Consider the hypothetical decomposition reaction: $A_{2}B_{4(l)} \rightarrow 2AB_{2(g)}$. Given that

Question

Consider the hypothetical decomposition reaction: $A_{2}B_{4(l)} ightarrow 2AB_{2(g)}$. Given that $\Delta U = 1.5 	ext{ kcal/mol}$ and $\Delta S = 10 	ext{ cal K}^{-1} 	ext{mol}^{-1}$ at a constant temperature of $400 	ext{ K}$. The value of the Gibbs free energy change ($\Delta G$) for this process is (Assume $R = 2 	ext{ cal K}^{-1} 	ext{mol}^{-1}$)

Professor PC Thomas Classes · Answer

(a) : First, we calculate the enthalpy change $\Delta H$ using $\Delta H = \Delta U + \Delta n_g RT$. The change in gaseous moles $\Delta n_g = 2 - 0 = 2$. Thus, $\Delta H = 1.5 	ext{ kcal} + (2 	imes 2 	imes 10^{-3} 	ext{ kcal/K} 	imes 400 	ext{ K}) = 1.5 + 1.6 = 3.1 	ext{ kcal/mol}$. Next, we apply the Gibbs equation: $\Delta G = \Delta H - T\Delta S$. Using $\Delta S = 10 	ext{ cal K}^{-1} = 0.01 	ext{ kcal K}^{-1}$: $\Delta G = 3.1 	ext{ kcal} - (400 	ext{ K} 	imes 0.01 	ext{ kcal K}^{-1}) = 3.1 - 4.0 = -0.9 	ext{ kcal/mol}$.