For the oxidation of iron
`4Fc_((s))+3O_(2(g))to2Fe_((2))O_(3(s))`,
the entropy change is `-549.45 JK^(-1)mol^(-1)` at 298 K. Though it has negative entropy change the reaction is spontaneous. Why?
`(Delta_(r)H^(theta)=-164xx10^(3)J ml^(-1))`

Explanation

`DeltaG=DeltaH-TDeltaS`
`=1648xx10^(3) J mol^(-1)-298(-549.45)`
`=1648xx10^(3)+163xx10^(3)=-1485xx10^(3)`
`DeltaG` is negative.
Since `DeltaG` is negative, though entropy change is negative the reaction takes place spontaneously.