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Is testing metal oxide different from testing metal hydroxide using a litmus paper?

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Litmus paper does not test for either metal oxides or metal hydroxides; indeed, it will not change color at all. Try it: put dry $\ce{CaO}$ on dry litmus paper. Litmus does change color with pH+, the negative log10 ratio of $\ce{H+}$ ions to $\ce{OH-}$ ions (the ions may actually be more complex, such as $\ce{H3O+}$, but the idea is the same). This means the substance is in aqueous solution, i.e. in water.

Litmus also changes color with non-metals in solution, such as $\ce{NH3}$, which forms $\ce{NH4OH}$ in water, or with acetic acid, having an excess of $\ce{H+}$ ions.

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