Elemental bromine can, in principle, be produced from aqueous bromide ions by a sequence of coupled reactions that do not involve the direct use of electricity. A chemical plant has access to large quantities of the five reactions listed below (all $
\Delta G^\circ$ values are for 298 K).
| Label | Reaction | $
\Delta G^\circ(\text{kJ}\,\text{mol}^{-1}$) |
| --- | --- | --- |
| A | 2 Br⁻(aq) + Cl₂(g) → Br₂(l) + 2 Cl⁻(aq) | +3.2 |
| B | Cl₂(g) + H₂(g) → 2 HCl(g) | –185 |
| C | H₂(g) + Br₂(l) → 2 HBr(g) | +53 |
| D | 2 HBr(g) + Cl₂(g) → 2 HCl(g) + Br₂(l) | –91 |
| E | Br₂(l) + 2 Cl⁻(aq) → 2 Br⁻(aq) + Cl₂(g) | –3.2 |
Only chlorine gas (Cl₂), hydrogen gas (H₂), and aqueous chloride ion (Cl⁻) are available on site in addition to the aqueous bromide feed. Gaseous hydrogen chloride (HCl) may be vented or absorbed as desired.
a. Part 1: (a) Propose a sequence that uses the minimum number of the provided reactions to convert aqueous Br⁻ to elemental Br₂ with a negative overall ΔG∘. List the reactions in the order you would run them and indicate any stoichiometric scaling you apply.
b. Part 2: (b) Show the detailed cancellation of intermediates to obtain a single net reaction expressed with the smallest whole-number coefficients.
c. Part 3: (c) Compute the cumulative ΔG∘ for your net reaction from part (b) and state whether the process is spontaneous under standard conditions.
d. Part 4: (d) The plant manager suggests that running only Reaction A should suffice. Using thermodynamic reasoning based on ΔG∘, explain why Reaction A alone is an inadequate industrial route to Br₂ despite its favorable equilibrium constant being close to unity.