Under what temperature conditions are the following reactions spontaneous?

a.   Because the reaction is endothermic, \({\Delta}\) H is positive. Entropy increases as the solid becomes a gas and a liquid, so\({\Delta}\)  S is positive. Since \({\Delta}\) S favors a spontaneous reaction but \({\Delta}\) H does not, to maximize \({\Delta}\)S, this reaction is spontaneous at high temperatures.

b.   Because this reaction is exothermic, the sign on  H is negative. Going from more moles of gas to fewer decreases entropy, so  \({\Delta}\)S is negative. The enthalpy encourages spontaneity; entropy discourages it. To minimize entropy, this reaction will be spontaneous at low temperatures.

c.   Because this reaction is endothermic, \({\Delta}\) H is positive. A solid turning to a gas results in an increase in entropy, so  S is positive. While \({\Delta}\) S is favorable for a spontaneous reaction, \({\Delta}\) H is not. To maximize the effect of \({\Delta}\) S, high temperatures are required. Therefore this reaction will be spontaneous at high temperatures.