# What is the definition of thermodynamic stability?

The term thermodynamic stability is used on this site, but I can't find a good definition. Is is a quantitative or a qualitative concept? Does it apply to a single compound, or a pair of compounds? Does it a relative or an absolute value?

An answer to another question, Thermodynamic stability of benzene derivatives , states

Thermodynamic stability of compounds can be determined by obviously enthalpy of formation ($$\Delta H_{_\mathrm f}$$) of individual compounds. The enthalpy of formation will be lesser if the compound is formed from its constituent elements enjoys some greater stability.

The enthalpy of formation considers the synthesis of a given compound from the elements. If the enthalpy of formation of two substances like bromomethane and chloromethane are different, it might be due to differences in bond strengths (or electronic states) in the two compounds, or differences in bond strengths (or electronic states) comparing elemental bromine and elemental chlorine.

I do understand the concept of thermodynamically favored product. In this case, there are competing reactions leading to different products. Because they start with the same reactants, there is no issue about the reference state. However, if I compare two substance with different composition (i.e. not isomers), I don't know what it means to compare their thermodynamic stability. I also understand local and global minima, as discussed in this answer which references a single set of atoms that undergoes transformation. The problem arises when comparing compounds with different sets of atoms.

Thermodynamics usually is pretty well defined. Thermodynamic stability, however, is a bit of a mystery to me.

• The lack of a clear cut definition (i.e. proposed by those well-known bodies) clearly shows that you are not alone. I personally think that 'stability' in any form only makes sense as a relative concept and that is why I am always very aggravated by the homework assignments to sort carbocations (et.al.) by their stability. As an absolute property: any well in a energy surface is thermodynamically stable, like a molecule that survives plenty of vibrations... but well, that's just my opinion. Feb 19 at 23:18
• Oh well, that linked question and answer really gut my blood pumping... who is teaching this stuff?! Feb 19 at 23:24
• Take it as an energy content. Of course in ideal case it would be better to have a "normalised stability", which in some cases is possible. For instance benzene is more stable than cyclohexane as per pi electrons. I agree that comparing different things isn't really necessary, but I have no examples in mind in which we do this comparison other than in a vague way. When it comes to quantities, we analyse reactions or transformations in which elemental composition is globally the same. Feb 20 at 11:44
• Bumps on energy surface are the very example for kinetic stability (opposed to thermodynamic stability).
– Greg
Feb 20 at 13:23
• @porphyrin but this is unrelated to the question, it just bring in the issue of kinetics. But OP doesn't seem concerned by this aspect, but about the quantity H of formation itself. Feb 21 at 10:44

The full phrase should be thermodynamic stability with respect to ____, where the dash indicates a process, or a chemical reaction.

A mixture of hydrogen and oxygen is thermodynamically unstable with respect to water formation.

Similarly, a diamond is not forever (which may not please De Beers and ladies). It is thermodynamically unstable with respect to conversion to graphite.

Also, thermodynamic stability is a relative term which is often contrasted with reactivity or kinetic stability. Diamond is kinetically stable at room temperature for the same process (lucky ladies can smile again).

• This is as to say "with respect to its formation". I upvoted but it does not say anything that is not already contemplated. Basically OP questions about the meaning of assigning 0 enthalpy of formation to elements in their standard state, and specifically to the fact that Cl2 and Br2 (or anything which is not a single atom) can have different energy stored in. Also, it is nice to recall the kinetic aspect, but that isn't really related to the question. Personally I cannot answer if not that enthalpy of formation must be used for what it is. This answer is correct but doesn't really answers. Feb 21 at 14:29
• We shouldn't restrict to formation only. As I said, it could be any chemical reaction or process. We can say Mn(III) is thermodynamically unstable with respect to disproportionation to Mn(II) and Mn(IV). Feb 21 at 15:30
• Yes fine. But it does not answer the question, for which I also do not have a clear and coincise answer different than what I said in my first comment. That is, we don't really (or should not) assign any meaning to thermodynamical stability different than what it is: standard enthalpy (or G) of formation of the given compound. That can be used of course to close other cycles, as you said. Feb 21 at 15:38

The modern definition of thermodynamic stability is the state of maximum entropy.

Some background information is necessary to make sense of this. I hope you will find the following helpful!

Phenomenologically, thermodynamic stability is the absence of visible change. This is the 'original' definition, employed by experimentalists during the 18th and 19th centuries. If repeated observations of your system - such as measurements of its temperature, pressure, density, colour, etc - don't indicate any change, you can tentatively regard it as stable.

