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Applied to a chemical species, the term expresses a thermodynamic property in reference to a standard, stating that one state is lower in energy than another. The tag should be applied to questions seeking answers with respect to the stability (or instability) of a certain chemical species, molecular entity and/or electronic structure. It must not be applied to questions about the reactivity of particular chemical species.

When applied to a chemical species the term expresses a thermodynamic property. In general this is a relative concept stating that one state has a lower energy than another.
The IUPAC goldbook defines the term stable:

As applied to chemical species, the term expresses a thermodynamic property, which is quantitatively measured by relative molar standard Gibbs energies. A chemical species $\ce{A}$ is more stable than its isomer $\ce{B}$ if $\Delta_\mathrm{r}G^\circ > 0$ for the (real or hypothetical) reaction $$\ce{A -> B},$$ under standard conditions. If for the two reactions: \begin{align} \ce{P &-> X + Y}&& (\Delta_\mathrm{r} G_1^\circ)\\ \ce{Q &-> X + Z}&& (\Delta_\mathrm{r} G_2^\circ)\\ \Delta_\mathrm{r} G_1^\circ &> \Delta_\mathrm{r} G_2^\circ,\\ \end{align} $\ce{P}$ is more stable relative to the product $\ce{Y}$ than is $\ce{Q}$ relative to $\ce{Z}$. Both in qualitative and quantitative usage the term stable is therefore always used in reference to some explicitly stated or implicitly assumed standard. The term should not be used as a synonym for unreactive or 'less reactive' since this confuses thermodynamics and kinetics. A relatively more stable chemical species may be more reactive than some reference species towards a given reaction partner.

As stability is a relative concept, this tag may also be specified for questions seeking information about the instability of certain chemical species. The IUPAC goldbook defines unstable as the opposite of stable:

The opposite of stable, i.e. the chemical species concerned has a higher molar Gibbs energy than some assumed standard. The term should not be used in place of reactive or transient, although more reactive or transient species are frequently also more unstable. (Very unstable chemical species tend to undergo exothermic unimolecular decompositions. Variations in the structure of the related chemical species of this kind generally affect the energy of the transition states for these decompositions less than they affect the stability of the decomposing chemical species. Low stability may therefore parallel a relatively high rate of unimolecular decomposition.)

The tag should be applied to questions seeking answers with respect to the stability (or instability) of a certain chemical species, molecular entity and/or electronic structure. It must not be applied to questions about .

The term "inert" involves both concepts, stability and reactivity (IUPAC goldbook):

Stable and unreactive under specified conditions.