In all cases, acids yield protons ( or hydronium ions H3O+) and bases yield OH- (hydroxide) ions in aqueous solutions.
The H3O+ ion is considered to be the same as the H+ ion as it is the H+ ion joined to a water molecule. The proton cannot exist in aqueous solution, due to its positive charge it is attracted to the electrons on water molecules and the symbol H3O+ is used to represent this transfer.
The equation can be written as:
H+ + H2O(l) → H3O+(aq).
This is hydrolysis as it is involving water as a reactant.
Consider the first equation in the question , the ionisation equation of water:
H2O(l) + H2O(l)→H3O+(aq) + OH-(aq)
The H3O+ is the conjugate acid of H2O. So H3O+ is used as a shorthand for a proton in aqueous solution. In a non-aqueous solution the proton would form a different structure.
The second equation:
H2O(l) → H+(aq) + OH-(aq)
Shows that H2O is made up of equal parts H+ and OH- ions and is amphoteric (can be an acid or a base) having a deprotonated form (OH-). The ionic component is at a very low concentration and a water molecule is generally considered covalent with a dipole moment favouring a slight positive charge.
The H3O+ ion concentration in pure water at 25° C is 10^-7 dm^-3. This can be written as:
[H3O+] = 10^-7
where the symbol [ ] means the "molarity of" (units in moles dm^-3).
The number of H3O+ and OH- ions formed by the ionisation of pure water must be equal ( from the equation):
[H3O+] = [OH-] = 10^-7).
This shows that pure water is neither acidic or basic, it is neutral. The product of [H3O+] = [OH-] is the ionic product of water.
[H3O+][OH-]=10^-7 × 10^-7 = 10^-14
shows that in aqueous (water) solutions, whether acidic, basic or neutral, the product of the ion concentrations equals 10^-14.
Acidic solutions contain more H3O+ ions than OH- ions. For basic solutions it is the reverse.
Therefore a water solution is :
Neutral when [H3O+]= 10^-7.
Acidic when [H3O+] > 10^-7.
Basic when [H3O+] < 10^-7.