# Relationship between pKa and pKb

The $\mathrm{p}K_\mathrm{a}$ of $\ce{NH3}$ is $38$. Does it stand for the following equilibrium:

$$\ce{NH4+ <=> NH3 + H+} \tag{1}$$ With $K_\mathrm{a} = 10^{-38}$ for reaction $(1)$, indicating that the conjugate acid of $\ce{NH3}$ is quite weak?

The $\mathrm{p}K_\mathrm{b}$ of $\ce{NH3}$ is $4.74$. Does it stand for the following equilibrium:

$$\ce{NH3 + H2O <=> NH4+ + OH-} \tag{2}$$ With $K_\mathrm{b} = 10^{-4.74}$ for reaction $(1)$, indicating that $\ce{NH3}$ is a weak base?

Also: $$\mathrm{p}K_\mathrm{a} + \mathrm{p}K_\mathrm{b} = 42.74 \neq 14$$

• Regarding the last equation, it is only applicable to the sum of the pKa of a species HX and the pKb of its conjugate base, X-. Since both the pK values above are referring to NH3 itself, the formula is not valid. However, if you were to add pKa(NH4+) and pKb(NH3), you would indeed get 14. May 2 '16 at 15:03

The $$\mathrm{p}K_\mathrm{a}$$ of $$\ce{NH3}$$ is $$38$$.

This means, the reaction this value is describing is:

$$\ce{NH3 <=> NH2- + H+}$$

The $$\mathrm{p}K_\mathrm{b}$$ of $$\ce{NH3}$$ is $$4.74$$.

This means, the reaction this value is describing is:

$$\ce{NH3 + H+ <=> NH4+}$$

There is a lot of misuse going on with the term $$\mathrm{p}K_\mathrm{a}$$ since many people are too lazy to say

The $$\mathrm{p}K_\mathrm{a}$$ of $$\ce{NH3}$$’s conjugate acid is $$9.26$$

$$\ce{NH4+ <=> NH3 + H+}$$

rather than

The $$\mathrm{p}K_\mathrm{a}$$ of $$\ce{NH3}$$ is $$9.26$$.

$$\ce{NH3 <=> NH2- + H+}$$

but that is really what they should be doing. Thankfully, when looking up values in a table the person compiling the table (hopefully) knew what they were doing and used the correct terminology.

Only for a $$\mathrm{p}K_\mathrm{a}$$ and a $$\mathrm{p}K_\mathrm{b}$$ that describe the same reaction (from opposite viewpoints) is it true that $$\mathrm{p}K_\mathrm{a} + \mathrm{p}K_\mathrm{b} = 14$$.

• Since the pKa of ammonia is 38, does that mean the pKb of the azanide ion is -24? Jul 1 at 16:10
• @LamGyro Yes. One bloody hell of a strong base.
– Jan
Jul 1 at 17:22