Consider the following reaction, which is involved in the purification of iron from its ores. Some relevant thermodynamic data is shown below.
Fe2O3 (s) + 3CO(g) → 2Fe(s) + 3 CO2 (g) ΔS° = 15.2 J/K
Substance | ∆Hf° (kJ/mol) | S° (J/K/mol) | ∆Gf° (kJ/mol) |
Fe2O3(s) | –824.2 | 87.40 | ?? |
CO(g) | –110.5 | 197.6 | –137.2 |
Fe(s) | 0 | ?? | 0 |
CO2(g) | –393.5 | 213.6 | –394.4 |
a) Find ΔH° for the reaction above.
b) Find S° for solid iron.
c) Find ∆Gf° for Fe2O3.
*** I know the answers, I just need help on the steps. ***
a)
dH= Hprod - Hreact
dH = (2*0 + 3*-393.5) - (-824.2 + 3*-110.5)= -24.8 kJ
b)
dS = Sprod - Sreact
dS = 2*S-Fe + 3*S-CO2 - (S-Fe2O3 + 3*S-CO)
15.2 = 2*S-Fe + 3*213.6 - (87.4 + 3*197.6)
S-Fe = ((15.2) - (3*213.6 - (87.4 + 3*197.6) ))/2
S-Fe = 27.3 J/molK
c)
dG for Fe2O3
so
dG = dGprod - dGreact
dG = dH - T+dS = (-24800) - 298*(15.2) = -29329.6 J/mol = -29.32 kJ/mol
so
-29.32 = 2*0 + 3*-394.4 - (G-Fe2O3 + 3*-1372.)
-29.32 + 3*394.4 -3*(137.2) = dG-Fe2O3
dG - Fe2O3 = -742.28 kJ/mol
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