Can reaction that is endothermic with a decrease in entropy occur spontaneously? Why?

1 Answer
Truong-Son N.
May 9, 2018

No.

An endothermic process absorbs energy into the system. If its entropy then decreases, then the system has tried to condense that energy further.

Energy naturally wants to spread out, so if you compress it and add more and more energy in, the system is going to want to spread the energy out and get rid of it.

Another way to view this is from the Gibbs' isothermal relation:

#DeltaG = DeltaH - TDeltaS#

where #G# is the Gibbs' free energy, #H# is enthalpy, and #S# is entropy.

When the process is endothermic with respect to the system, #DeltaH_(sys) > 0#. A decrease in entropy for the system yields #DeltaS_(sys) < 0#. Temperature must always be positive in units of #"K"#, so...

#overbrace(DeltaG_(sys))^(???) = overbrace(DeltaH_(sys))^((+)) - overbrace(T)^((+))cdot overbrace(DeltaS_(sys))^((-))#

And a positive minus a negative is always positive. Thus, this process is always nonspontaneous, since #DeltaG_(sys) > 0#.

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