### Video Transcript

In this video, we will learn about
K๐ and K๐, the acid and base dissociation constants. We will learn how to write their
expressions and practice calculating their values for some acids and bases.

What are K๐ and K๐? K๐ and K๐ are equilibrium
constants for the dissociation of weak acids and bases in solution, usually aqueous
solution. K๐ is the acid dissociation
constant, sometimes known as the acid ionization constant, and K๐ is the base
dissociation constant or base ionization constant. The value of K๐ or K๐ indicates
the strength of an acid or base. K๐ is a measure of the strength of
an acid in solution, and K๐ is a measure of the strength of a base in solution.

Letโs imagine this diagram
represents an acid or a base, which breaks apart or dissociates in solution into
ions. When all of the reactant
dissociates into ions, we say that that acid or base is strong. When some of the reactant
dissociates into ions and some of the ions reassociate to form the reactant, we say
the acid or base is weak. An equilibrium is formed when a
weak acid or base dissociates in solution. And therefore we can determine the
equilibrium constant for that acid or base in much the same way as other equilibrium
constants are determined.

Letโs derive a general expression
for K๐, the acid dissociation constant. To derive a general expression for
K๐, we need a general reaction equation for a weak acid HA dissociating or ionizing
in solution. When a weak acid HA dissociates in
aqueous medium, the reaction equation is HA plus H2O reacting reversibly to give Aโ
plus H3O+. The hydronium ion produced comes
from the reaction of water with a hydrogen ion from the weak acid HA. Water plus a hydrogen ion forms the
hydronium ion.

We can derive the equilibrium
constant for this reversible reaction in much the same way as other equilibrium
constants are determined. K is equal to the concentration of
all the products multiplied by each other divided by the concentration of all the
reactants multiplied by each other. Substituting the products and
reactants from our general reaction equation, we get the concentration of the anions
Aโ multiplied by the concentration of the cations, in this case the hydronium ions,
H3O+, divided by the multiplication product of the reactant concentrations. Square brackets mean concentration
in terms of molar units, or molarity, which is moles per liter or moles per
decimeter cubed.

When the solution is dilute, the
concentration of water is very large relative to the concentration of the other
species and is essentially unchanging. Or at least we assume that the
concentration of water doesnโt change. For this reason, we do not include
the concentration of water in the denominator. Instead, we make its concentration
a constant, lowercase k. If we then take waterโs constant to
the left-hand side, we get capital K multiplied by small k equals the concentration
of the products multiplied with each other divided by the concentration of the weak
acid. And the left-hand side value we
call K๐. This is the general expression for
the acid dissociation constant K๐.

Because we donโt need to consider
waterโs concentration, we can rewrite this reaction equation more simply: HA in
equilibrium with its ions Aโ and H+. Since we have removed water, we can
change the hydronium ion to a simple hydrogen ion. For this reason, we might sometimes
find the K๐ expression without a hydronium ion. And instead a hydrogen ion will be
in its place. The equilibrium constant for a weak
base dissociates in water K๐ is derived in much the same way.

Letโs simplify by removing water
right from the start so we donโt need to do a long derivation. And we get the general reaction
equation for a weak base BOH, which is BOH dissociating reversibly into its ions
OHโ, the hydroxide ion, and B+. Then, the base dissociation
constant K๐ is equal to the molar concentrations of the ion products multiplied
with each other divided by the molar concentration of the weak base. This is the general equation for
the base dissociation constant K๐ when a weak base dissociates in aqueous
medium.

Letโs put the acid dissociation
expression back and have a look at these two expressions. Because the base and acid are weak,
they only disassociate to a small extent. And sometimes the denominators are
referred to as the original or starting concentrations. But we must remember that these
expressions are actually for equilibrium situations. K๐ and K๐, like other equilibrium
constants, depend on temperature. Temperature influences or affects
how far an equilibrium sits to the right or to the left. In other words, the equilibrium
will sit more to the right or more to the left depending on whether the forward
reaction is endothermic or exothermic and depending on the temperature under which
the equilibrium exists. For this reason, 25 degrees Celsius
is a common temperature at which K๐ or K๐ is determined. In this way, these values have
meaning when they are compared with each other or have meaning when the temperature
changes.

Now, letโs practice writing K๐ and
K๐ for a weak acid and a weak base.

HCN, or hydrocyanic acid, is a weak
acid. This is the equation for the
dissociation of this weak acid in solution. We can write the acid dissociation
constant for this acid K๐ is equal to the molar concentrations of the ion products
multiplied with each other divided by the molar concentration of the acid HCN. Note that because the mole ratio of
H+ to CNโ is one as to one, these two concentration values will be the same. If the stoichiometry was not one as
to one, the concentrations would not be the same. However, the stoichiometry of the
products is usually one as to one, even in the case of polyprotic acids, which lose
their protons one at a time, forming different equilibrium reactions. In other words, they undergo a
stepwise dissociation. But this is a discussion for
another video.

