Estimate the standard Gibbs free energy and the equilibrium constant at \(1000 \mathrm{~K}\) for the reaction

\[ \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) \]

Given that the standard heat of reaction \(\Delta H_{298}^{0}\) and standard Gibbs free energy of the reaction \(\Delta G_{f, 298}^{0}\) for the formation of products are \(-41,450 \mathrm{~J} / \mathrm{mol}\) and \(-28.888 \mathrm{~J} / \mathrm{mol}\) respectively. The specific heat data in \(\mathrm{kJ}\) as function of temperature are as follows:

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Components CO2(g) a x 10 45.369 8.688 H2(g) 27.012 3.509 CO(g) 28.068 4.631 HO(g) 28.850 12.055