Synthesis gas, a mixture that includes the fuels CO and H₂,is used to produce liquid hydrocarbons and methanol. It is madeat pressures up to 100 atm by oxidation of methane followed bythe steam re-forming and water-gas shift reactions. Because theprocess is exothermic, temperatures reach 950–1100C, and theconditions are such that the amounts of H₂, CO, CO₂, CH₄, and H₂O leaving the reactor are close to the equilibrium amounts forthe steam re-forming and water-gas shift reactions:CH₄(g) +H₂O(g) ⇌CO(g)+  3H₂(g) (steam re-forming)CO(g) +H₂O(g) ⇌CO₂(g)+ H₂g) (water-gas shift) (a) At 1000.°C, what are ΔG° and ΔH° for the steam re-formingreaction and for the water-gas shift reaction? (b) By doubling the steam re-forming step and adding it to thewater-gas shift step, we obtain the following combined reaction:2CH₄(g) +3H₂O(g) ⇌CO₂(g) +CO(g)+ 7H₂(g) Is this reaction spontaneous at 1000.°C in the standard state? (c) Is it spontaneous at 98 atm and 50.% conversion (when 50.%of the starting materials have reacted)? (d) Is it spontaneous at 98 atm and 90.% conversion?

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Chapter17: Spontaneity, Entropy, And Free Energy
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Synthesis gas, a mixture that includes the fuels CO and H₂,is used to produce liquid hydrocarbons and methanol. It is madeat pressures up to 100 atm by oxidation of methane followed bythe steam re-forming and water-gas shift reactions. Because theprocess is exothermic, temperatures reach 950–1100C, and theconditions are such that the amounts of H₂, CO, CO₂, CH₄, and H₂O leaving the reactor are close to the equilibrium amounts forthe steam re-forming and water-gas shift reactions:CH₄(g) +H₂O(g) ⇌CO(g)+  3H₂(g) (steam re-forming)CO(g) +H₂O(g) ⇌CO₂(g)+ H₂g) (water-gas shift) (a) At 1000.°C, what are ΔG° and ΔH° for the steam re-formingreaction and for the water-gas shift reaction? (b) By doubling the steam re-forming step and adding it to thewater-gas shift step, we obtain the following combined reaction:2CH₄(g) +3H₂O(g) ⇌CO₂(g) +CO(g)+ 7H₂(g) Is this reaction spontaneous at 1000.°C in the standard state? (c) Is it spontaneous at 98 atm and 50.% conversion (when 50.%of the starting materials have reacted)? (d) Is it spontaneous at 98 atm and 90.% conversion?

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