Question

Hematite, Fe₂O₃(s), can be converted to pure iron, Fe(s), in many ways. The solid can be thermally decomposed:​

(a) Fe₂O₃(s) → 2 Fe(s) + 3/2 O₂(g).​

Or, it can be reacted with carbon, hydrogen, or aluminum:​

(b) Fe₂O₃(s) + 3/2 C(s) → 2 Fe(s) + 3/2 CO₂(g)

(c) Fe₂O₃(s) + 3 H₂(g) → 2 Fe(s) + 3 H₂O(g)

(d) Fe₂O₃(s) + 2 Al(s) → 2 Fe(s) + Al₂O₃(s)

At 1000 K, what is the standard Gibbs free energy for reaction (a)?

Select one:

a. +550 kJ mol^-1

b. -86.6 kJ mol^-1

c. -275 kJ mol^-1

d. -913 kJ mol-1
​Can you please show working :)

Answer 1

(a) Fe2O3(s) → 2 Fe(s) + 3/2 O2(g).​

ΔH = ΔH⁰_fproducts – ΔH⁰_freactants

ΔH = [(2x ΔH⁰_fFe(s) )+ ((3/2) x ΔH⁰_{fO2 (g)} )]- [ ΔH⁰_fFe2O3(s) ]

    = [(2x(0))+((3/2)x(0))] - [-824.248] kJ/mol

    = 824.248 kJ/mol

ΔS = ΔS⁰_{f  products} – ΔS⁰_{f  reactants}

ΔS = [(2x ΔS⁰_f  Fe(s) )+ ((3/2) x ΔS⁰_{f  O2 (g)} )]- [ ΔS⁰_fFe2O3(s) ]

    = [(2x(27.28))+((3/2)x(205.03))] - [87.4] J/(mol-k)

    = 274.7 J/(mol-k)

= 0.2747 kJ/(mol-K)

We know ΔG = ΔH - T ΔS Where T = 1000K

= 824.248 - ( 1000 x 0.2747 ) kJ/mol

= +550 kJ/mol

Therefore option (a) is correct