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The standard enthalpy of formation $\Delta H_f^°$ of pure elements is zero by definition. Why is that a convention? It is true that enthalpy is defined unless a constant (like energy and entropy), but enthalpy of formation is actually a variation of enthalpy, so we don't really care.

Also, how could we possibly choose something else than zero if there's no heat transfer?

Note: I'm using General Chemistry (Ralph Petrucci)

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  • $\begingroup$ Entropy is absolute. No standards required. Energy, as you note, does require a reference. I am hard pressed to think of a reference besides elements in their standard state that would be so simple, universal, and reasonably self-consistent. $\endgroup$
    – Zhe
    Aug 25, 2020 at 14:23
  • $\begingroup$ Energy definitely needs a reference but energy change does not. $\endgroup$ Aug 25, 2020 at 14:26
  • $\begingroup$ Well, the enthalpy of formation of pure elements from pure elements is indeed zero. $\endgroup$
    – Poutnik
    Aug 25, 2020 at 15:07
  • $\begingroup$ Note that by the Chemistry SE site policy ( in contrary to e.g. Physics SE), using LaTeX or MathJax formatting for question titles is highly discouraged, as it affects information indexing/searching. $\endgroup$
    – Poutnik
    Aug 25, 2020 at 15:27
  • $\begingroup$ Enthalpy is similar to gravific energy. It needs a reference. For gravific energy, the zero is arbitrary, and it is at the sea level. For enthalpy considerations, it is also arbitrary, The zero has been once decided to be defined by the pure elements. Other choices could have been possible, like the situation where all atoms are separated from one another. But the scientists all agreed to accept that the zero enthalpy is obtained when the elements are in their pure state at ordinary temperature and pressure. $\endgroup$
    – Maurice
    Aug 25, 2020 at 15:56

1 Answer 1

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It starts with this: The standard enthalpy of formation of any substance, $\Delta H^\circ_\mathrm{f}$, is (by convention) defined as the enthalpy change for the reaction at 1 bar and a specified temperature (usually $\pu{298.15 K}$), in which the product is 1 mole of that substance, and the reactants are its component elements in their respective standard states.

For instance, $\Delta H^\circ_\mathrm{f}$ for $\ce{H2O_{(l)}}$ is equal to $\Delta H^\circ$ for the following reaction at standard state:

$$\ce{H2_{(g)} + 1/2O2_{(g)}->H2O_{(l)}},$$

since $\ce{H2_{(g)}}$ and $\ce{O2_{(g)}}$ are the respective standard states for hydrogen and oxygen.

Once you've accepted this definition as the convention for determining $\Delta H^\circ_\mathrm{f}$ for any substance, it directly follows that the value of $\Delta H^\circ_\mathrm{f}$ for any element in its standard state must be zero. For instance, $\Delta H^\circ_\mathrm{f}$ for $\ce{H2_{(g)}}$ is equal to $\Delta H^\circ$ for the following reaction:

$$\ce{H2_{(g)} -> H2_{(g)}},$$

which is necessarily zero.

To give an analogy: Suppose you define the "altitude of formation", $\Delta z_f$, of any location on earth as the change in altitude necessary to reach that location from sea level.

Hence $\Delta z_f$ for the summit of Mt. Everest is $\Delta z$ for the altitutude change associated with:

$$\ce{sea level -> summit of Everest},$$

which is 29,029 feet.

It necessarily follows, from this convention, that $\Delta z_f$ for any location at sea level is zero, since that would be equal to $\Delta z$ for:

$$\ce{sea level -> sea level}$$.

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    $\begingroup$ Ooooh! Thank you so much, this is what I've been looking for so far. Maybe I was misinterpreting the other answers, though. I'll accept your answer because I consider it to be the clearest one. The key word was "once you have accepted this convention, it directly follows..." that is coherent with how I expected it to be. Some books, after defining the enthalpy of formation, say we choose (not that it directly follows) the zero for pure elements as a convention. I suppose that was bad phrasing or maybe mistranslations in the italian edition. $\endgroup$ Aug 27, 2020 at 9:38

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