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For example, why do some solutions not cause any injuries at pH 2 while HCl does?

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Injury is not solely related to how strongly acidic a solution is, as there are several mechanisms by which organic matter is damaged from exposure to acids, not just protonation. It is also highly dependent on the type and length of exposure. Aqueous $\ce{HF}$ is likely considerably corrosive after skin contact even at pH 2, mostly because of $\ce{F^-}$ which is a rather reactive ion with a strong tendency to abstract $\ce{Ca^{2+}}$ (in fact, the fact that $\ce{HF}$ is a weak acid makes it even more dangerous because the undissociated $\ce{HF}$ is much less polar and the molecules can cross the skin barrier more easily, allowing direct access to muscle and bone which can be severely damaged). Aqueous $\ce{HCN}$ also forms weak acids, but again $\ce{CN^-}$ ions are extremely toxic as they block cell respiration. The risk is compounded by the fact that $\ce{HCN}$ is a very volatile substance and can be released as a gas from concentrated or acidic solutions.

With regards to $\ce{HCl}$, you need to be a bit more specific. What kind of injury? $\ce{HCl}$ itself is a relatively safe acid in dilute solution, even though it's a strong acid, as it does not have strongly oxidising/reducing/dehydrating/toxic properties and is only volatile at rather high concentrations. Remember that $\ce{HCl}$ is even used as an integral part of our digestive system, being the species that allows stomach acids to reach pH 1-2.

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