# Calculate ΔG° for the reduction of the oxides of iron and copper by carbon at 650K, represented by the equations: a) 2Fe_2 O_3 (s) + 3C (graphite) ---> 4Fe (s) + 3CO_2 (g) b) 2CuO (s) + C...

Calculate ΔG° for the reduction of the oxides of iron and copper by carbon at 650K, represented by the equations:

a) 2Fe_2 O_3 (s) + 3C (graphite) ---> 4Fe (s) + 3CO_2 (g)

b) 2CuO (s) + C (graphite) ---> 2Cu (s) + CO_2 (g)

Values of ΔG°f at 700 K are -92 kJ/mol for CuO (s), -632 kJ/mol for Fe_2 O_3 (s), and -395 kJ/mol for CO_2 (g).

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### 1 Answer

We know for any reaction, ΔG°reaction = ΔG°(f)products – ΔG°(f)reactants

a) For the first reaction, at 700K,

ΔG° = 3*ΔG°(f)CO2 + 4*ΔG°(f)Fe– 2*ΔG°(f)Fe2O3– 3*ΔG°(f)C

= 3*(-395) + 4*0 – 2*(-632) – 3*0 (since ΔG°(f) of all pure elements, in their standard state is zero).

= -1185+1264 = 79 kJ/mol.

By similar methods,

b) For the second reaction, at 700K,

ΔG° = ΔG°(f)CO2 + 2*ΔG°(f)Cu– 2*ΔG°(f)CuO– ΔG°(f)C

= (-395) + 2*0 – 2*(-92) – 1*0

= -395+184 = -211 kJ/mol.

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