Estimate the standard Gibbs free energy and the equilibrium constant at 1 bar and \(800 \mathrm{~K}\) for the reaction

\[ \mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g}) \]

Given that the standard heat of reaction, \(\Delta H_{298}^{0}\), and standard Gibbs free energy of the reaction, \(\Delta G_{298}^{0}\), for the formation of products are \(-92.11 \mathrm{~kJ} / \mathrm{mol}\) and \(-33.494 \mathrm{~kJ} / \mathrm{mol}\) respectively. The specific heat data in \(\mathrm{kJ}\) as function of temperature are as follows:

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Components x 10 NH3(g) 29.747 25.108 N2(g) 27.270 4.930 H2(g) 27.012 3,509