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I have seen several questions on standard states, but none quite get at the issue I'm having in understanding them. In Elements of Physical Chemistry by Atkins and de Paula, they describe standard states for pure substances as the state of the substance at 1 bar pressure at a given temperature and in a given phase of matter. As I read their explanation, standard states exist for all phases of matter at a given temperature, regardless of whether they are thermodynamically stable or not.

For example, Argon would have three standard states at 100 K: one for the solid at 1 bar and 100 K, another for the liquid at the same $p$ and $T$, and another for the gas at the same $p$ and $T$. This makes sense to me, because even though two of these states are unstable, they still can be defined in principle; these standard states, while having the same $p$ and $T$ have different energies, densities, enthalpies, etc. In my mind, this also agrees with the fact that we have non-zero enthalpies of phase transitions.

However, Wikipedia states

The standard enthalpy change of formation for an element in its standard state is zero

which seems to contradict the idea that standard states exist for all of the phases of matter for a given temperature. As I read this, it seems to imply that only the thermodynamically stable phase at the given temperature is the standard state, and other phases of matter for the same element at 1 bar and the same temperature do not have a standard state. I have seen a similar definition in Principles of Chemistry by Munowitz.

Can someone clarify what "standard state" actually means? Every time I read a new definition I feel less certain I really know. Is this just a case where different authors use the same term to refer to different things?

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    $\begingroup$ It should say element in the reference state, see chempedia.info/info/reference_state_of_an_element $\endgroup$
    – Karsten
    Nov 4, 2022 at 2:44
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    $\begingroup$ @Karsten That is the terminology that Atkins and de Paula use. If that is the correct terminology (which I feel is likely the case), then it seems that many (perhaps even most) other books and online resources are very sloppy in their use of terminology and freely interchange standard state and reference state. $\endgroup$
    – scmartin
    Nov 4, 2022 at 3:28
  • $\begingroup$ What they mean is the natural thermodynamic equilibrium state of the substance as it exists at 1 bar and 298 K. $\endgroup$ Nov 4, 2022 at 11:18
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    $\begingroup$ Wikipedia now uses the term "reference state" for choosing the allotrope in defining enthalpy of formation, and "standard state" to describe the state of that allotrope and all other species in the defining chemical equation. $\endgroup$
    – Karsten
    Nov 4, 2022 at 15:33

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[OP] Can someone clarify what "standard state" actually means?

Standard state has a common definition across the field of thermodynamics. Each species, in combination with the physical state, has a standard state; often, these standard states are hypothetical (e.g. a solute at 1 mol/L concentration behaving ideally like an infinitely diluted solute).

[OP] As I read this, it seems to imply that only the thermodynamically stable phase at the given temperature is the standard state, and other phases of matter for the same element at 1 bar and the same temperature do not have a standard state.

This is imprecise language, skipping one step. For the definition of enthalpy of formation, you need the elements in a defined state (without giving the chemical equation). This should be called "reference state" (IUPAC Gold Book entry) of the element, and it includes which allotrope of the element is used, and in which physical state. For ions, it also includes using the aqueous hydronium ion as reference state. Once you know which reference state you agree on (i.e. white or red phosphorus, iodine in the solid or gaseous state, hydronium ion rather than another ion), you also stipulate that this reference species is at standard state, and is at the temperature for which the thermodynamic data is given.

The term reference state is mentioned explicitly in a IUPAC recommendation from 1981:

The use of subscript f was discussed in paragraph 3.3. When ° is additionally used, as in $\Delta_fH°$, the implication is that both the compound in question and its constituent elements are in standard states and that the elements, moreover, are in their reference states; for any given temperature the reference states of the elements will normally be those that are stable at the chosen standard-state pressure and at that temperature.

Stable refers to the state (allotrope and physical state) with the lowest Gibbs energy, in this context.

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