Computer program is described for numerical solution of chemical equilibria in complex systems by using nonlinear algebraic equations. Free-energy minimization technique is used

Gordon, S.

Mcbride, B. J.

English

NASA Technical Reports Server

December 1972	 B72-10718 
NASA TECH BRIEF 
Lewis Research Center 
NASA Tech Briefs announce new technology derived from the U.S. space program. They are issued to encourage 
commercial application. Tech Briefs are available on a subscription basis from the National Technical Information 
Service, Springfield, Virginia 22151. Requests for individual copies or questions relating to the Tech Brief program may 
be directed to the Technology Utilization Office, NASA, Code K, Washington, D.C. 20546. 
Computer Program for 
Calculation of Complex Chemical Equilibrium Compositions 
^1
The problem: 
To obtain knowledge of chemical equilibrium compo-
sition of a chemical system which, would permit calcu-
lation of theoretical thermodynamic properties for the 
system. These properties can be applied to a wide variety 
of problems in chemistry and chemical engineering. 
The solution: 
A computer program has been developed to solve 
numerically, through the use of nonlinear algebraic 
equations, chemical equilibria in complex systems. A 
free-energy minimization technique is used. 
How it's done: 
The program permits calculations such as chemical 
equilibrium for the following assigned thermodynamic 
states:
(1) Temperature and pressure; 
(2) Enthalpy and pressure; 
(3) Entropy and pressure; 
(4) Temperature and volume or density; 
(5) Internal energy and volume or density; and 
(6) Entropy and volume or density. 
Other problems capable of being calculated are: 
(1) Theoretical rocket performance; 
(2) Chapman-Jouguet detonations; and 
(3) Shock tube parameter calculations. 
The condition for equilibria may be stated in terms 
of any of several thermodynamic functions such as the 
minimization of the Gibbs free energy or Helmholtz 
free energy. If it is desired to use temperature and pres-
sure to characterize a thermodynamic state, the Gibbs 
free energy is most easily minimized since temperature 
and pressure are its natural variables. Similarly, the
Helmholtz free energy is most easily minimized if the 
thermodynamic state is characterized by temperature and 
volume (or density). 
Topics included in the complex equilibrium calcu-
lations are: mathematical analysis and techniques for 
obtaining chemical equilibrium; formulas for obtaining 
thermodynamic mixture properties and derivatives; cri-
teria for inclusion of condensed phases; calculations at 
a triple point, inclusion of ionized species; and appli-
cations. 
Notes: 
1. This program is written in FORTRAN IV for IBM-
7094 computer and in FORTRAN H for IBM-360. 
These programs replace previously published com-
puter program LERC-28 1. 
2. Some applications for these programs are the design 
and analysis of equipment such as compressors, 
turbines, nozzles, engines, shock tubes, heat ex-
changers, and chemical processing equipment. 
3. Inquiries concerning these programs should be di-
rected to: 
COSMIC 
112 Barrow Hall 
University of Georgia 
Athens, Georgia 30601 
Reference: LEW-1 1714 for IBM-7094 
LEW-1 1740 for IBM-360 
Source: Sanford Gordon and
Bonnie J. McBride
Lewis Research Center 
(LEW-1 1714) (LEW-1 1740) 
fb Category 09 
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This document was prepared under the sponsorship of the National	 Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States 	 information contained in this document, or warrants that such use 
Government nor any person acting on behalf of the United States 	 will be free from privately owned rights.
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Computer program for calculation of complex chemical equilibrium compositions

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