Given the following data :

Determine at what temperature the following reaction is spontanous?
`FeO(s)+C_("graphite")toFe(s)+CO(g)`

Options

A. 298 K
B. 668 K
C. 966K
D. `DeltaG^(@)` is +ve, hence the reaction will never be spontaneous.

Answer

C

Explanation

`DeltaH_("reaction")=sum{DeltaH_(f" "Fe(s))^(@)+DeltaH_(f" "CO" "(g))^(@)}-{DeltaH_(f" "FeO(s))^(@)+DeltaH_(f" "C("graphite"))^(@)}`
`=(0-110.5)-(-266.3+0)=155.8kJ" "mol^(-1)`
`DeltaS_("reaction")=sum[S_(Fe(s))^(@)+S_(Co(g))^(@)]-[S_(FeO(s))^(@)+S_(C("graphite"))^(@)]`
`=(27.28+197.6)-(57.49+5.74)`
`=161.65JK^(-1)" "mol^(-1)`
For spontaneous reaction, `T gt (DeltaH)/(DeltaS),T gt (155.8xx1000)/(161.65)`
`thereforeT gt 966K`