Fe2O3(s) + 3 CO(g) −→ 2 Fe(s) + 3 CO2(g)
Given:
2 Fe2O3(s) −→ 4 Fe(s) + 3 O2(g)
∆H = 1616.6 kJ/mol
CO(g) −→ C(s) + 1
2
O2(g)
∆H = 110.5 kJ/mol
C(s) + O2(g) −→ CO2(g)
∆H = −393.5 kJ/mol
Answer in units of kJ/mol.
To find the enthalpy change (∆H) for the reaction Fe2O3(s) + 3 CO(g) → 2 Fe(s) + 3 CO2(g), you can use the concept of Hess's Law.
Hess's Law states that if a reaction can be expressed as the sum of two or more reactions, then the enthalpy change for that reaction is equal to the sum of the enthalpy changes of the individual reactions.
In this case, we can break down the given reaction into three separate reactions:
1. 2 Fe2O3(s) → 4 Fe(s) + 3 O2(g)
(∆H = 1616.6 kJ/mol) - This is the given reaction.
2. CO(g) → C(s) + 1/2 O2(g)
(∆H = 110.5 kJ/mol) - This is the given reaction.
3. C(s) + O2(g) → CO2(g)
(∆H = -393.5 kJ/mol) - This is the given reaction.
Now, let's manipulate the equations and their corresponding enthalpy changes to obtain the desired reaction:
Step 1: Reverse reaction 1 by multiplying it by -1:
-2 Fe2O3(s) + 4 Fe(s) + 3 O2(g)
Step 2: Multiply reaction 2 by 3 to obtain the same number of CO molecules as in the desired reaction:
3 CO(g) → 3 C(s) + 3/2 O2(g)
Step 3: Multiply reaction 3 by 2 to obtain the same number of CO2 molecules as in the desired reaction:
2 C(s) + 2 O2(g) → 2 CO2(g)
Now we can add all the reactions together:
-2 Fe2O3(s) + 4 Fe(s) + 3 O2(g) + 3 CO(g) + 3 C(s) + 3/2 O2(g) + 2 C(s) + 2 O2(g) → 2 Fe(s) + 3 CO2(g) + 2 CO2(g)
Simplifying the equation gives us:
-2 Fe2O3(s) + 4 Fe(s) + 5/2 O2(g) + 3 CO(g) + 5 C(s) → 4 Fe(s) + 5 CO2(g)
Notice that the Fe(s) and CO(g) on both sides cancel out, leaving us with:
-2 Fe2O3(s) + 5 C(s) + 5/2 O2(g) → 5 CO2(g)
Now we can sum up the enthalpy changes of the individual reactions to obtain the overall enthalpy change for the desired reaction:
∆H = ∆H1 + ∆H2 + ∆H3
∆H = (1616.6 kJ/mol) + (3 * 110.5 kJ/mol) + (2 * -393.5 kJ/mol)
∆H = 1616.6 kJ/mol + 331.5 kJ/mol - 787 kJ/mol
∆H = 1161.1 kJ/mol
Therefore, the enthalpy change (∆H) for the reaction Fe2O3(s) + 3 CO(g) → 2 Fe(s) + 3 CO2(g) is 1161.1 kJ/mol.