The Ostwald process for the commercial production of nitric acid involves three steps: a. Calculate \(\Delta H^{\circ}, \Delta S^{\circ}, \Delta G^{\circ}\), and \(K\) (at \(298 \mathrm{~K}\) ) for each of the three steps in the Ostwald process (see Appendix 4 ). b. Calculate the equilibrium constant for the first step at \(825^{\circ} \mathrm{C}\), assuming \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not depend on temperature. c. Is there a thermodynamic reason for the high temperature in the first step, assuming standard conditions?

In the Ostwald process, the three steps for commercial production of nitric acid involve the following reactions: 1. \(4 \mathrm{NH_{3}(g)} + 5 \mathrm{O_{2}(g)} \rightarrow 4 \mathrm{NO(g)} + 6 \mathrm{H_{2}O(g)}\) 2. \(2 \mathrm{NO(g)} + \mathrm{O_{2}(g)} \rightarrow 2 \mathrm{NO_{2}(g)}\) 3. \(\mathrm{NO_{2}(g)} + \mathrm{H_{2}O(l)} \rightarrow \mathrm{HNO_{3}(aq)} + \mathrm{NO(g)}\) After calculating the \(\Delta H^{\circ}, \Delta S^{\circ},\) and \(\Delta G^{\circ}\) values for each step, we can calculate the equilibrium constant \(K\) at \(298 \mathrm{~K}\) using the relation \(K = e^{[-\Delta G^{\circ}/(RT)]}\). For the first step at \(825^{\circ} \mathrm{C}\), we can use the Van't Hoff equation to calculate the equilibrium constant \(K\): \(K = e^{[\Delta S^{\circ}/R - \Delta H^{\circ}/(RT)]}\). The high temperature in the first step ensures that the reaction moves forward because the rate of the reaction depends on temperature. Moreover, at higher temperatures, the entropy becomes more significant, and since the reaction has a positive entropy change, it suggests a more spontaneous reaction at high temperatures. Thus, the high temperature in the first step helps the Ostwald process run efficiently and ensures the desired product formation.