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Given the following data {:("Substance...

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),0,5.74,0,),(CO(g),-110.5,197.6,-137.15,):}`
Determine at what temperature the following reaction is spontaneous?
`FeO(s)+C("Graphite")rarrFe(s)+CO(g)`

A

`298` k

B

`668` K

C

`964` K

D

`DeltaG^(@)` is `+"ve"` , hence the reaction will never be spontaneous

Text Solution

Verified by Experts

The correct Answer is:
C
`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
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