pH

Pure water can react with itself very slightly in an acid-base reaction.  The equilibrium constant for this reaction is 10^-14. Note that water does not self ionize because protons are so reactive that they cannot exist free in nature.

H₂O   +   H₂O   D   H₃O⁺   +   HO^-

The concentrations in the equilibrium equation are given in moles per liter, which is molarity. The equilibrium equation for the self-ionization of water is given by the following expression.

The concentration of the hydronium ion must equal the concentration of the hydroxide ion. Since they are the same, the equilibrium equation can be written as...

Since the equilibrium constant is so small, the concentration of the water minus the amount of the water that reacted would equal essentially the same as the original water concentration. If this concentration was one mole per liter, than the equilibrium equation can be now written as...

The square root of 10^-14 is equal to 10^-7. Therefore, the molarity of the hydronium ion concentration is equal to 10^-7 for pure water. 

This is not a convenient way to express acidity so another method was devised. The logarithm of 10^-7 is -7. If this were changed to a positive number, we would have a convenient means of expressing hydronium ion concentrations.

Acidity can now be given as the negative log of the hydronium ion concentration (pH) instead of an exponential number. Negative log is given the symbol p and hydronium concentration is abbreviated as H.  Acidity in aqueous solutions is almost always expressed by the term pH. This concept is used only for solutions with a concentration of 1 molar or less.

pH = -log[H₃O⁺]

Since the log of 10^-7 is equal to -7, the acidity of pure water is equal to a pH of 7.