Final answer:
To calculate the enthalpy change for the reaction of carbon with steam to produce CO and H2, we use Hess's Law to manipulate and combine given thermochemical equations. By reversing and adjusting the provided reactions, we find that the ΔHrxn is 766.6 kJ.
Step-by-step explanation:
To calculate the reaction enthalpy (Δhrxn) for the combustion of carbon to produce carbon monoxide (CO) and hydrogen (H₂) gas, one can use Hess's Law and the given thermochemical equations. We start by considering the provided equations:
- C(s) + O₂(g) → CO₂(g), ΔH = -393.5 kJ (Equation 1)
- 2CO(g) + O₂(g) → 2CO₂(g), ΔH = -566.0 kJ (Equation 2)
- 2H₂(g) + O₂(g) → 2H₂O(g), ΔH = -483.6 kJ (Equation 3)
Reverse Equation 3 and divide Equation 2 by 2 to align with our target reaction C(s) + H₂O(g) → CO(g) + H₂(g):
- 2H₂O(g) → 2H₂(g) + O₂(g), ΔH = +483.6 kJ
- CO₂(g) → CO(g) + ½O₂(g), ΔH = +283.0 kJ
Summing these adjusted reactions gives us:
- C(s) + 2H₂O(g) - CO₂(g) + 2H₂(g), ΔH = +483.6 kJ + 2(+283.0 kJ)
Upon simplifying, we get:
- C(s) + H₂O(g) → CO(g) + H₂(g), ΔH = ΔHrxn = +483.6 kJ + 283.0 kJ
Thus, the total ΔHrxn for the reaction is 766.6 kJ.