This Demonstration calculates the number of moles at equilibrium for the reversible, exothermic reaction that synthesizes ammonia \(\textnormal{NH}_3\) from hydrogen and nitrogen , known as the Haber process. This reaction typically takes place near 200 bar and 675 to 725 K. The system starts with 1 mol \(\textnormal{NH}_3\) and goes to equilibrium. Use sliders to add additional moles of \(\textnormal{N}_2\), \(\textnormal{H}_2\), and \(\textnormal{NH}_3\). Vary pressure and temperature with sliders. Because 4 mol of reactants form 2 mol of product, raising the pressure shifts equilibrium toward products. Gases are assumed ideal, but at the high pressures used for this reaction, significant deviation from ideal behavior is likely.

The reaction \(N_2 + 3H_2 \rightleftharpoons 2NH_3\) is used in the Haber process. The moles of each component at equilibrium is:

where \(\eta_{i,add}\) are the moles of component \(i=(N_2, H_2, NH_3)\) added, \(\nu_i\) is the stoichiometric coefficient and \(\xi\) is the extent of reaction (mol). Initially, only 1 mol NH₃ is present.
The mole fraction at equilibrium \(y_i\) is: where \(\eta_{total}\) is the total number of moles.
The dimensionless equilibrium constant \(K_{eq}\) is

\(K_{eq} = e^{-\Delta G / RT }\)

where \(\Delta G = \Delta H_r - T\Delta S_r\) is the standard state Gibbs free energy of reaction at temperature T(K) and \(R\) is the ideal gas constant (J/(mol K)).
Then the extent of reaction is found by solving the equation below:

\( K_{eq} = \prod(y_i P)^{-V_i} = \frac{(y_{NH_3} P)^2}{(y_{N_2} P) (y_{H_2}P)^3} = \frac{(y_{NH_3})^2}{y_{N_2} (y_{H_2})^3} \cdot \frac{1}{P^2}\)

where P is the pressure (bar).

This simulation was created in the Department of Chemical and Biological Engineering, at University of Colorado Boulder for LearnChemE.com by Vladislav Denisenkov and Abijith Trichur Ramachandran under the direction of Professor John L. Falconer. It is a JavaScript/HTML5 implementation of a simulation by Benjamin L. Kee and Rachael L. Baumann (https://demonstrations.wolfram.com/ChemicalEquilibriumInTheHaberProcess/).This simulation was prepared with financial support from the National Science Foundation. Address any questions or comments to LearnChemE@gmail.com. All of our simulations are open source, and are available on our LearnChemE Github repository.

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