If `Ag_(2)O (s)` is ecposed to atmosphere having pressure 1 atm and temperature 1 atm and temperature `27^(@)C`. Under these conditions comment whether it will dissociate spontaneously or not.
`2Ag_(2)O (s) hArr 3Ag(s)+O_(2)(g)`
`{:("Given :",,DeltaH_(f)^(@)" (kJ/mol)",DeltaS^(@)" (J/K mol) at "27^(@)C),(,Ag(s),0,42.0),(,Ag_(2)O(s),-30,121.0),(,O_(2)(g),0,204.0):}`
(Air consist of `20% O_(2)` by volume)
Take `: R=8.3 JK^(-1) mol^(-1)`

Explanation

`DeltaG^(@)=DeltaH^(@)-T DeltaS^(@)`
`DeltaH^(@)=DeltaH_(f)^(@)("product")-DeltaH_(f)^(@) ("reactants")`
`=2xx30=60 kJ`
`DeltaS^(@)=204+4(42)-2(121)=+130`
`DeltaG^(@)=DeltaH^(@)-T DeltaS^(@)=60000-300xx130`
`DeltaG^(@)=21000 J=-RT ln K`
`log K=-(21000/(300xx8.3xx2.3))`
`K_(p)=2.15xx10^(-4)` atm
The dissociation of `Ag_(2)O` is nonspontaneous at `27^(@)C`