Why does `"NaOH"` only react with one acidic proton in salicylic acid even though both the carboxyl and the hydroxyl groups could potentially react with it?

`"NaOH"` would react as a base with only one of these protons on salicylic acid for the first deprotonation:

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Yes, technically, salicylic acid has two acidic protons. But there is a significant difference in their acidities. Each proton has its own `"pKa"`, which is a way of measuring acid strength. More negative / less positive `"pKa"` means the proton is more acidic (its `"O"-"H"` bond is weaker) and it is easier for it to get deprotonated by `"OH"^(-)` first.

This is a thermodynamic quality, and is therefore also a measure of the energetic favorability of one proton's dissociation over another for the first deprotonation.

• Carboxylic acid protons in general usually have a `"pKa"` around `5`.
• Alcoholic protons in general usually have a `"pKa"` around `15 - 17`.

Remember that a difference of `1` on a `"p"` scale (such as `"pH"`, `"pKa"`, etc) is an order of magnitude. For example, a `"pKa"` of `4` vs. `5` means that the compound with `"pKa"` `5` is `10` times more basic.

So, it is over `10000000000` (`10^10`) times more energetically favorable for the carboxyl proton to come off first by reaction with `OH^(-)` than for the alcoholic proton to come off first.