explain how the ionization of a strong acid differs from that of a weak acid in a solution.?

Bear with me as I think this out:

Arrhenius definition: Acids are compounds that produce [H+] in water.
Bronsted-Lowry definition: Acids release [H+] in water.
Either way, you still get [H+] in water.

Ionization = formation of ions. Water is amphoteric and can act either as an acid or base.
Ionization of water: 2 H20(l) H3O+(aq) + oH-
Kw = [H3O+][OH-] = 1.0x10^-14
        (hydronium)(hydroxide)
        [H30+] or [OH-] by itself is 1.0x10^-7
So the strong the acid, the more H30+ it produces and the lower the pH is because it ionizes almost completely in water.

Example 1: a strong acid such as HCI ionized almost completely in water.
HCI(aq) + H2O ----> Cl- (aq) + H3O (aq)
A 0.1M solution of HCI would contain about 0.1M H3O+, 0.1MCl-, and almost no HCl.
pH= -log [H3O+] = -log(0.1) = 1.0pH

Example 2: Week acids ionize much less. In HF, for example, only about 8% of the molecules are ionized at any given time.
HF(aq) + H2O ---> F- (aq) + H30+ (aq)
A 0.1M solution of HF would contain about 0.008M H3O+, 0.0008M F-, and 0.09M HF and has the pH of about 2.0.