How can we explain solubility of hydrogen sulfide in water?

On my most recent high-school chemistry exam I had a longform question where I was supposed to compare the solubilities in room-temperature water under normal pressure of a few molecules. According to the question $\ce{H2S}$ is very weakly soluble in water, and I needed to explain why.


I suggested that the difference in electronegativity between $\ce{H}$ and $\ce{S}$ is around $0.38$ (on the Pauling scale), which is very close to the threshold we use to categorize polar and non-polar bonds $(0.4).$ So, although the $\ce{H-S}$ bond is technically non-polar, making the whole molecule non-polar, it is very close to being polar, which might make the molecule a very slight dipole, favorizing solubility in water, a polar solvent


The teacher accepted this explanation, although they took away points because I did not mention the hydrogen bonds that supposedly form between the hydrogen sulfide and water molecules.


This confused me because I thought that hydrogen bonds can only form between hydrogen atoms in a $\ce{H-O},$ $\ce{H-N}$ or $\ce{H-F}$ bond and a very electronegative atom in a covalent bond such as $\ce{N},$ $\ce{O},$ or $\ce{F},$ which is what I find in most high-school level resources.


What am I missing out on? Can $\ce{H2S}$ form hydrogen bonds (even very weak) with water when dissolved?




Hydrogen sulfide is actually relatively strongly soluble in water compared with other low-polarity gases. In Earth Science SE, [this answer](https://earthscience.stackexchange.com/questions/22416/do-carbon-dioxide-hydrates-exist-in-nature/22525#22525) explains that water-ice hydrates are most likely to be found with gases having low solubility in liquid water such as methane, and in particular methane hydrates are more common than hydrogen-sulfide hydrates because (on a molar basis) **hydrogen sulfide is 80 times as soluble as methane.**


Hydrogen sulfide is too weak as a hydrogen-bonding agent and an acid for either of these attributes to play much of a role in its relatively large solubility. Rather, the relatively large sulfur atom is more easily polarized than the hydrogen and carbon of methane, so hydrogen sulfide can interact more strongly with water through a dipole-induced dipole interaction. The induced polarity imparted to the hydrogen sulfide also contributes to its being more acidic than methane despite carbon and sulfur having nearly identical electronegativities.


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