispersion and overlap). Similarly, linear expressions are used for residual properties:

hres/RTc = (hres/RTc)0 + ω (hres/RTc)1

sres/R = (sres/R)0 + ω (sres/R)1

Once you have values for Z, hres, and sres, then values for all other residual properties can be computed using standard thermodynamic relations. Finally, the correlation estimates the pure-fluid fugacity coefficient by

ln(φ) = ln(φ)0 + ω ln(φ)1

The Macatea calculator will provide values for each of the quantities shown in these equations. For details on the computational procedure, see B. I. Lee and M. G. Kesler, AIChE J, 21, 510 (1975).

  1. Do not use this correlation for water or other strongly polar substances.
  2. As with any analytic equation of state, this correlation is unreliable in the immediate neighborhood of the critical point: Tc ± 2K and Pc ± 0.4 bar
  3. Many nonpolar substances solidify at some temperature 0.3Tc < T < 0.55Tc. If your temperature is in this range, verify that it is in fact fluid: the Lee-Kesler correlation applies only to fluids, not solids.
  4. If your state is near the vapor-liquid saturation curve and you wish to compare the results from this program with those computed from a Lee-Kesler table or chart, see the caution on interpreting the phase from such a table or chart.
  5. This program will identify the fluid phase (vapor, gas, liquid, dense fluid), based on the correlation and the data you supply. As an independent check, we recommend that you know the phase at your T and P, before using this correlation.
Data You Must Provide

To use the correlation, you will need to enter five things about your fluid:

  1. Critical temperature, Tc (in Kelvin).
  2. Critical pressure, Pc (in bar).
  3. Temperature, T (in Kelvin) at the state of interest.
  4. Pressure, P (in bar) at the state of interest.
  5. A value for the acentric factor ω or the normal boiling point Tb.
    • You may enter a value for the acentric factor, or let the program compute the Lee-Kesler value.
    • If you want the program to compute an acentric factor, you must enter the normal boiling point (in Kelvin) for your fluid.
Perform a Calculation


  1. Enter Critical Properties for Your Fluid
    • Critical temperature Tc (in Kelvin)   
    • Critical pressure Pc (in bar)   
  2. Enter Normal Boiling Point or Acentric Factor
    • Normal boiling point (in Kelvin) or acentric factor ω
  3. Enter Your State Condition
    • Temperature T (in Kelvin)   
    • Pressure P (in bar)