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 1/0.
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 dissolved in pure $\ce{H2O}$, 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 maybe 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 its conjugate base.
The greater is the value of $\mathrm pK_\mathrm a$, the weaker will be the acid and the stronger its conjugate 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 its conjugate acid.
The greater is the value of $\mathrm pK_\mathrm b$, the weaker will be the base and the stronger its conjugate 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, $\mathrm{pOH} > 7$.
$^*$ of a solution made by adding a defined amount of acid or base to pure water.
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 $pK_a$
What is the pKa Range for weak acids and bases?
Bases don't have a $\mathrm{p}K_\mathrm{a}$. To discuss the strength of a base, you can look at the $\mathrm{p}K_\mathrm{a}$ of the conjugate acid, though.
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
To be called a strong acid in an aqueous system, the acid has to dissociate completely, or at least almost completely. An acid with a $\mathrm{p}K_\mathrm{a}$ of, say, 2 added to neutral water at a concentration of, say, 1 mol/L would not dissociate much. In fact, approximately 90% of it would be in the acid form (protonated) and only approximately 10% would be present as the conjugate base (deprotonated).
It is not clear where the separation between strong and weak acids should be. Usually, it is sufficient to memorize that $\ce{HCl, H2SO4 and HNO3}$ are common strong acids, and their $\mathrm{p}K_\mathrm{a}$ values are usually given as lower than zero. If an acid were to dissociates completely, the equilibrium constant would not be defined, and the $\mathrm{p}K_\mathrm{a}$ value would not be defined.
Am I correct in assuming that the following is true?
- $7 < \mathrm pK_\mathrm a < 11$ is for a weak base
- $\mathrm pK_\mathrm a > 11$ is for a strong base
No, because bases don't have a $\mathrm{p}K_\mathrm{a}$. It is true that as the $\mathrm{p}K_\mathrm{a}$ of the conjugate acid increases, the conjugate base is stronger. There is nothing special about an acid with a $\mathrm{p}K_\mathrm{a}$ of 7. Whether the $\mathrm{p}K_\mathrm{a}$ of an acid is 6.9, 7.0 or 7.1, it is still an acid.
One use of the $\mathrm{p}K_\mathrm{a}$ is to define the pH-range a buffer composed of that acid and its conjugate base would have. The simplest buffer (one part acid and one part conjugate base) will have a pH approximately equal to the $\mathrm{p}K_\mathrm{a}$ value of the acid. Similarly, a pH indicator will switch colors when the pH is near the $\mathrm{p}K_\mathrm{a}$ of the conjugate acid form (the protonated form) of the indicator. The underlying reason is the same: when $\mathrm{p}K_\mathrm{a}$ = pH, the concentrations of protonated and deprotonated species (conjugate acid and base) will be almost equal (exactly equal for ideal solutions).
