In an industrial process

CHEMISTRY · Multi-part · AP · Chemistry · Thermodynamics and Electrochemistry · Thermodynamics and Electrochemistry

Problem

In an industrial process, the endergonic transformation Y→XY \rightarrow X, ΔG∘=+65 kJ mol−1\Delta G^\circ = +65\,\text{kJ\,mol}^{-1} must be driven by coupling it to an exergonic electrochemical reaction carried out in a separate but connected compartment at 298 K298\,\text{K}. The company considers using the overall reaction of a hydrogen-oxygen fuel cell, 2 H2(g)+O2(g)→2 H2O(l)2\,\text{H}_2(g) + O_2(g) \rightarrow 2\,\text{H}_2\text{O}(l), which under standard conditions has an open-circuit cell potential E∘=+1.23 VE^\circ = +1.23\,\text{V} and involves the transfer of 4 moles of electrons per mole of the above reaction. Faraday’s constant: F=96 485 C mol−1 e−F = 96\,485\,\text{C\,mol}^{-1}\,\text{e}^{-} (a) Calculate the standard free-energy change, ΔG∘\Delta G^\circ(fuel cell), for the hydrogen-oxygen reaction. Include the appropriate sign and units. (b) Write a balanced overall equation that couples one mole of Y→XY \rightarrow X with a fractional or integral number, nn, of the fuel-cell reaction so that electrons are conserved and no net intermediates appear. (c) Determine the smallest value of nn (assume nn can be fractional if necessary) that makes the overall ΔG∘\Delta G^\circ no greater than −25 kJ mol−1-25\,\text{kJ\,mol}^{-1}. Show your calculation clearly. (d) Identify and discuss two practical considerations, other than thermodynamic favorability, that the plant must address when implementing this coupled electrochemical-chemical process on a large scale.

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