Gibbs Free Energy Minimization Applied to the Haber Process

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Consider the high-pressure synthesis of ammonia (), known as the Haber process. This Demonstration shows plots of the mole fractions of all three components (, , and , in red, blue, and green, respectively) for temperatures ranging from 420 K to 800 K.


At very high pressure or low temperature, as expected from Le Chatelier's principle, the mole fraction of ammonia is significantly larger.

Here, the method of Gibbs free energy minimization is applied to efficiently solve the ammonia synthesis problem. Experimental values of the Gibbs free energy for all three components are taken from [1]. In addition, the residual Gibbs free energy is calculated using the Peng–Robinson equation of state.

Finally, the same problem is solved using the arc-length continuation technique and the reaction coordinates method (dotted line). These results are compared with the ones obtained using the Gibbs free energy minimization approach (solid diamonds) for the two selected temperatures of 450 K and 650 K. Excellent agreement is found between the two approaches.


Contributed by: Housam Binous, Ahmed Bellagi, Brian G. Higgins, Ahmed Aheed, and Mohammad Mozahar Hossain (January 2015)
Open content licensed under CC BY-NC-SA




[1] I. Barin and G. Platzki, Thermochemical Data of Pure Substances, 3rd ed., New York: VCH Publishers, Inc., 1995.

[2] S. I. Sandler, Chemical and Engineering Thermodynamics, 3rd ed., New York: John Wiley & Sons, 1999.

[3] H. Binous, A. Aheed and M. M. Hossain, "Haber Process and Steam-Coal Gasification: Two Standard Thermodynamic Problems Elucidated Using Two Distinct Approaches," Computer Applications in Engineering Education Journal, DOI: 10.1002/cae.21672.

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