Why acids have a small pK value while bases have a higher pK value ?

I assume when you ask about pK you mean pKa. pKa is small for acids because of the definition. Ka = [H+][A-]/[AH] and pKa = -log₁₀Ka so the greater the disassociation to H+ and A- the smaller the pKa, therefore acids have smaller pKa's than bases.

 

Note that bases have smaller pKb's where Kb = [HB+][OH-]/ and pKb = -log₁₀Kb

Edited August 29, 201015 yr by cypress

Don't forget that [math]K_w =[K_a ][K_b ] [/math]. So Ka and Kb must be inversely proportional.

Are you just wondering why the scale is "the wrong way up"? with strong acids getting a small number?

If so that's because they chose to get rid of the minus sign.