Question

Using Hess's law, calculate the ΔH value for the following reaction:?

FeO (s) + CO (g) → Fe (s) + 3CO₂

Use these three reactions:

1. Fe₂O₃ (s) + 3CO (g) → 2Fe (s) + 3CO₂ (g) ΔH = -25 kJ
2. 3Fe₂O₃ (s) + CO (g) → 2Fe₃O₄ (s) + CO₂ (g) ΔH = -47.0 kJ
3. Fe₃O₄ (s) + CO (g) → 3FeO (s) + CO₂ (g) ΔH = +38.0 kJ

Answer 1

\(\large FeO (s) + CO (g) → Fe (s) + \color{red}{3}CO_2\)

The number of carbons aren't balanced in the equation given.

Assuming it should be: \(\large FeO (s) + CO (g) → Fe (s) + CO_2\)

to (1): divide by 2
to (2): reverse, divide by 6
to (3): reverse and divide by 3

(1) 1/2 Fe₂O₃ (s) + 3/2 CO (g) → Fe (s) + 9/6 CO₂
(2) 1/3 Fe₃O₄ (s) + 1/6 CO₂→ 1/2 Fe₂O₃ (s) + 1/6 CO (g)
(3) FeO (s) + 1/3CO₂ (g)→ 1/3Fe₃O₄ (s) + 1/3 CO (g)

cancel CO2

(1) 1/2 Fe₂O₃ (s) + 9/6 CO (g) → Fe (s) + 9/6 CO₂
(2) 1/3 Fe₃O₄ (s) + 1/6 CO₂→ 1/2 Fe₂O₃ (s) + 1/6 CO (g)
(3) FeO (s) + 2/6 CO₂ (g)→ 1/3Fe₃O₄ (s) + 2/6 CO (g)

Cancel CO

(1) 1/2 Fe₂O₃ (s) + 6/6 CO (g) → Fe (s) + 6/6 CO₂
(2) 1/3 Fe₃O₄ (s) → 1/2 Fe₂O₃ (s)
(3) FeO (s) → 1/3Fe₃O₄ (s)

Cancel \(Fe_2O_3\) and \(Fe_3O_4\)

(1) 6/6 CO (g) → Fe (s) + 6/6 CO₂
(2) →
(3) FeO (s) →

Add up: FeO (s) + 6/6 CO (g) → Fe (s) + 6/6 CO₂