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At 1 atm and 298 K, entropy change of th...

At 1 atm and 298 K, entropy change of the reaction, `4Fe(s)+3O_(2)(g)to2Fe_(2)O_(3)(s)` is -549.4`J*K^(_1)`. In this reaction, if `DeltaH=-1648kJ`, then predict whether the reaction is spontaneous or not.

Text Solution

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As the reaction enthalpy is negatives ot he reaction is exothermic. Therefore, heat released by the given reaction will be equal to the heat absorbed by the surroudings, consequently they entropy of the surroundings will increase. Heat absorbed by the surroundings`=(-)xx`heat released by the system`=-DeltaH=-(-1648)kJ=+1648kJ`
`therefore `Change in entropy of the surroundings,
`DeltaS_("surr")=-(DeltaH)/(T)=(1648xx10^(3))/(298)J*K^(-1)=5530.2J*K^(-1)`
thus, in this reaction `DeltaS_("univ")=DeltaS_("sys")+DeltaS_("surr")`
`=(-549.4+5530.2)J*K^(-1)=+4980.8J*K^(-1)`
Since `DeltaS_("univ")gt0`, the reaction will occur spontaneously.
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