Estimate the `K_(sp)` of `AgBr`. Given `Delta_(f)H^(Θ)` of `Ag^(o+), Br^(Θ)`, and `AgBr` are `25.31,-28.9`, and `-23.8kcal, DeltaS^(Θ)` of `Ag^(o+), Br^(Θ)`, and `AgBr` are `17.7, 19.3,` and `-26.6 cal//K`.

Explanation

`AgBr(s) hArr Ag^(o+) + Br^(Θ)`
To determine `K_(sp)`, one can calculate `DeltaG^(Θ)` from `DeltaH^(Θ)` and `S^(Θ)` data.
`DeltaH^(Θ) = Delta_(f)H^(Θ) + Delta_(f)H^(Θ) (Br^(Θ)) - Delta_(f)H^(Θ) (AgBr)`
`=(25.31 kcal) + (-28.9 kcal)-(-23.8 kcal)`
`= 20.2 kcal`
`DeltaS^(Θ) = S^(Θ) (Ag^(circ)) + S^(Θ) (Br^(Θ)) - S^(Θ) (AgBr)`
`= (17.7 cal K^(-1)) + (19.3 cal K^(-1)) - (25.6 cal K^(-1))`
`= 11.4 cal K^(-1)`
`DeltaG^(Θ) = DeltaH^(Θ) - T DeltaS^(Θ) = (20200cal) - (298K) (11.4cal K^(-1))`
`= 16800 cal`
`DeltaG^(Θ) = (-2.30RT) (log K_(sp))`
`log K_(sp) = (-DeltaG^(circ))/(2.30RT) = (-16800cal)/((2.30)(1.99calK^(-1))(298K)) = 123`
`K = 4.8 xx 10^(-13)`