Cliffs AP Chemistry, 3rd Edition

7. 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