In a closed flask at \( 600 \, \mathrm{K} \), one mole of \( \mathrm{X_2Y_4(g)} \) attains equilibrium as given below:
\( \mathrm{X_2Y_4(g)} \rightleftharpoons 2\mathrm{XY_2(g)} \)
At equilibrium, \( 75\% \) \( \mathrm{X_2Y_4} \) was dissociated and the total pressure is \( 1 \, \mathrm{atm} \). The magnitude of \( \Delta_{\mathrm{f}}G^{\ominus} \) (in \( \mathrm{kJ\, mol^{-1}} \)) at this temperature is _________. (Nearest Integer)
(Given: \( R = 8.3 \, \mathrm{J\, mol^{-1}\, K^{-1}} \); \( \ln 10 = 2.3 \), \( \log 2 = 0.3 \), \( \log 3 = 0.48 \), \( \log 5 = 0.69 \), \( \log 7 = 0.84 \))
