Calculate the enthalpy change for the reaction `Fe_2O_3 +3CO to 2Fe +3CO_2` from the following data.
`2Fe +3/2 O_2 to Fe_2O_3 , DeltaH`=-741 kJ
`C+1/2O_2 to CO , DeltaH`=-137 kJ
`C+O_2 to CO_2 , DeltaH`=-394.5 kJ

Explanation

`DeltaH_(f)(Fe_(2)O_(3))=--741kJmol^(-1)`
`DeltaH_(f)(CO)=--137kJmol^(-1)`
`DeltaH_(f)(CO_(2))=--394.5kJmol^(-1)`
`Fe_(2)O_(3)rarr3COrarr2Fe+3CO_(2)DeltaH_(r)=? `
`DeltaH_(r)=sum(DeltaH_(f))_("product")-sum(DeltaH_(f))_("reatants")`
`DeltaH_(r)=[2DeltaH_(f)(Fe)+3DeltaH_(f)(CO_(2))]-[DeltaH_(f)(Fe_(2)O_(3))+3DeltaH_(f)(CO)]`
`DeltaH_(f)=[0+3(-394.5)]-[-741+3(-137)]`
`DeltaH_(f)=[-1183.5]-[-1152]`
`DeltaH_(f)=-1183.5+1152=-31.5kJ mol^(-1)`