Do bases contain hydrogen ions (h+)

One definition of an acid is a molecule that can donate a H+ ion. So for example if you have an acid such as hydrochloric acid (HCl) in water, HCl will donate it's H+ to the H2O molecule, forming Cl- and H3O+.  

In contrast, a base is a molecule that accepts H+ ions. This means a base such as NH3 reacts with H2O to form OH- and NH4.

So when pH is measured, it is the ratio of H3O+ ions to OH- ions. If there are more H3O+ ions, you then know that there are more acidic molecules in the solution, since they must be giving away their H+ ions.  

So a solution with an acid in it will have more H3O+ ions (which can be described as H+ ions) in it. However, an acid by itself will have nothing to donate H+ ions to.

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