Consider the reaction for the dissolution of ammonium nitrate:
`NH_(4)NO_(3)(s) rarr NH_(4)^(o+)(aq) +NO_(3)^(Theta) (aq)`
`DeltaH =+29.8 KJ mol^(-1), DeltaS = 108.0 J K^(-1) mol^(-1)`.
Calculate the change in entropy of the surroundings and predict whether the reaction is spontaneous or not at `25^(@)C`?

Explanation

The reaction is endothermic, `DeltaH = 29.8 k J mol^(-1)`
`:.` Entropy change in surroundings
`Delta_(surr)S =- (Delta_(sys)H)/(T) =- (29.8 xx 10^(3))/(298) =- 100.0 J K^(-1) mol^(-1)`
`Delta_(sys)S = 108.0 J K^(-1) mol^(-1)`
`:. Delta_("total")S = Delta_(sys)S + Delta_(surr)S = 108.0 - 100.0`
`= 8.0 J K^(-1) mol^(-1)`
There is increase in total enegry so ammonium nitrate dissolves spontaneously.