Understanding the difference between Ka/Kb and Kw

[makaela2L]

From what I understand, Ka/Kb values are used to denote the dissociation constants for weak acids and bases, whereas Kw is the dissociation constant for strong acids and bases, right? So then, in that context, do the pKa and pKb define pH and pOH in relation to weak acids and bases?
- I'm just having trouble relating the concepts of pKa and pKb topH and pOH.

[Nicole Li 2B]

You are correct in that Ka and Kb denote the dissociation constants for weak acids and bases. However, Kw is the dissociation constant of water for the reaction 2H2O --> OH- + H3O+. Kw will always equal 10^-14, and a helpful relationship to remember is that (Ka)(Kb)=Kw=10^-14.

The letter "p" in chemistry represents the -log function. Specifically, pKa is calculated by taking -log(Ka) and pKb is calculated by taking -log(Kb). In reference to the second part of your question, we can relate pKa to pH and pKb to pOH by:

Ka=[H+][A-]/[HA]

We can group this function to make the [H+] more distinct: Ka=[H+] x ([A-]/[HA]).

We can then take the -log of both sides: pKa=pH-log([A-]/[HA]) to find the relationship between pKa and pH.

The same process can be carried out for Kb=[OH-][BH]/[B].

I hope this helps!