# What is the pKa Range for weak acids and bases?

Am I correct in assuming that the following is true?

• $\mathrm pK_\mathrm a < 3$ is for a strong acid

• $3 < \mathrm pK_\mathrm a < 7$ is for a weak acid

• $7 < \mathrm pK_\mathrm a < 11$ is for a weak base

• $\mathrm pK_\mathrm a > 11$ is for a strong base

$\mathrm pK_\mathrm a$ is negative log of the acid dissociation constant ($K_\mathrm a$).

$$\mathrm pK_\mathrm a = -\log K_\mathrm a$$

Acid dissociation constant is the equilibrium constant of the dissociation of ions of an acid in an aqueous solution. Consider a weak acid $\ce{HA}$. Weak acids do not dissociate completely in aqueous solution. The equilibrium for the dissociation of such acids can be expressed as

$$\ce{HA + H2O <=> H3O+ + A-}$$

The equilibrium constant for this reaction(dissociation) will be

$$K_\mathrm a = \frac{\ce{[H3O+][A^{-}]}}{\ce{[HA]}}$$

It can be seen that the greater is the extent of dissociation, the greater will be the value of $K_\mathrm a$. Or, the stronger is the acid, the greater will be its $K_\mathrm a$.

Since, $\mathrm pK_\mathrm a$ is negative log of $K_\mathrm a$, it's values will be greater for weaker acid.

There is no sharp boundary between weak and strong acid. Wikipedia defines strong acids as acids which ionize completely in aqueous solution. So, an acid, say $\ce{HA}$ , is said to be strong if one mole of this acid dissociates in aqueous solution to give one mole of $\ce{H+}$ and one mole of $\ce{A-}$. Now $K_\mathrm a$ of such an acid will be 1.

Usually, $\mathrm{pH}$ is used to measure the acid strength, which is negative log of $\ce{H+}$ ion concentration. $$\mathrm{pH} = -\log\ce{[H+]}$$

The concentration of $\ce{H+}$ ions in water is $10^{-7}$ (It has been found out experimentally). Hence, its $\mathrm{pH}$ is $-\log(10^{-7}) = 7$. For acids stronger than $\ce{H2O}$, the concentration of $\ce{H+}$ ions, $\ce{[H+]} > 10^{-7}$. So, $\mathrm{pH} < 7$ for acids and $\mathrm{pH} > 7$ for bases.

What you are referring to may actually be $\mathrm{pH}$ and in that case the ranges you've given are may be correct. But once again there is no clear difference between weak and strong.

There is a simple relation between $\mathrm{pH}$ and $\mathrm pK_\mathrm a$, $$\mathrm{pH} = \frac{1}{2}[\mathrm pK_\mathrm a - \log c]$$ where $c$ is concentration of the acid. You can derive this relation using Ostwald's dilution law.

Similarly, we have $K_\mathrm b$, $\mathrm pK_\mathrm b$ and $\mathrm{pOH}$ for bases which are basic analogues of $K_\mathrm a$, $\mathrm pK_\mathrm a$ and $\mathrm{pH}$. These variables show the strength of a base.

Conclusion

• The greater is the value of $K_\mathrm a$, the stronger will be the acid and the weaker will be the base.

• The greater is the value of $\mathrm pK_\mathrm a$, the weaker will be the acid and the stronger will be the base.

• The greater is the value of $\mathrm{pH}$, the weaker will be the acid and the stronger will be the base. For acids, $\mathrm{pH} < 7$ and for bases, $\mathrm{pH} > 7$.

• The greater is the value of $K_\mathrm b$, the stronger will be the base and the weaker will be the acid.

• The greater is the value of $\mathrm pK_\mathrm b$, the weaker will be the base and the stronger will be the acid.

• The greater is the value of $\mathrm{pOH}$, the weaker will be the base and the stronger will be the acid. For bases, $\mathrm{pOH} < 7$ and for acids, $\mathrm{pOH} > 7$.

• It should be noted that the final expression for pH is valid only when the dissociation constant of the acid is small and the autodissociation of water can be neglected. – Buck Thorn Jan 27 '19 at 12:32

Not quite, what you are describing is the pH scale, although the two terms are related, according to the Columbia University document Acidity, Basicity and $pK_a$, $pK_a$ is

It turns that that the $pK_a$ of an acid is the $pH$ at which it is exactly half dissociated

The full derivation is on the document (and a bit long to post here with explanations).

But another explanation is provided in the document $pH$ and $pK_a$, where they state

$pK_a$ tells you if a given molecule is going to either give a proton to water at a certain $pH$, or remove a proton

So, to answer your question, in terms of $pK_a$, strong and weak acids and bases can be defined by the following table of examples:

Image source: Strength of Acids and Bases, a key point is that there is no clear boundary that defines strong from weak acids or bases.

They conclude with the following very generalised rule for $pK_a$:

For acids: the stronger the acid, the smaller the $pK_a$

For bases: the stronger the base, the larger the $pK_a$

• It's interesting that the table shown here propagates the view that the $pK_a$ of water is 15.7. It should be understood that this is wrong, that value (for thermodynamic consistency with the other tabulated values) should be 14.0. – Buck Thorn Jan 27 '19 at 10:37