Pure water conducts electricity very slightly, which shows that it contains ions. They form when one water molecule passes a hydrogen ion to another.
The molecule that gives the hydrogen ion becomes a hydroxide ion, \mathrm{OH^-}, and the one that takes it becomes an oxonium ion, \mathrm{H_3O^+}. The reaction goes both ways, so the ions soon turn back into water molecules.
At 25 °C only about 2 in every billion water molecules have given away a hydrogen ion at any moment, so water is only very slightly ionized.
Square brackets stand for concentration in mol/L, so \mathrm{[H^+]} is the concentration of hydrogen ions. In pure water at 25 °C, \mathrm{[H^+]} and \mathrm{[OH^-]} are both 1.0 × \mathrm{10^{-7}} mol/L.
Their product, \mathrm{[H^+][OH^-]}, is 1.0 × \mathrm{10^{-14}} \mathrm{(mol/L)^2} at 25 °C. It is called the ionic product of water and stays the same in any dilute aqueous solution at that temperature.
Because the product is fixed, knowing one of the two concentrations is enough to work out the other.
In 0.1 mol/L hydrochloric acid, the acid supplies hydrogen ions, so \mathrm{[H^+]} is 0.1 mol/L, or \mathrm{10^{-1}} mol/L. The hydroxide ions fall to \mathrm{10^{-13}} mol/L, so the product is unchanged.
In 0.1 mol/L sodium hydroxide solution the opposite happens: \mathrm{[OH^-]} is \mathrm{10^{-1}} mol/L and \mathrm{[H^+]} falls to \mathrm{10^{-13}} mol/L.
The extra ions combine with ions of the other kind to form water, so hydrogen ions and hydroxide ions are both present in every aqueous solution, but more of one always means less of the other.
A solution is neutral when \mathrm{[H^+]} equals \mathrm{[OH^-]}, as in pure water or in a solution of common salt.
It is acidic when \mathrm{[H^+]} is greater than \mathrm{[OH^-]}, and basic, or alkaline, when \mathrm{[OH^-]} is greater than \mathrm{[H^+]}.
At 25 °C, a neutral solution therefore has a hydrogen ion concentration of 1.0 × \mathrm{10^{-7}} mol/L, an acidic one has more and a basic one has less.
The ionization of water takes in heat, so it goes further at higher temperatures and the ionic product grows. It is about 1.0 × \mathrm{10^{-14}} \mathrm{(mol/L)^2} at 25 °C but about 9.6 × \mathrm{10^{-14}} \mathrm{(mol/L)^2} at 60 °C.
In pure water at 60 °C, \mathrm{[H^+]} and \mathrm{[OH^-]} are both about 3.1 × \mathrm{10^{-7}} mol/L.
The water is still neutral, because the two concentrations are still equal. A value of 1.0 × \mathrm{10^{-7}} mol/L marks a neutral solution only at 25 °C.