Is a reaction that is endothermic and becomes less positionally random spontaneous or non spontaneous? What about more positionally random? Is there enough information to tell?

Question

Is a reaction that is endothermic and becomes less positionally random spontaneous or non spontaneous?  What about more positionally random?  Is there enough information to tell?

Cameron Andrews · Accepted Answer

Yes, it is certainly nonspontaneous, at all temperatures, if there is more order in the products, AND the reaction absorbs energy from the surroundings.

If there is less order in the products, AND the reaction absorbs energy from the surroundings, it is not obvious without knowing the temperature.

Recall the relationship between Gibbs' free energy, enthalpy, and entropy:

#DeltaG = DeltaH - TDeltaS#

We know that:

When a reaction is endothermic, energy is absorbed, and thus, #DeltaH > 0#. Furthermore, when a reaction becomes more ordered (less "positionally random"), the entropy has decreased (entropy increases with more motion in the system and vice versa), meaning that #DeltaS < 0#.

Thus, #DeltaG# is necessarily positive since #T >= "0 K"#, always. Let us assume that #T > 0#:

#color(blue)(DeltaG) = (+) - (+)(-)#

#= (+) - (-)#

#= (+) + (+)#

#= color(blue)((+))#

Therefore, the reaction is nonspontaneous at all temperatures if #DeltaH > 0# AND #DeltaS < 0#.

However, if #DeltaS > 0# (i.e. the particles become more "positionally random"), then it matters what the temperature is...

#color(red)(DeltaG) = (+) - (+)(+)#

#= (+) - (+)#

#= color(red)(???)#

Thus, this kind of reaction is nonspontaneous at low temperatures, and spontaneous at high temperatures.

Cooper Anderson · Answer

undefined An endothermic reaction that becomes less positionally random is typically non-spontaneous. However, if the reaction becomes more positionally random, it can be spontaneous, provided that the increase in entropy (randomness) outweighs the energy required for the endothermic process. Whether the reaction is spontaneous or non-spontaneous depends on the balance between enthalpy (heat) and entropy (randomness), and more information would be needed to determine this balance accurately.