[salleebrowne]

I know that the concentration of H⁺ determines the pH, but is there a certain pH value that defines a strong acid?

[opti384]

Some strong acids will be HCl and HNO₃. Also, you might want to look at pK_a instead of the pH value if you are to determine whether an acid is strong or weak.

[salleebrowne]

I guess what I really want to know is whether or not a weak acid can still have a low pH like around 2 or 1.

[opti384]

Yes it could. As pH is related to concentration, a weak acid could also have a low pH value.

[rabolisk]

Strength and concentration are related but different. Concentration of [H⁺] determines pH. When we say a strong acid, we mean an acid that will dissociate almost completely in water. Mathematically, these are acids whose pKa is less than that of H₃O⁺, which is -1.7.  If you have a highly concentrated weak acid, you can give rise to a very acidic solution (low pH), but the acid itself is always weak. You can almost think of strength as an intensive property and concentration as an extensive property.