Where are you seeing questions asking you about this? In theory, you can stick with the usual calculations you know for pH, pOH, pKa, pKb for values between 0 and 14. If the math gives you a negative number - or a number greater than 14 - you haven't done anything "wrong" per se. It's unlikely on the real test that you'd get a situation with an acid that weak (or base that strong), but I'd be willing to bet that to answer the question correctly, you wouldn't have to change any of the problem-solving techniques you've learned to use for when a pKa is, say, 5.
Look beyond general chemistry and you'll find that this is actually a common question. For example, consider the typical alpha proton on a carbonyl compound. It has a pK
a around 17. There's an entire chapter (at least) in every organic chemistry text book dedicated to the water based reactivity of the that proton, so understanding the impact of pK
a on reactivity in a conceptual fashion is very useful. If you think about the aldol condensation reaction, you are adding OH- to remove the alpha proton and initiate the reaction. Because water has a pK
a of 15.7, we know that OH- is a weaker base than the carbanion formed after deprotonating the alpha proton, but the values are close enough that OH- should be able to deprotonate about 1 to 5% of the alpha protons. This creates the perfect environment for the nucleophilic anion to attack a nearby neutral ketone and form a new carbon-carbon bond. If the base were too strong, then you'd deprotonate too many ketones and there wouldn't be any electrophiles to attack. If the base were too weak, then you wouldn't generate enough carbanions to see a reaction to any detectable extent. Knowing that the pK
as are within two of one another is important to the reaction.
As far as calculation-based questions go, it's important to know the pK
a so you know what you are dealing with. For instance, if they gave you a hypothetical acid with pK
a = -7, then you should immediately think that it's a strong acid (like HCl and HNO
3, it has a negative pK
a). Knowing that, you in turn know that it fully dissociates and you can simply assume [HX] = [H+] and calculate pH using pH = -log[HX]. If the pK
a lies between 2 and 12, then you know it's weak enough that the HH equation applies (if it's a buffer). So even in calculation questions it's helpful to know what pK
a < 0 tells us, what pK
a > 14 tells us, and what happens when K
a is too close to [H+].