# How does pKa relate to the acidity of a substance?

Dec 10, 2015

The $\text{pKa}$ is just the negative base 10 logarithm of the $\text{Ka}$. In other words:

"pKa" = -log("Ka")

For example, ammonia has a $\text{pKa}$ of about $36$. A higher $\text{pKa}$ indicates a weaker acid. This is because:

10^(-"pKa") = "Ka"

We can see that the $\text{Ka}$, which is known as the acid dissociation constant, is higher for higher degrees of dissociation, and vice versa. Thus, the lower the $\text{Ka}$, the weaker the acid.

The lower the $\text{Ka}$, the higher the $\text{pKa}$ must be for ${10}^{- \text{pKa}}$ to decrease. We can prove that like so:

"pKa"_("NH"_3) = 36

10^(-36) = "Ka"_("NH"_3)

And then...

"pKa"_("NH"_4^(+)) = 9.4

10^(-9.4) = "Ka"_("NH"_4^(+))

And of course...

${10}^{- 36} \text{ << } {10}^{- 9.4}$

That means ammonium dissociates much more than ammonia does in water ($26.6$ orders of magnitude more). In fact, an ammonium hydroxide solution readily equilibrates to be pretty much all ammonia and water.