Problem 541
Given that \(\mathrm{k}=8.85\) at \(298^{\circ} \mathrm{K}\) and \(\mathrm{k}=.0792\) at \(373^{\circ} \mathrm{K}\), calculate the \(\Delta \mathrm{H}^{\circ}\) for the reaction of the dimerization of \(\mathrm{NO}_{2}\) to \(\mathrm{N}_{2} \mathrm{O}_{4}\). Namely, \(2 \mathrm{NO}_{2}(\mathrm{~g}) \rightleftarrows \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g})\).
Problem 543
Calculate the enthalpy change, \(\Delta \mathrm{H}^{\circ}\), for the reaction $$ \mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})=2 \mathrm{NO}(\mathrm{g}) $$ given the equilibrium constants \(4.08 \times 10^{-4}\) for a temperature of \(2000^{\circ} \mathrm{K}\) and \(3.60 \times 10^{-3}\) for a temperature of \(2500^{\circ} \mathrm{K}\).
Problem 545
The equilibrium constant and standard Gibbs free energy change for ammonia synthesis at \(400^{\circ} \mathrm{C}\) or \(673^{\circ} \mathrm{K}\) are \(1.64 \times\) \(10^{-4}\) and \(11,657 \mathrm{cal} /\) mole, respectively. The equation for this reaction is (1) \(\quad \mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{NH}_{3}(\mathrm{~g})\) Calculate the equilibrium constants and standard free energy changes for (2) \((1 / 2) \mathrm{N}_{2}(\mathrm{~g})+3 / 2 \mathrm{H}_{2}(\mathrm{~g})=\mathrm{NH}_{3}(\mathrm{~g})\) and (3) \(2 \mathrm{NH}_{3}(\mathrm{~g}) \rightarrow \mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g})\)
Problem 547
Calculate \(\Delta \mathrm{G}^{\circ}\) and \(\mathrm{K}_{\mathrm{p}}\) at \(25^{\circ} \mathrm{C}\) for $$ \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) $$ \(\Delta \mathrm{G}^{\circ} \mathrm{f}\) for \(\mathrm{H}_{2}(\mathrm{~g}), \mathrm{CO}_{2}(\mathrm{~g}), \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\), and \(\mathrm{CO}(\mathrm{g})\) are 0, \(-94,2598,-54.6357\), and \(-32.8079 \mathrm{Kcal} / \mathrm{mole}\) respectively.
Problem 548
If the standard free energy of formation of HI from \(\mathrm{H}_{2}\) and \(\mathrm{I}_{2}\) at \(490^{\circ} \mathrm{C}\) is \(-12.1 \mathrm{~kJ} /\) mole of \(\mathrm{HI}\), what is the equilibrium constant for this reaction? Assume \(\mathrm{R}=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{deg}^{-1}\)
Problem 550
Sulfur exists as \(S_{2}\) vapor at temperatures between \(700^{\circ} \mathrm{C}\) and \(1500^{\circ} \mathrm{C}\). At \(1473 \mathrm{k}\) it combines with hydrogen according to the equation $$ \mathrm{H}_{2}(\mathrm{~g})+(1 / 2) \mathrm{S}_{2}(\mathrm{~g}) \rightarrow \mathrm{H}_{2} \mathrm{~S}(\mathrm{~g}) $$ At \(750^{\circ} \mathrm{C}\) the equilibrium constant is \(1.07 \times 10^{2}\) and at \(1200^{\circ} \mathrm{C}\) it is \(4.39\). Determine the heat of reaction in the temperature range \(750^{\circ} \mathrm{C}\) to \(1200^{\circ} \mathrm{C}\), and the change in free energy at each of these temperatures.
Problem 551
In the human body, the enzyme phosphoglucomutase catalyzes the conversion of glucose-1-phosphate into glucose \(-6-\) phosphate: glucose-1-phosphate \(\rightleftarrows\) glucose-6-phosphate. At \(38^{\circ} \mathrm{C}\), the equilibrium constant, \(\mathrm{k}\), for this reaction is approximately 20. Calculate the free energy change, \(\Delta \mathrm{G}^{\circ}\), for the equilibrium conversion. Calculate the free energy change \(\Delta \mathrm{G}\) for the nonequilibrium situation in which [glucose-1phosphate \(]=0.001 \mathrm{M}\) and [glucose \(-6-\) phosphate \(]\) \(=0.050 \mathrm{M}\)
Problem 552
Calculate the equilibrium constant at \(25^{\circ} \mathrm{C}\) for the reaction: $$ \mathrm{S}+3 / 2 \mathrm{O}_{2} \rightleftarrows \mathrm{SO}_{3} $$ The heat formation of \(\mathrm{SO}_{3}\) at \(25^{\circ} \mathrm{C}\) is \(-94.45 \mathrm{Kcal} / \mathrm{mole}\) and the standard molar entropy changes for \(\mathrm{S}, \mathrm{O}_{2}\), and \(\mathrm{SO}_{3}\) at \(25^{\circ} \mathrm{C}\) are \(7.62,49.0\) and \(61.24 \mathrm{cal} / \mathrm{mole}^{\circ} \mathrm{K}\), respectively.
