Question #44051

Consider the gas-phase synthesis reaction at $300\text{ K}$:

$\ce{A(g) + 2B(g) -> C(g)}$

The standard thermodynamic parameters at $300\text{ K}$ are provided below:

$\begin{array}{|c|c|c|c|} \hline \text{Species} & \Delta H^\circ_f \text{ (kJ mol}^{-1}\text{)} & S^\circ_m \text{ (J K}^{-1}\text{mol}^{-1}\text{)} & C^\circ_{p,m} \text{ (J K}^{-1}\text{mol}^{-1}\text{)} \\ \hline \ce{A(g)} & 20 & 250 & 50 \\ \ce{B(g)} & 10 & 150 & 40 \\ \ce{C(g)} & 0 & 350 & 30 \\ \hline \end{array}$

Assuming the molar heat capacities at constant pressure ($C^\circ_{p,m}$) are independent of temperature, determine the standard Gibbs free energy change ($\Delta G^\circ$) for the reaction at $500\text{ K}$.

(Given: $\ln(5/3) = 0.51$)