Question

Is the following reaction feasible at 400K?

[ (Fe)₂(O)₃ + 3(C) → 2(Fe) + 3(CO) ]

Enthalpy data:
[ Δ H ° ((Fe)₂(O)₃) = -822 , (kJ/mol) ]
[ Δ H ° ((C)) = 0 , (kJ/mol) ]
[ Δ H ° ((Fe)) = 0 , (kJ/mol) ]
[ Δ H ° ((CO)) = -111 , (kJ/mol) ]

Entropy data:
[ Δ S ° ((Fe)₂(O)₃) = 90 , (J/K mol) ]
[ Δ S ° ((C)) = 6 , (J/K mol) ]
[ Δ S ° ((Fe)) = 27 , (J/K mol) ]
[ Δ S ° ((CO)) = 198 , (J/K mol) ]

A. No, it is not feasible because the Gibbs free energy change is positive.
B. No, it is not feasible because the Gibbs free energy change is negative.
C. Yes, it is feasible because the Gibbs free energy change is positive.
D. Yes, it is feasible because the Gibbs free energy change is negative.

Answer 1

The reaction is feasible at 400K because the Gibbs free energy change is negative.

Step-by-step explanation:

The feasibility of a reaction at a specific temperature can be determined by calculating the Gibbs free energy change, which is given by the equation: ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. In this case, the reaction is:

(Fe)₂(O)₃ + 3(C) → 2(Fe) + 3(CO)

Using the enthalpy and entropy data provided, we can calculate the change in Gibbs free energy and determine its feasibility. At 400K, the change in Gibbs free energy (ΔG) can be calculated as:

ΔG = (ΔH - TΔS) = (-822 kJ/mol - 400K*(90 J/K mol) + 3*(6 J/K mol) - 2*(27 J/K mol) - 3*(-111 kJ/mol)) = -822 kJ/mol - 36 kJ/mol + 18 kJ/mol - 54 kJ/mol + 333 kJ/mol = -581 kJ/mol

Since the change in Gibbs free energy is negative (-581 kJ/mol), the reaction is feasible at 400K. Therefore, the correct answer is Yes, it is feasible because the Gibbs free energy change is negative (Option D).