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For the oxidation of iron 4Fc((s))+3O(...

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))`

Text Solution

Verified by Experts

One decide the spontaneity of a reaction by considering.
`triangleS_("total") i.e, (triangleS_(sys)+triangleS_(sum))`. For calculating `triangleS_("surr")` we have to consider the heat absorbed by the surroundings which is equal to `-triangle_r, ,H^@.` At temperature T, entropy change of the `triangleS_("surr")=(triangle_(r)H^@)/T` surroundings is `triangleS_("surr")=(triangle_(r)H^@)/(T)` (at constant pressure)
`=(-1648 xx 10^(3)" J mol"^(-1))/(298K)`
`=5530" JK"^(-1)" mol"^(-1)`
Thus, total entropy change for this reaction.
`triangle_(r)S_("total")=" 5530 JK"^(-1) mol^(-1) +("-549.4JK"^(-1) mol^(-1))=" 4980.6 JK"^(-1) mol^(-1)`
This shows that the above reaction is spontaneous.
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