For the given reaction:
\[
\mathrm{X_2(g) + Y_2(g) \rightleftharpoons 2XY(g)}
\]
The following data table is provided at \(600 \, \mathrm{K}\):
& \(\Delta_f H \, (\mathrm{kJ/mol})\) & \(S_m \, (\mathrm{J\,K^{-1}\,mol^{-1}})\)
\(\mathrm{X_2}\) & 80 & 140
\(\mathrm{Y_2}\) & 8 & 250
\(\mathrm{XY}\) & 42 & 200
\endtabular
Calculate \(\Delta_r G\) at \(600 \, \mathrm{K}\).