pKa and pKb

[Lindsey Chheng 1E]

why does a smaller pKa or pKb correspond to a stronger acid and strong base?

[WesleyWu_1C]

A strong acid would have a higher Ka. For example, a strong acid could have Ka = 10^-1. The formula for pKa is pKa = -logKa. If you do -log(10^-1), you get pKa = 1. Therefore this strong acid has a low pKa.

I like to first think about Ka and then work backwards. A higher Ka means 10^-x where x is a small integer like 1, 2, etc. We know that -log(10^-x) is equal to x, which means a stronger acid has a lower pKa.

I hope this helps.

[Tai Metzger 3K]

the function p has a negative sign, resulting in larger inputs having smaller outputs. Thus, a larger Ka (and stronger acid) would have a smaller pKa.