What is the equilibrium composition of this system at that T and P if you start with a 1 mole of H2O and 2 moles of CO? Assume the heat of reaction is not a function of temperature.

Question

The “water-gas” shift reaction is catalyzed by an iron oxide/chromium oxide catalyst at 700 K and 2 bar.

H2O + CO ? CO2 +H2

Answer 1

Apply short-cut van`t Hoff equation to find ??G_700K^0 since heat of reaction is not a function of temperature:



Where ??G_T^0 is the Gibbs free energy for reaction @ 700K, T=700 K, T_R=298 K, ??H_R^0=?????H_(f,products)^0-? ?????H_(f,reactants)^0 ? and ??G_R^0=?????G_(f,products)^0-? ?????G_(f,reactants)^0 ?. Values for ??H_f^0 and ??G_f^0 are obtained from Appendix C-2:



Substitute known terms into van`t Hoff equation:



Apply definition of equilibrium constant:



Apply equilibrium criterion for gas phase reaction:



Where ??v_i =0. Assume all ?_i=1 since pressure is low enough to assume ideal gas behavior:



Apply stoichiometric table to get mole fractions in terms of extent of reaction: