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For the equilibrium NiO(s)+CO(g) hArr ...

For the equilibrium
`NiO(s)+CO(g) hArr Ni(s)+CO_(2)(g)`
`DeltaG^(ɵ) (J mol^(-1))=-20700-11.97 T`. Calculate the temperature at which the product gases at equilibrium at `1` atm will contain `400` ppm of carbon monoxide.

Text Solution

Verified by Experts

For the give reaction,
`NIO(s)+CO(g) overset(K_(p))(hArr)NI(s)+CO_(2)(g)`
`:. K_(p)=P_(CO_(2))/P_(CO)`
since `P_(CO) lt lt P_(CO_(2))`, hence
`K_(p)=1/P_(CO)=(1)/(400xx10^(-6))=2500`
we know, `DeltaG^(ɵ)=-RT ln K_(p)`
`:. ln K_(p)=(-DeltaG^(@))/(RT)=(-(-20700-11.97T))/(RT)`
or `ln K_(p)=(20700+11.97T)/(RT)`
`rArr ln (2500)=(20700+11.97T)/(8.314xxT)`
`rArr ln (2500)(8.314T)=20700+11.97 T`
`rArr 65.049T=20700+11.97T`
`rArr 65.049T-11.97T=20700`
`rArr 53.079 T=20700`
or `T=20700/53.079 ~~ 389.9 K`
`:.` Temperature at equilibrium `=389.9 K`
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