I am looking for an endothermic reaction dH > 0 for which the net volume change is negative, e.g. gases reacting to form a liquid. Does anybody have an illustrative example?

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    $\begingroup$ $\Delta H^o <0$ would be an exothermic reaction (thermal energy is released) (at constant p, with pV-work only). Are you looking for an endothermic reaction with $\Delta V <0$, or an exothermic reaction with $\Delta V <0$? $\endgroup$
    – theorist
    Sep 21 '21 at 3:59
  • $\begingroup$ @theorist Right, of course, I was sloppy… I am looking for an endothermic reaction. $\endgroup$
    – Jan Joswig
    Sep 21 '21 at 4:08

An example of an endothermic reaction with $\Delta V < 0$ is:

$$\ce{C(graphite)->C(diamond)}, \,\,\,\,\Delta H^o_r (\pu{298.15 K}) = 1.871 ± \pu{0.074 kJ//mol}$$

Source: https://atct.anl.gov/Thermochemical%20Data/version%201.118/species/?species_number=951

And $\Delta V < 0$ because:

$$\rho_{diamond} = \pu{3.515 g//cm^3}; \,\,\ \rho_{graphite} = \pu{2.16 g//cm^3}$$

You'd expect this with diamond, since its formation is favored by high temperatures and pressures.

Source: Wolfram Mathematica Chemical Database (not the primary source, but Wolfram doesn't give that in their answer).

An entire class of reactions that would satisfy your requirements would be most* combustion reactions, when run in reverse (making them endothermic), and at a high enough temperature that water would be gaseous, e.g.:

$$\ce{ 12CO2(g) + 11 H2O (g)->C12H22O11(s) + 12 O2(g)}$$

$$\ce{3 CO2(g) + 4 H2O(g)-> C3H8(g) + 5 O2(g)}$$

[*This wouldn't work with the combustion of methane, which has equal numbers of reactant and product molecules (that's of course not considering small volume changes due to non-ideality, which could go either way).]

For three other examples of endothermic reactions with $\Delta V<0$, see my answer here: Any examples of reactions where simpler molecules are combined into more complex ones and are endothermic at the same time?

  • $\begingroup$ Thank you, these are very helpful examples! $\endgroup$
    – Jan Joswig
    Sep 21 '21 at 4:50

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