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A thermodynamically unfavorable process can be made favorable by coupling it to a spontaneous reaction which involves a series of reactions with a common intermediate.

Which of the following would be an example of a coupled reaction to produce a spontaneous reaction?

A

The formation of ethyne from elemental carbon and hydrogen based on the following reactions:

$2C + H_2 \longrightarrow C_2H_2 \quad ΔG^o= 209 \text{ kJ}$

$C + 2H_2 \longrightarrow CH_4 \quad ΔG^o= -50.8 \text{ kJ}$

$\cfrac{3}{2}C + \cfrac{1}{2}CH_4 \longrightarrow C_2H_2 \quad ΔG^o= -150.9 \text{ kJ}$

B

Extraction of solid copper from copper (I) sulfide based on the following reactions:

$Cu_2S \longrightarrow 2Cu + S \quad ΔG^o= +86.2 \text{ kJ}$

$S + O_2 \longrightarrow SO_2 \quad ΔG^o= -300.4 \text{ kJ}$

C

Extraction of oxygen from iron (III) oxide based on the following reactions:

$Fe2O_3 \longrightarrow 2Fe + \cfrac{3}{2}O_2 \quad ΔG^o= 740 \text{ kJ}$

$2Fe + 3 Cl_2 \longrightarrow 2 FeCl_3 \quad ΔG^o= -334 \text{ kJ}$

D

The formation of dinitrogen tetrahydride based on the following reactions:

$N_2+ 2H_2 \longrightarrow N_2H_4 \quad ΔG^o= 159 \text{ kJ}$

$N_2+ 3H_2 \longrightarrow NH_3 \quad ΔG^o= -16.7 \text{ kJ}$

$NH_3+ NH_3 \longrightarrow N_2H_4+ H_2 \quad ΔG^o= -142.3 \text{ kJ}$

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