This simulation calculates the number of moles at equilibrium for a gas-phase reaction \(A ⇋ rB\) at constant temperature; set the value of \(r\) (1/2, 1, 3/2, or 2) with buttons. The equilibrium constant for the reaction is \(K_{eq} = 0.5\) and components A and B are ideal gases. Initially the container is filled with 5 mol of reactant A, and equilibrium is obtained at either constant pressure (set pressure with a slider) or constant volume (set volume with a slider). The bar graph displays the number of moles at equilibrium, including the moles of inert gas (select the moles of inert with a slider). The height of the piston or container is proportional to the final volume.

The number of moles of each species in this reaction at equilibrium (values shown on the chart) determines the extent of reaction \(\xi\):

$$ n_A = n_{A,0} - \xi, $$ $$ n_B = r\xi, $$

where \(n_{A}\) and \(n_B\) are the moles of reactant and product at equilibrium (mol), \(n_{A,0} = 5\) is the moles of reactant present initially, and \(r\) is the ratio of moles of product to moles of reactant. The equilibrium constant \(K_{eq}\) is: $$ K_{eq} = {P_B}^r/P_A,$$

where \(P_A = y_AP\) is the partial pressure of the reactant, \(P_B = y_BP\) is the partial pressure of the product, and \(P\) is the total pressure (bar). The mole fraction of each species at equilibrium is: $$y_A = n_A/n_{total},$$ $$y_B = n_B/n_{total},$$

where the total number of moles is \(n_{total} = n_{A,0} + n_I + \xi(r-1)\), with \(n_I\) the number of moles of any inert component in the mixture. The extent of reaction is found by setting \(K_{eq} = 0.5\) and solving for \(\xi\).

This simulation was created in the Department of Chemical and Biological Engineering, at University of Colorado Boulder for LearnChemE.com by Jackson Dunlap under the direction of Professor John L. Falconer and Michelle Medlin, with the assistance of Neil Hendren and Drew Smith. It is a JavaScript/HTML5 implementation of a Mathematica simulation by Garrison Vigil and Rachael L. Baumann. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988) in collaboration with Washington State University. Address any questions or comments to LearnChemE@gmail.com. If this simulation is too big or too small for your screen, zoom out or in using command - or command + on Mac or ctrl - or ctrl + on Windows.