# For oxidation of iron. 4Fe(s)+3O_(2)(g)rarr2Fe_(2)O_(3)(s) entropy change is- 549.4 JK^(-1)mol^(-1) at 298 K. Inspite of negative entropy change o

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For oxidation of iron.
4Fe(s)+3O_(2)(g)rarr2Fe_(2)O_(3)(s)
entropy change is- 549.4 JK^(-1)mol^(-1) at 298 K. Inspite of negative entropy change of this reaction, why is the reaction spontaneous?
(Delta_(r)H^(Ө) for this reaction is -1648xx10^(3)J"mol"^(-1))

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One decides the spontaneity of a reaction by considering
DeltaS_("total")(DeltaS_("sys")+DeltaS_(surr")). For calculating DeltaS_("surr") have to consider the heat absorbed by the surroundings which is equal to -Delta_(r)H^(Ө) . At temperature T, entropy change of the surroundings is
DeltaS_("surr")=-(Delta_(r)H^(Ө))/(T) (at constant pressure)
=-((-1648xx19^(3)J "mol"^(1)))/(298K)
5530 JK^(-1)"mol"^(-1)
Thus, total entropy change for this reaction
Delta_(r)S_("total")=5530JK^(-1)"mol"^(-1)+
" " (-549.4JK^(-1)"mol"^(-1))
=4980.6 JK^(-1)"mol"^(-1)
This shows that the above reaction is spontaneous.