For oxidation of iron , 4Fe + 3O_{2 ---->}2Fe₂O₃ , inspite of negative entropy change of this reaction why is the reaction spontaneous ?

Entropy change : - 549.4J/k mol

Enthalpy of reaction : -1648 x 10³ J/mol

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Solution

The spontaneity of the reaction is not only dependent on the entropy change of the reaction, but one more factor is there which is defined as the Gibbs free energy.
It is defined as
G = H - T * S
and the change of this quantity should be negative for the reaction(or any process) to be spontaneous.
ΔG = ΔH - TΔS

Now taking T = 27 degrees Celcius = 300 K (room temperature)

we have
ΔG = -1648 * 10^3 - 300* (-549.4 )
= -1648000 + 164820
= - 1483180 J/mol

hence the Gibbs free energy change is negative, so the reaction is spontaneous.
And this concept can be applied anywhere(to any process) in this universe.

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