Weak and strong acids and pH

Acids are proton donors. Bases are proton acceptors.  Acids and bases react by proton transfer.
These are the Bronsted-Lowry definitions. 

H2O can act as both an acid and a base:  H2O(l) + H2O(l)  H3O+ + OH
This reaction is described as strongly reactant favoured because it occurs to a very small (but measureable) extent in pure water.

Substances referred to as acids are stronger than water. 
Strong acids are stronger than water and stronger than H3O+
Weak acids are stronger than water and weaker than H3O+

pH = –log[H3O+] aqueous solution
has no effect on litmus
aqueous solution
turns blue litmus red and has a lower pH than H2O


acid

CH3OH
not acidic
H2O
NH4+
weak acid

weak acid
H3O+
HCl, HBr,HI
HNO3 H2SO4 HClO4
strong acids

The reaction of strong acids with water is product-favoured (in these cases all of the acid dissolved forms products).
HCl(aq) + H2 H3O+ + Cl (aq)
The H3O+ concentration or [H3O+] in the aqueous solution of a strong acid is equal to the concentration of the acid.
Thus the pH can be directly calculated from the  concentration.
For 1
HCl, [H3O+] is also 1
 and the pH is 0. 

Reaction of weak acids with water is reactant-favoured (the extent depending on the acid).
[H3O+] in their aqueous solutions is lower than the initial concentration of the weak acid.
The pH of these solutions is higher than a strong acid in the same concentration.

How do I know if an acid is weak or strong?
There are very few common strong acids.  The formula for these are given in the table above.  If you learn that these are strong, it is fair to assume that other acids that you may encounter are weak.