To understand why the oxidation of iron can be spontaneous despite a negative entropy change, we need to delve into the concepts of Gibbs free energy and the relationship between enthalpy, entropy, and temperature. The spontaneity of a reaction is determined by the Gibbs free energy change (ΔG), which is given by the equation:
Gibbs Free Energy Equation
ΔG = ΔH - TΔS
In this equation:
- ΔG is the change in Gibbs free energy.
- ΔH is the change in enthalpy.
- T is the absolute temperature in Kelvin.
- ΔS is the change in entropy.
Analyzing the Given Values
For the oxidation of iron, we have:
- ΔH = -1648 × 103 J/mol (which indicates that the reaction is exothermic)
- ΔS = -5.4 J/K·mol (indicating a decrease in disorder)
Calculating ΔG
To determine whether the reaction is spontaneous, we need to calculate ΔG at 298 K:
Substituting the values into the Gibbs free energy equation:
ΔG = ΔH - TΔS
ΔG = (-1648 × 103 J/mol) - (298 K × -5.4 J/K·mol)
Calculating the second term:
298 K × -5.4 J/K·mol = -1609.2 J/mol
Now, substituting this back into the equation:
ΔG = -1648 × 103 J/mol + 1609.2 J/mol
ΔG = -1648 × 103 J/mol + 0.0016092 × 103 J/mol
ΔG ≈ -1646.39 × 103 J/mol
Interpreting the Result
Since ΔG is negative, this indicates that the reaction is spontaneous at 298 K. Even though the entropy change (ΔS) is negative, the large negative enthalpy change (ΔH) dominates the equation, making ΔG negative overall.
Understanding the Implications
This scenario illustrates an important principle in thermodynamics: a reaction can be spontaneous even when it leads to a decrease in entropy, as long as the enthalpy change is sufficiently negative. In this case, the release of energy during the oxidation of iron drives the reaction forward, overcoming the decrease in disorder.
Real-World Example
Think of it like a snowball rolling down a hill. The snowball represents the energy released (enthalpy), and the hill's slope represents the disorder (entropy). Even if the snowball makes the surrounding area less organized (like the negative entropy), the downhill momentum (negative enthalpy) keeps it rolling forward.
In summary, the oxidation of iron is spontaneous at 298 K due to the significant exothermic nature of the reaction, which outweighs the unfavorable entropy change. This balance between enthalpy and entropy is crucial in determining the spontaneity of chemical reactions.
