The industrial synthesis of methanol can be represented directly by CO _2(g)+3 , H…

CHEMISTRY · Single correct · A Level · Chemistry · Energetics · Energetics

Problem

The industrial synthesis of methanol can be represented directly by CO2(g)+3 H2(g)⟶CH3OH(l)+H2O(l).\text{CO}_2(g)+3\,\text{H}_2(g)\longrightarrow \text{CH}_3\text{OH}(l)+\text{H}_2\text{O}(l). Standard enthalpies of formation (in kJ mol−1\text{kJ}\,\text{mol}^{-1}) are ΔHf∘[CO2(g)]=−393.5\Delta H_f^\circ[\text{CO}_2(g)]= -393.5, ΔHf∘[CH3OH(l)]=−238.6\Delta H_f^\circ[\text{CH}_3\text{OH}(l)]= -238.6, ΔHf∘[H2O(l)]=−285.8\Delta H_f^\circ[\text{H}_2\text{O}(l)]= -285.8. Engineers sometimes run the process through two measured steps: 1. CO2(g)+H2(g)⟶CO(g)+H2O(l)\text{CO}_2(g)+\text{H}_2(g)\longrightarrow \text{CO}(g)+\text{H}_2\text{O}(l) (reported ΔH1=+41.2 kJ\Delta H_1=+41.2\,\text{kJ}) 2. CO(g)+2 H2(g)⟶CH3OH(l)\text{CO}(g)+2\,\text{H}_2(g)\longrightarrow \text{CH}_3\text{OH}(l) (reported ΔH2=−90.7 kJ\Delta H_2=-90.7\,\text{kJ}) Which of the following values for ΔH1\Delta H_1 would make the two-step route thermally consistent with the direct route? (a) +1.08×102 kJ+1.08\times10^{2}\,\text{kJ} (b) +41.2 kJ+41.2\,\text{kJ} (c) −40.2 kJ-40.2\,\text{kJ} (d) +40.2 kJ+40.2\,\text{kJ}

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