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Pretty much the title. I've heard it said that no (see, e.g here, answer by Lukas Schaedler). To quote his argumentation:

No. Exergonic reactions may be both exothermic or endothermic. Endergonic reactions are endothermic only.

Endergonic and exergonic relate to changes in free energy (delta G), while endothermic and exothermic are related to changes in enthalpy (delta H).

Gibb’s equation written in form of free energy (G), enthalpy (H) and entropy (S) changes:

delta G = delta H - T . delta S

Therefore, it’s possible for an exergonic reaction (delta G < 0; decrease in free energy) to be both exothermic (delta H < 0; heat is released) or endothermic (delta H > 0; heat is consumed). The second scenario may happen if :

T . delta S > delta H

On the other hand, endergonic reactions are endothermic only; delta H needs to be positive and greater than T . delta S in order to delta G > 0

But it's not really clear to me why. In particular, in the example given, why is $\Delta S \ge 0$ (which in my understanding would be necessary to force $\Delta G = \Delta H - T\Delta S$ to be negative)?

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    $\begingroup$ Reactions with ΔG negative are simply non existant. $\endgroup$
    – Maurice
    Commented Sep 1, 2021 at 16:47
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    $\begingroup$ @Maurice - Huh? The definition of an endergonic reaction is one where $\Delta G^\circ > 0$. There are plenty of reactions where this is not the case. $\endgroup$
    – Todd Minehardt
    Commented Sep 1, 2021 at 17:13
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    $\begingroup$ @Damian Birchler: Posts outside chemistry.se may move (or become defunct). Thus, it is better to repost (within reason) the argumentation clearly labeled as a quotation (the > sign at the beginning of the line yields the vertical bar). $\endgroup$
    – Buttonwood
    Commented Sep 1, 2021 at 17:33
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    $\begingroup$ @Todd Minehardt. Challenge : Which reaction can you give as an example of ΔG° < 0 ? $\endgroup$
    – Maurice
    Commented Sep 1, 2021 at 19:07
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    $\begingroup$ @Maurice - Any spontaneous reaction? I mean, the answer to the OP's query is that "endergonic reactions are defined as those where $\Delta G^\circ > 0$." That's it. It's a definition. $\endgroup$
    – Todd Minehardt
    Commented Sep 1, 2021 at 20:03

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The person who posted that answer on Quora was probably confused about the significance of $\Delta S$ as it relates to spontaneity. For isolated systems in general the sign of $\Delta S$ (the change in the entropy of the system) is the relevant criterion determining whether a process is spontaneous, since the entropy of the surroundings remains constant, so changes in the entropy of the universe are limited to the system.

$\Delta G$ is of course the relevant criterion for constant temperature and pressure processes. When the change is negative (exergonic) the process is spontaneous. This places no constraints on $\Delta H$ other than that it should satisfy

$$\Delta H \le T\Delta S$$

which can be interpreted as meaning that changes in the entropy of the surroundings must more than compensate for any potential decrease in the entropy of the system: if the entropy of the system decreases (is negative) then the entropy change of the surroundings ($-\Delta H/T$) must be positive and greater than this in magnitude:

$$\Delta S_\textrm{surr} \ge -\Delta S$$

Freezing of any pure substance above its melting point is an example of a process that is not spontaneous but exothermic. By extension, the reverse is also true: melting of a substance above its freezing point is exergonic (spontaneous) yet requires an input of heat (endothermic).

Note also that $\Delta G^\circ$ determines the position of equilibrium since $\Delta G^\circ = -RT \log K_\textrm{eq}$, but does not suffice to say whether the reaction is spontaneous. For that you need to compute $\Delta G = \Delta G^\circ + RT \log Q$, that is you need information about the starting concentrations.

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  • $\begingroup$ "Freezing above the melting point", can this be achieved? In the lab? $\endgroup$
    – Damian Birchler
    Commented Jan 5 at 16:27
  • $\begingroup$ Should it have been "below its melting point"? $\endgroup$
    – Damian Birchler
    Commented Jan 5 at 16:37
  • $\begingroup$ @DamianBirchler No, I imagine not. That was the point of the (endergonic) example, since the question was whether an exothermic process could be endergonic. $\endgroup$
    – Buck Thorn ♦
    Commented Jan 5 at 17:51
  • $\begingroup$ Yeah, I'm starting to get it now. "Endergonic/not spontaneous" means doesn't happen under the given conditions (temperature, pressure, concentrations, etc.), period. I think my confusion stemmed from the fact that I've always considered "the reaction" to be, e.g., A + B -> C. But it doesn't really make sense to say "A + B -> C" is (not) spontaneous, one would have to say "A + B -> C is not spontaneous at temperature T, pressure p and so forth". To summarize, any reaction is both exo- and endergonic - it depnds on the conditions (temperature, pressure, voltage, ...). $\endgroup$
    – Damian Birchler
    Commented Jan 6 at 11:38
  • $\begingroup$ I've also learned from Wikipedia (can't recall the page anymore, though) that the plain "A + B -> C" would be called a "process", which only together with a range of conditions makes for a full "reaction". I.e. "process" and "conditions" = "reaction". I find this terminology helpful. I don't know, however, if it's widely shared. $\endgroup$
    – Damian Birchler
    Commented Jan 6 at 11:45

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