Acids and Bases part II

For a review of acids and bases, click the following link:

Acids and Bases

Autoionization of Water

In our discussion of acids and bases so far, we've learned that acids and bases are often defined the effects of their dissociation. Interestingly enough, water also dissociates.

The dissociation of water is the following equation:

$2H_2O_((l)) ↔ H_3O_((aq))^+ + OH_((aq))^-$

Where $H_3O^+$ is the hydronium ion and $OH^-$ is the hydroxide ion.

The equilibrium constant of this dissociation is $10^(-14)$ , which is an incredibly small amount. This explains why we don't see our water dissociating suddenly; only a negligible amount dissociates. When water is left alone, only an infinitesmally small amount will dissociate.

This equilibrium constant is given a special name: the autoionization constant of water $(K_w)$ which is $10^(-14)$ at room temperature.

$K_w=[H_3O^+][OH^-]=10^(-14)$

NOTE: $[H_2O]$ is left out of the equilibrium expression since it's a liquid.

Acid/Base Ionization Constants

Acids and Bases have ionization constants as well. Acids dissociate by the following general equation:

$HA + H_2O ↔ H_3O^+ + A^-$

Where $HA$ is the acid, $H^+$ the hydronium ion, and $A^-$ the now deprotonated acid.

The acid ionization constant $(K_a)$ is therefore equal to:

$K_a=([H^+][A^-])/[HA]$

If the acid dissociates a lot, then the numerator $K_a$ value will be large. Conversely, if the acid dissociates only slightly, the $K_a$ will be small. We can express the relative strength of an acid by the value of $K_a$ ; the larger the $K_a$ , the more the acid dissociates. We can also make the statement that strong acids have large $K_a$ values whereas weak acids have small $K_a$ values.

Similarly, the ionization constant of a base is represented by the following equation:

$B + H_2O ↔ BH^+ + OH^-$

Where $B$ is the base, $BH^+$ is the now protonated base, and $OH^-$ the hydroxide ion.

The base ionization constant $(K_b)$ is given as:

$K_b=([BH^+][OH^-])/[B]$

Just like with acids, a high $K_b$ indicates a strong base. The extent of the bases dissociation is directly correlated with the $K_b$ value.

Here are some common ionization constants:

Sulfuric	$H_2SO_4$	Large
Perchloric	$HClO_4$	$10^9$
Chloric	$HClO_3$	$10^3$
Oxalic	$H_2C_2O_4$	$5.9x10^(-2)$
Carbonic Acid	$H_2CO_3$	$4.3x10^(-7)$
Acetic	$CH_3COOH$	$1.76x10^(-5)$
Formic Acid	$H_2CO_2$	$1.77x10^(-4)$

Notice that the strong acids have a large $K_a$ - in the case of sulfuric, the $K_a$ is literally given as large as it's difficult to measure. For the weak acids, the $K_a$ is small.

Ionization Constant Relationship

An interesting relationship can be found between the $K_a , K_b, and K_w$ of a solution:

$[K_w]=[K_a][K_b]$

You can think of $K_a$ and $K_b$ as the acidic and basic characters respectively. In a solution of pure sulfuric acid, $K_a$ , the acidic character, is so large that there's practically little basic character. In mathematical terms:

$[K_b]=[[K_w]]/[[K_a]]$

One can convert between the acid and base character of a particular substance using this relationship.

This relationship is derived from the definition of $K_w$ : $[K_w]=[H_3O^+][OH^-]$ . This relationship explains that, as one increases the $H_3O^+$ concentration in a solution, usually by adding an acid, the concentration of $OH^-$ will decrease. The reverse is also true: if one adds a base into a solution, the concentration of $OH^-$ increases which means that the concentration of $H_3O^+$ decreases.

This relationship explains that there's a restriction on how solutions function: a solution cannot increase both its acidity and basicity at the same time. If one increases a solution's acidity, the solution's basicity will decrease correspondingly and vice-versa.

Dissociation Constant

The acid dissociation constant ( $pK_a$ ) is defined as:

$pK_a=-"log"(K_a)$

This should look familiar, as this is the same way we calculated pH, only instead of using $K_a$ , we used $[H^+]$ .

The base dissociation constant ( $pK_b$ ) is defined similarly:

$pK_b=-"log"(K_b)$

The acid and base dissociation constants apply to acids and bases, not solutions. This is the main distinguishment between the $pK_a$ and pH:

$pK_a$ applies to an acid, whereas pH applies to a solution.

To help understand this, imagine 5 beakers all with different concentrations of HCl. Since pH is a function of concentration, the pH will be different for each of the solutions. The $pK_a$ , however, will be the same for each acid since $pK_a$ is constant for an acid.

Additionally, since the dissociation constants are on a negative logarithmic scale, the smaller the dissociation constant, the stronger the acid/base. This may be confusing since it's the opposite of how we use $K_a$ and $K_b$ .

Summary

1. Water has an ionization constant of $10^(-14)$ .

2. The ionization constants $K_a$ and $K_b$ indicate the extent to which an acid/base dissociates in solution.

3. The larger the ionization constant, the stronger the acid/base.

4. One can convert between $K_a$ and $K_b$ using the relationship $[K_w]=[[K_a]]/[[K_b]]$ .

5. The dissociation constant is another metric that is used to express the strength of an acid/base.