$ OG^\circ $ for the reaction $ x + y \rightarrow z $ is – 4.606 kcal. The value of equilibrium constant of the reaction at $ 227 ^\circ C $ is : $ (R = 2.0 cal K^{–1} mol{–1} ) $
To find the equilibrium constant (K) for the reaction, we use the relationship between the standard Gibbs free energy change ($ riangle G^ ext{°}$) and the equilibrium constant (K): $$ riangle G^ ext{°} = -RT ext{ln}(K)$$ Given: $$ riangle G^ ext{°} = -4.606 ext{ kcal} = -4606 ext{ cal}$$ $$T = 227^ ext{°C} = 227 + 273 = 500 ext{ K}$$ $$R = 2.0 ext{ cal K}^{-1} ext{ mol}^{-1}$$ Substituting these values into the equation, we get: $$-4606 = -2.0 imes 500 imes ext{ln}(K)$$ Solving for K: $$ ext{ln}(K) = rac{4606}{2.0 imes 500} = 4.606$$ $$K = e^{4.606} hickapprox 100$$ Therefore, the equilibrium constant (K) is approximately 100.