Acrylonitrile is the starting material used in the manufacture of acrylic fibers (U.S. annual production capacity is more than two million pounds). Three industrial processes for the production of acrylonitrile are given below. Using data from Appendix 4, calculate \(\Delta S^{\circ}, \Delta H^{p},\) and \(\Delta G^{\circ}\) for each process. For part a, assume that $T=25^{\circ} \mathrm{C} ;\( for part \)\mathrm{b}, T=70 .^{\circ} \mathrm{C} ;$ and for part \(\mathrm{c}, T=700 .^{\circ} \mathrm{C}\) Assume that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not depend on temperature.

Using the Appendix 4, we need to find the standard enthalpies of formation and standard entropies of all reactants and products involved in the reactions for processes a, b, and c. Once we have found these values, we can calculate \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) for each process using the following formulas: \[\Delta H^{\circ} = \sum H^{\circ}_{\text{products}} - \sum H^{\circ}_{\text{reactants}}\] \[\Delta S^{\circ} = \sum S^{\circ}_{\text{products}} - \sum S^{\circ}_{\text{reactants}}\]

Now that we have the values of \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) for each process at the given temperatures, we can calculate \(\Delta G^{\circ}\) using the following equation: \[\Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ}\] where \(T\) is the temperature in Kelvin. Remember to convert the given temperatures in Celsius to Kelvin by adding 273.15 to the Celsius temperatures before plugging them into the equation. Calculate \(\Delta G^{\circ}\) for each process with their respective temperatures: a) For part a, \(T = 25^{\circ}\mathrm{C} \Rightarrow T = 298.15 \mathrm{K}\): \[\Delta G^{\circ}_a = \Delta H^{\circ}_a - (298.15 \mathrm{K})(\Delta S^{\circ}_a)\] b) For part b, \(T = 70^{\circ}\mathrm{C} \Rightarrow T = 343.15 \mathrm{K}\): \[\Delta G^{\circ}_b = \Delta H^{\circ}_b - (343.15 \mathrm{K})(\Delta S^{\circ}_b)\] c) For part c, \(T = 700^{\circ}\mathrm{C} \Rightarrow T = 973.15 \mathrm{K}\): \[\Delta G^{\circ}_c = \Delta H^{\circ}_c - (973.15 \mathrm{K})(\Delta S^{\circ}_c)\] With these equations, we can find the \(\Delta G^{\circ}\) values for each of the three processes.