A hundred years of chemical equilibrium calculations – The case of ammonia synthesis

• An equilibrium modeling exercise for a historically important process is presented.
• The model presented by Haber when receiving the Nobel prize in 1920 is used first.
• Gibbs energy based model requires extraction of property data from modern databases.
• The Gibbs model is solved by process simulators and modern math packages.
• The students are very impressed by the close agreement between the various results.

An exercise that involves a process of great historical importance – that of synthesizing ammonia from its elements – is presented. In the exercise, the students are required to calculate the equilibrium conversion to ammonia using three mathematical models: a regression model which is based on experimental equilibrium data obtained by Haber and le Rossignol over a hundred years ago; a model based on the Gibbs energy and ideal gas conditions; and the Gibbs energy model with gas phase non-ideality included. The use of state-of-the-art problem-solving tools, including mathematical software packages and process simulation programs, combined with reliable physical property databases for the equilibrium computations, is emphasized. On one hand, the exercise gives students an opportunity to become familiar with and to appreciate the precision of the experimental work and the manual calculations that were carried out more than a hundred years ago, and on the other hand, it gives them an opportunity to practice the use of the modern numerical problem-solving tools. It also helps them master the complex issues involved in phase and chemical equilibrium in reacting systems.