Acid strength refers to the potential of the acid to lose a proton. Acids that give up a proton easily are stronger. Acids that don't readily give up a proton are weaker. Here, I'll show you a reaction mechanism for an acid dissolving in water. I know you don't know what those are, but if you paid attention the first time I showed you, then you would. It's not my fault you weren't paying attention. Grow up. So yeah, mechanism...
For a little review, I'll note that the first reactant (A—H) is the acid. Water, the second reactant, is the base. And the products are the conjugate base of the reactant acid and hydronium, the conjugate acid of water, respectively. This reaction is reversible, so the hydronium could protonate the conjugate base of the original acid and leave us with the reactants again. But the equilibrium favors whichever side of the equation has the weaker acid. This might seem intuitive, actually. The acid that more readily gives up a proton (the stronger acid) will do so more and therefore will show up less. But unless we know which acid is weaker, that is, unless we have a way to measure acid strength, the knowledge doesn't really help us. Fortunately, quantifying the acid strength is possible. But this goes a bit beyond the scope of the textbook I'm using, which assumes the student remembers certain things from general chemistry. Besides, it involves math. So I'll just tell you that in organic chemistry, the figure that is typically used is pKa. That's the opposite of the common logarithm of the acid dissociation constant. The acid dissociation constant is determined by multiplying the equilibrium concentrations of the products and dividing this by the equilibrium concentration of the acid. Easy, right?
So I totally don't remember how those equilibrium concentrations are determined (with instruments, I guess). I just look up the pKa of the acid in question using a table of pKa values. That way, all I need to know is that the lower the pKa, the stronger the acid. My textbook states that typical pKa values for organic acids range from 5 to 50. I'm not sure where those numbers came from, but whatever. Be aware that some organic acids are not typical. Also, in lab, I dealt with inorganic acids all the time. Acids with negative pKa values are considered "strong" acids. Actually, Wikipedia says that strong acids are those with pKa values less than -2. Whatever. What it means for an acid to be "strong" is that essentially all of it will lose its protons to water. In other words, the equilibrium completely favors the products and none of the original acid is present in any concentration. So really, the strongest acid that exists in water is hydronium. Anything stronger just protonates the water to form hydronium.
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