Why tentatively? Because as you've alluded to, some changes can be tortuously slow, so unstable systems can appear stable because the intervals between each observation are fleeting by comparison with the system's rate of change. Such states are called 'metastable'.

The existence of metastable states severely limits the scope of this observational-based definition of stability. A more fundamental definition, that can distinguish between truly stable and merely metastable states is clearly desirable. This alternative, quantitative approach, involves measuring the energy changes that accompany different chemical reactions. This is a tricky process, because the differnet forms of energy transfer accompanying any reaction can be are numerous: heat (thermal conduction); work (exertion of a force or pressure); current (transfer of charge across an electrical potential); to name the most common ones. The basis of this approach is that chemical compounds store energy in their bonds, so by tabulating the energy changes associated with many different reactions, their capacities for storing energy can be calculated.

But remember! The defining property of energy is that it is conserved! A table of bond energies such as that described above cannot by itself function as an indicator of stability. A final step is needed, which is to identify a particular form of energy that is minimized by all chemical reactions, and which will therefore be amenable to the kind of 'potential well' analysis described in the linked answer by Thomij. This form, commonly called 'Gibbs energy', is the energy associated with a change in entropy. It's the increase of entropy that is the true driver of spontaneous processes. Accordingly, the condition of maximum stability for a chemical system is defined by the maximization of its entropy.

What is entropy?

Entropy is a measure of how the energy in a system is distributed among it's constituent particles. More statistically probable distributions have higher entropy. The most probable distribution has the highest entropy. Entropy is often described as a measure of disorder, although I personally find this exposition misleading. Entropy is a subtle and unnerving concept, which whole books have been written about, and which I've taken literally years to make peace with. The best text I can recommend is 'The Second Law' by Henry Bent.

What do you mean by 'the energy associated with an increase of entropy'?

Transfers of energy always accompany some other change, such as an increase in volume, or a flow of current, or a transfer of mass. Indeed, the 'forms' of energy familiar from high school are defined by the nature of their accompanying change (e.g. 'work of expansion' energy is that accompanying the exertion of a pressure, and thereby an increase in volume). An increase in entropy is simply another (admittedly more obscure) example of this. But you can think of entropy as a property somewhat analogous to volume, in the sense of being a feature of a system that can be changed by the application of a particular form of energy. In the case of entropy, the corresponding 'form' of energy is heat, rather than work. As alluded to here, there is a very close connection between temperature and entropy; in fact, a definition of temperature is the limiting ratio between the heat supplied to a system and the change in entropy that results.

• “The modern definition of thermodynamic stability is the state of maximum entropy” Modern? You mean 100+ years old? Thermodynamics as a concept didn’t exist in 18th century, so it makes absolutely zero sense to talk about “old definition”
– Greg
Feb 21 at 18:05
• This is not a constructive criticism now is it Greg. Firstly, it is perfectly reasonable to use the term modern to describe something that occurred more recently than something else, even if it is itself 100+ years old. By nature, 'modern' is a relative term. Secondly, while it's true that the laws of thermodynamics hadn't been discovered in the 18th century, the fundamental notions like heat, work and equilibrium had been recognized, and even put to use in the construction of steam engines. The concept of stability (the subject of the question) is certainly at least this old. Feb 22 at 20:11
• People knew about materials from the beginning of time, so does heat, yet talking about fire as an element that converts metals to gold or phlogiston theory doesn't say much about chemical processes or their stability points. The understanding of energy-like statefunctions, their role in stability criteria is the very beginning of what you call "modern thermodynamics" (nonstandard use). Also, the distinction between thermodynamic and kinetic stability, which is the core of the question can only be interpreted with "modern thermodynamics". I am sorry if it came out harsh.
– Greg
Feb 23 at 16:02
• Who said anything about fire as an element or phlogiston theory? I don't see what purpose your continued sniping serves. As for modern thermodynamics' distinction between thermodynamic and kinetic stability, I made this the core of my answer; the bit you completely ignored. Feb 23 at 17:48
• @Greg not to enter in your discussion but the distinction between thrrnodynamic and kinetic stability is not at the core of the question. It has just been inadvertently introduced into the discussion confusing the thread. I am thinking of writing an answer not really for the question itself but to fix some wrong concepts brought in the thread. Most seems to negate the existence of a state function they speak about, and its use. Feb 26 at 17:08