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Given that a solution contains $\ce{OH-}$ ions can we sufficiently determine the substance is a base? From my understanding, an acid may still contain $\ce{OH-}$ ions. However, the concentration of $\ce{H+}$ ions must exceed this. Is this correct?

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An acid can have some $\ce{OH-}$ ions, as well as $\ce{H+}$. It is the relative ratio that determines if the substance is acid or alkaline. Think of it as mismatching socks, where you must pair 10,000,000 red with 10,000,001 blue socks. There's one blue left over, so blue wins. (Hmm... in that analogy, think red and blue litmus, and there's one more $\ce{OH-}$ ion.)

Also, a zwitterion has both acidic and basic groups, and one can predominate over another, depending on the the pH.

Amino acids and sulfamic acid are two examples. Some amino "acids", such as arginine, are more basic, while aspartic acid is more acidic. The bumbling biochemist offers a more complete explanation of the behavior of zwitterions.

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