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I am wondering if there is any general rule of thumb

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    $\begingroup$ There are hardly any such simple generalisations that can be made in chemistry for the solubility of compounds. If the compound has a large nonpolar domain, clearly it won't be water soluble despite having an -OH group. $\endgroup$ Jul 19 '18 at 1:44
  • $\begingroup$ If we are making generalisations, I would say they are harmful. ;-) $\endgroup$
    – Karl
    Jul 19 '18 at 5:20
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Definitely not. For instance, palmitic acid with a pK$_\mathrm{a}$ of 4.75 has a water solubility of only 0.04 mg/L.

A general rule of thumb is that every oxygen can solubilize four carbon atoms but there are many exceptions. I addressed a similar question here.

Nitrogen also makes the compound more soluble, but there it depends very much on the pH.

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