- Given the following data:
Fe 2 O 3 (s) + 3 CO(g) →2 Fe(s) + 3 CO 2 (g) ∆H°= −27 kJ/mole
3 Fe 2 O 3 (s) + CO(g) →2 Fe 3 O 4 (s) + CO 2 (g) ∆H°= −61 kJ/mole
Fe 3 O 4 (s) + CO(g) →3 FeO(s) + CO 2 (g) ∆H°= 38 kJ/mole
Species ∆S°(J ⋅K–1⋅mole–1)
Fe 2 O 3 (s)87.0
CO(g) 190.0
Fe(s)27.0
CO 2 (g) 214.0
Fe 3 O 4 (s) 146.0
FeO(s)61.0
Calculate the approximate ∆G°(at 25°C) for the reaction
FeO(s) + CO(g) →Fe(s) + CO 2 (g)
A. −26 kJ/mole
B. −13 kJ/mole
C. 13 kJ/mole
D. 26 kJ/mole
E. 39 kJ/mole
Answer: B
To solve this problem, use the Gibbs-Helmholtz equation:
∆G°= ∆H°−T∆S°
Step 1:Solve for ∆H°. Realize that you will have to use Hess’s law to determine ∆H°. Be sure
to multiply through the stepwise equations to achieve the lowest common denominator (6), and
reverse equations where necessary.
sg s g
sg sg
sg sg
sgs gFe CO
3969
3
6222
6666
Fe O CO Fe CO
2Fe O CO Fe O CO
FeO CO Fe O CO
FeO CO
32
23
24
2
2
34 2
3
"
"
"
++
++
++
++
"
^ _ ^ _
^ _ ^ _
^ _ ^ _
^ _ ^ _
h i h i
h i h i
h i h i
h i h i
81
76
kJ/mole
kJ/mole
61 kJ/mole
- 96 kJ/mole
∆H kJ mole/ kJ mole/
6
%=-^96 =- 16
Energy and Spontaneity