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Chapter 20: Problem 11

Hydrogen is produced commercially by the reaction of methane with steam: $$\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+3 \mathrm{H}_{2}(g)$$ a. Calculate \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) for this reaction (use the data in Appendix 4). b. What temperatures will favor product formation at standard conditions? Assume \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not depend on temperature.

Short Answer

Expert verified
a. Using the values from Appendix 4 and the equations: $$\Delta H^{\circ} = \sum \Delta f H^{\circ}(\text{products}) - \sum \Delta f H^{\circ}(\text{reactants}),$$ and $$\Delta S^{\circ} = \sum S^{\circ}(\text{products}) - \sum S^{\circ}(\text{reactants}),$$ calculate the standard enthalpy change (∆H°) and the standard entropy change (∆S°) for the reaction. b. To find the temperature that favors product formation at standard conditions, use the Gibbs free energy equation: $$T = \frac{\Delta H^{\circ}}{\Delta S^{\circ}}$$ Calculate the temperature using the obtained values for ∆H° and ∆S°. Product formation is favored at temperatures above this point.

Step by step solution

01

Calculate the standard enthalpy change (∆H°) for the reaction

Refer to Appendix 4 for the standard enthalpies of formation (∆fH°) values for each of the species in the reaction: $$\mathrm{CH}_{4}(g) + \mathrm{H}_{2}\mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g) + 3 \mathrm{H}_{2}(g)$$ Using the given values from Appendix 4, calculate the standard enthalpy change for the reaction (∆H°) using the following equation: $$\Delta H^{\circ} = \sum \Delta f H^{\circ}(\text{products}) - \sum \Delta f H^{\circ}(\text{reactants})$$
02

Calculate the standard entropy change (∆S°) for the reaction

Refer to Appendix 4 for the standard molar entropies (S°) values for each of the species in the reaction: $$\mathrm{CH}_{4}(g) + \mathrm{H}_{2}\mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g) + 3 \mathrm{H}_{2}(g)$$ Using the given values from Appendix 4, calculate the standard entropy change for the reaction (∆S°) using the following equation: $$\Delta S^{\circ} = \sum S^{\circ}(\text{products}) - \sum S^{\circ}(\text{reactants})$$
03

Determine the temperatures that favor product formation

Using the Gibbs free energy equation, ∆G° = ∆H° - T∆S°, and the calculated values of ∆H° and ∆S° from steps 1 and 2, determine the temperature at which product formation is favored. At this temperature, ∆G° = 0. Rearrange the Gibbs free energy equation to solve for the temperature, T: $$T = \frac{\Delta H^{\circ}}{\Delta S^{\circ}}$$ Calculate the temperature with the obtained values for ∆H° and ∆S°. This temperature is the point where the reaction becomes spontaneous, and higher temperatures will favor product formation, while lower temperatures will favor reactant formation. Based on your answer, you can conclude the temperatures that favor product formation at standard conditions.

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