Given the following data:
`{:("Substance", DeltaH^(@)"(KJ//mol)", S^(@)"(J//mol K)", DeltaG^(@)"(KJ//mol)"),(FeO(s),-266.3,57.49,-245.12),(C("Graphite"), 0, 5.74, 0),(Fe(s),0,27.28,0),(CO(g),-110.5,197.6,-137.15):}`
Determine at what temperature the following reaction is spontaneous?
`" "FeO(S) + C("Graphite") rarr Fe(s) + CO(g)`

Options

A. `298` k
B. `668` K
C. `964` K
D. `DeltaG^(@)` is `+"ve"` , hence the reaction will never be spontaneous

Answer

C

Explanation

`DeltaG=DeltaH - TDeltaS`
`DeltaH = sum DeltaH_(p) - sum DeltaH_(R)`
`DeltaH =- 110.5 + 266.3 = 155.8` KJ
`DeltaS = sumS_(p) - sumS_(R)`
`DeltaS = 197.6 + 27.28 - (57.5 + 5.74) = 161.64 J//"mole" `K
For reaction to be spontaneous, `DeltaG lt 0`
`DeltaH-TDeltaS lt 0" "implies " " T gt (DeltaH)/(DeltaS) = (155800)/(161.64)=964` K