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Is water an acid or a base?
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If you take into consideration the self-ionization of water, it's both, at the same time.
2 H~2~O -> H~3~O^+^ + ^-^OH
AFAIU, it doesn't change the PH neutrality.
I understand that they self combine/react again? But is that reaction still water?
Autoionization and the reverse reaction are constantly happening in water, and when the reaction is happening at the same rate forward and backward the system is said to be "at dynamic equilibrium" (aka, stuff is happening, but there's no net change)
In pure water, the equilibrium concentration of hydronium and hydroxide are equal, so it's said to be neutral. At room temperature, that equilibrium concentration is approximately 1*10^-7 moles per liter, which gives a pH of 7 (since pH is defined as the negative log _10 of hydronium concentration)