Lao-Tzu pretty much covered most of the basics (or should I say... acidics) about strong acids. I'd just like to make a few more comments, just to clarify some things. Also, I'm writing this under the assumption that you have a rudimentary understanding of acids and bases and know that pH = -log10 {H+} where {H+} is the concentration of H+ in a solution (or, equivalently, hydronium ion)
1. Yes, strong acids DO have a pH
This is sorta obvious, but if you're a chemistry n00b, this is a point that one may wonder about. For example, you have an undilute solution of HCl, whose H+ activity (sorta like concentration, except not) is 10.0 M. The pH will be -log10 (10.0) = -1.00. So yeah, you can have negative pH with such strong acids. Another thing to note is that yes, strong acids DO have acid dissociation constants, Ka. Unlike those of weak acids, though, their acid dissociation constants are greater than 1. Typically, much greater. For example, Hydrochloric acid has a pKa of -8.0. This would mean it's Ka is 10-(-8.0) = 100,000,000. This is pretty effing large. Looking at the dissociation equation:
HCl + H2O --> H3O+ + Cl-
Such a large Ka would mean that the right side of the equation is STRONGLY favored. This also generally applies to OTHER strong acids. This is also why we don't use the equilibrium arrows on strong acids: it goes so much to the right side that it's treated as if it dissociates completely.
I suppose now would be a good time to say that the strength of an acid is measured by how much it dissociates. Which is, of course, put into numbers with an acid dissociation constant. So that's why "strong acids" are deemed strong: they dissociate so much, since their acid dissociation constants are greater (much greater) than 1, so the products (hydrogen ion and conjugate base) are favored.
Ah, Mr. Marx's favorite mantra in his AP Chemistry class. (Our class made a shirt out of it, which says "I am the conjugate base of a strong acid," implying our own ineptitude, regardless of how inept we truly were).
So, just a quick rundown of what a conjugate base is. Let's take the example of Hydrochloric acid again. Let's just take another quick look at the dissociation reaction.
HCl + H2O --> H3O+ + Cl-
HCl is the strong acid. Water, in this equation, acts as a base. HCl "donates" a proton (i.e. a hydrogen ion) to water, and water becomes the "conjugate acid," or the hydronium ion (H3O+). The chloride ion is all alone; it is the "conjugate base," the acid's leftover after it dissociates. Make sense?
Well, what I mean by calling this particular conjugate base pathetic is that it's not very good as a base. According to the Bronsted-Lowry theory of acids and bases, and acid is a proton DONATOR, and a base is a proton ACCEPTER (water accepts the hydrogen ion/proton, which is why it acted as a base). To see how it's not a very good base, let's first take a look at the conjugate base of a WEAK acid.
If you have a weak acid, such as acetic acid (HC2H3O2), it undergoes the following dissociation reaction with water:
HC2H3O2 + H2O <--> H3O+ + C2H3O2-
The acetate ion, C2H3O2-, is the conjugate base of acetic acid. Now if you start with the acetate ion (e.g. you have an ionic compound, put it into water, and it breaks up into its cation and acetate), it will react with water (a process called hydrolysis). The equation for this is:
C2H3O2- + H2O <--> HC2H3O2 + OH-
This is a basic hydrolysis reaction. The acetate ion acts as a base, and the water acts as an acid (it gives a proton to the acetate ion to form the original weak acid). Just hydrolysis at work.
Well, back to strong acids: the conjugate base of a strong acid is pathetic as a base because it does not hydrolyze. Let's look at what such a hydrolysis reaction WOULD look like for the chloride ion:
Cl- + H2O --> HCl + OH- (N.B. THIS REACTION NEVER HAPPENS!!! In reality, chloride ion + water --> no reaction)
The reason is simply because of how strong the acid HCl is. Remember how the acid dissociation constant is greater than 1, a lot greater than 1? Well, because it's so strong, it's hardly going to go the other way, at all. Any HCl in water will want to dissociate
PFQ. You could look at it mathematically and invoke the base dissociation constant of this reaction, but then I'd be getting into a whole new realm of things. If you know how to find the base dissociation constant, you'll find that for such strong acids, the constant will be tiny, very tiny, so barely (or no) OH- will come of the reaction.
So remember: the conjugate base of a strong acid is PATHETIC!
You know how the taste of acids is supposed to be sour? Well, I wouldn't recommend that you try this with strong acids, unless you rather enjoy burning sensations on your tongues. Also, don't let it touch your skin. Unless you like burning skin. If that kinda thing turns you on, go ahead. We all know the story: Little Johnny used to be / but isn't any more / For what he thought was H2O was H2SO4.
I'd recommend the taste test thing with a weak acid, like citric acid. Which is found in orange juice. hmm... oranges.
4. Diprotic strong acids do not split up ENTIRELY
A diprotic acid is an acid that has two hydrogen ions. For a strong diprotic acid, we'll look at H2SO4, sulfuric acid (I think it may be the only diprotic strong acid). It has two hydrogen ions. See them? Good. know them. Love them. ... Or not.
We know it's a strong acid. So it completely dissociates. There is a CATCH however! The catch is that it's strong but only for one proton. Let's see how it dissociates in water:
H2SO4 + H2O --> HSO4- + H3O+
That happens completely, no equilibrium. It completely dissociates into a bisulfate (or hydrogen-sulfate) ion, HSO4-, and a hydrogen ion (which is basically equivalent to the hydronium ion, H3O+, as the hydrogen attaches to water). As expected, the bisulfate ion is PATHETIC as a base. However, it CAN act as an acid, albeit a weak one, not nearly as strong as sulfuric acid. Let's see how:
HSO4- + H2O <--> SO4-2 + H3O+
I'd like to point out that since the bisulfate ion isn't a very strong acid, only a small amount of hydrogen ion is produced from this reaction. Also, just to clarify, the sulfate ion, SO4-2, can hydrolyze, to form the bisulfate ion and hydroxide, OH-.
Sources:
Mr. Marx, my AP Chemistry teacher
My Chem textbook (specific reference to come later)
Wikipedia, for the pKa of hydrochloric acid. (revision from 1/2/2006)