When ammonia gas dissolves in
water, ammonium hydroxide is formed. This is a weak base. Ammonium hydroxide dissociates to
form an equilibrium with its ions, NH4+ and OHโ, the ammonium and hydroxide
ions. We can write the K๐ expression for
this base dissociation as follows. K๐ is equal to the molar
concentrations of the ion products multiplied with each other divided by the molar
concentration of ammonium hydroxide. In this example, we again have a
molar ratio of the product ions one as to one. And so we know these values are the
same.

In a moment, we will practice
calculating the actual value of K๐ for a weak acid. But first letโs investigate what
the size of a K๐ or K๐ value actually means. What information does it give
us? What does the size of K๐ or K๐
tell us?

We know that K๐ or K๐ is equal to
the molar concentrations of the products multiplied with each other divided by the
molar concentration of the reactant. If K๐ or K๐ is a large value,
this tells us that the numerator value is large relative to the denominator
value. In other words, the products of the
dissociation reaction are favored, meaning the acid or base is relatively strong in
that it dissociates to a large degree. Now, I say relatively because K๐
and K๐ are only for weak acids and bases. But even weak acids or bases have
relative strengths.

When K๐ or K๐ is a small value,
this tells us that the numerator value is small relative to the denominator value,
meaning the acid or base in its undissociated form is favored. That acid or base is relatively
weak, meaning only a little bit of it dissociates. So, again, K๐ or K๐โs size
indicates or is related to the acid or base strength.

Now itโs time to practice.

Calculate the K๐ value of a
0.2-molar aqueous solution of propanoic acid with a concentration of H+ ions of 1.62
times 10 to the negative three molar. Give your answer to one decimal
place. (A) 4.8 times 10 to the negative
four moles per liter. (B) 6.6 times 10 to the negative
five moles per liter. (C) 1.6 times 10 to the negative
two moles per liter. (D) 5.2 times 10 to the negative
seven moles per liter. Or (E) 1.3 times 10 to the negative
five moles per liter.

Propanoic acid is CH3CH2COOH. We know this from the name stem
โprop,โ meaning three carbons in the chain, โanโ telling us there are single bonds
between carbon atoms, and the suffix -oic acid telling us this is a carboxylic acid
with a carboxyl group. Propanoic acid is a weak acid,
meaning in solution it dissociates to a small degree, forming an equilibrium
according to this equation. The dissociation products are the
ions CH3CH2COOโ and the hydrogen ion. We are asked to find K๐, the acid
dissociation constant for this weak acid.

We are told the starting
concentration of the acid, 0.2 molar. And we are told the hydrogen ion
concentration in solution, 1.62 times 10 to the negative three molar. Letโs start by writing the
expression for K๐. K๐ is equal to the molar
concentrations of the ion products, which are the propanoate ion and the hydrogen
ion, multiplied with each other divided by the molar concentration of propanoic
acid, the reactant. Square brackets refer to molar
concentration, or molarity, which is moles per liter or moles per decimeter
cubed.

We are given the denominator value
in terms of molarity, 0.2 molar. And we are given the hydrogen ion
concentration in terms of molarity too, 1.62 times 10 to the negative three
molar. But we donโt know the concentration
of the propanoate ion. However, from the balanced
equation, we know that the molar ratio of the anion to the hydrogen cation is one as
to one. And so the concentration of the
propanoate anion must be the same as that of the hydrogen ion.

Letโs now put in our values. We get 1.62 times 10 to the
negative three molar for the concentration of the anions multiplied by 1.62 times 10
to the negative three molar for the concentration of the hydrogen ions divided by
0.2 molar, which is the concentration of propanoic acid. And the value of the answer is 1.31
times 10 to the negative five. These two units can cancel, and so
the unit in the answer is molar, which is moles per liter. Note that sometimes K๐ and its
relative K๐, the base dissociation constant, are expressed without units.

We were asked to give our answer to
one decimal place. So letโs round off, and we get 1.3
times 10 to the negative five moles per liter, which corresponds with answer option
(E). The K๐ value for this propanoic
acid equilibrium is 1.3 times 10 to the negative five moles per liter.

Letโs sum up what weโve learnt in
this video. We learnt about K๐ and K๐, the
acid and base dissociation or ionization constants. We saw that for a weak acid in
solution HA dissociating to form an equilibrium with its ions, Aโ and H+, the K๐
expression will be the molar concentrations of the ion products multiplied with each
other divided by the molar concentration of the reactant, which is the weak
acid. And for a weak base dissociating
into its ions in solution and forming an equilibrium, the K๐ expression is K๐ is
equal to the molar concentrations of the ion products multiplied with each other
divided by the molar concentration of the reactant, which is the weak base.

We learnt that K๐ and K๐, like
other equilibrium constants, are temperature dependent and change according to the
temperature. We saw that this is because the
values in the numerator and denominator of a K๐ or K๐ expression will change as an
equilibrium shifts due to temperature change. We also learnt that the value or
size of K๐ or K๐ indicates or is a measure of the acid or base strength.