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*](http://en.wikipedia.org/wiki/Acid_strength). 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](http://en.wikipedia.org/wiki/Law_of_dilution).


Similarly, we have $K\_\mathrm b$, $\mathrm pK\_\mathrm b$ and [$\mathrm{pOH}$](http://en.wikipedia.org/wiki/PH#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.


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Not quite, what you are describing is the [pH scale](http://en.wikipedia.org/wiki/PH), although the two terms are related, according to the Columbia University document [Acidity, Basicity and $pK\_a$](http://www.columbia.edu/%7Ecrg2133/Files/CambridgeIA/Chemistry/AcidityBasicitykPa.pdf), $pK\_a$ 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 $pK\_a$](http://kchem.weebly.com/uploads/8/6/0/4/8604167/6_ph_and_pka.pdf), 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:


![enter image description here](https://i.stack.imgur.com/qzj49.gif)


Image source: [Strength of Acids and Bases](http://pharmacy.nova.edu/Pharmacodynamics/Modules/AcidsSaltsBases/Main_P3.html), 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 $pK\_a$
> 
> 
> 


 7


> 
> 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.


### So what can I learn from the $\mathrm{p}K\_\mathrm{a}$ of 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).


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