Acid Strength
Strong acid completely ionizes in solution, whereas a
weak acid only partially ionizes. In other words, the
strength of an acid depends on the equilibrium:
If the equilibrium lies far to the right, the acid is
strong….It completely ionizes.
If the equilibrium lies to the left, the acid is weak… only a
small percentage of the acid molecules ionize.
Weak Acids
In contrast to HCl, HF is a weak acid, one that
does not completely ionize in solution:
HF solution contains a large number of intact (or
un-ionized) HF molecules; it also contains some
H3O+(aq) and F-(aq)
The degree to which an acid is strong or weak depends on the attraction between the anion of the acid (the
conjugate base) and the hydrogen ion, relative to the attractions of these ions to water. Recall that HA is a generic
formula for an acid. The degree to which the following reaction proceeds in the forward direction depends on the
strength of the attraction between H+ and A-:
Autoionization of Water and pH
Water is amphoteric; it can act as either an acid or a base. Even when
pure, water acts as an acid and a base with itself, a process called
autoionization:
As indicated by the double arrow in the equation, the reaction is an equilibrium.
The equilibrium expression for the autoionization of water is:
• When [H3O+] = [OH-], the solution is neutral.
Kw = {H3O+][OH-] = (1.0 x 10-7) (1.0 x 10-7) = 1.0 x 10-14
• When [H3O+] > [OH-], the solution is acidic.
• When [H3O+] < [OH-], the solution is basic.
The pH Scale
The
acidity
of
an
aqueous
solution
depends
on
the
concentration of hydronium ions, [H3O+]. To describe the
acidity of a solution, we usually use the pH scale.
The pH of a solution is defined as the negative base-10
logarithm of the hydronium ion concentration (in mol/L).
Strong Acids
•
Because the ionization of a strong acid is complete, the
concentration of hydronium ion at equilibrium is equal to the
starting concentration of the strong acid.
•
For instance, if we prepare a 0.10 M solution of HCl, the
concentration of hydronium ion in the solution is 0.10 M. All
the HCl ionizes, and no HCl molecules remain. Thus, at
equilibrium (when the ionization is complete), [HCl] = 0 M and
[H3O+] = [Cl-] = 0.10 M. Therefore, the pH of the solution is:
Sample
Problem
Calculate the pH of an aqueous solution at 25 oC that is (a) 0.035 M in
HI, (b) 1.2 x 10-4 M in HNO3, and (c) 6.7 x 10-5 M in HClO4.
Strategy HI, HNO3, and HClO4 are all strong acids, so the concentration of
hydronium ion in each solution is the same as the stated concentration of the
acid.
Setup (a) [H3O+] = 0.035 M
(b) [H3O+] = 1.2 x 104 M
(c) [H3O+] = 6.7 x 10-5 M
Solution (a) pH = - log (0.035) = 1.46
(b) pH = -log (1.2 x 10-4) = 3.92
(c) pH = - log (6.7 x 10-5) = 4.17
Strong Bases
In a solution that is 0.018 M in NaOH, for example, [OH] = 0.018 M. Its
pH can be calculated in two ways:
and then
pH = -log (5.56 x 10-13 M) = 12.28
or we can calculate the pOH with the following Equation
pOH = -log (0.018 ) = 1.75
and then
pH + pOH = 14.00
pH = 14.00 – 1.75 = 12.28
Weak Acids and Acid Ionization Constants
Most acids are weak acids, which ionize only to a limited extent in
water. At equilibrium, an aqueous solution of a weak acid contains a
mixture of aqueous acid molecules, hydronium ions, and the
corresponding conjugate base. The degree to which a weak acid ionizes
where Ka is the equilibrium constant for the reaction. More specifically, Ka
is called the acid ionization constant. The magnitude of Ka indicates
how strong a weak acid is. A large Ka value indicates a stronger acid,
whereas a small Ka value indicates a weaker acid.
Weak Bases and Base Ionization Constants
Just as most acids are weak, most bases are also weak. The ionization of a weak
base is incomplete and is treated in the same way as the ionization of a weak
acid. In this section, we will see how the ionization constant for a weak base, Kb,
is related to the pH of an aqueous solution.
where Kb is the equilibrium constant—known as the base ionization
constant.
where B is the weak base and HB is its conjugate acid. The equilibrium
expression for the ionization is:
What is the pH of a 0.040 M ammonia solution? Kb = 1.8 x 10-5
The Ionization Constant, Kb
Buffers: Solutions That Resist pH Change
Most solutions significantly change pH when an acid or
base is added to them. A buffer resists pH change by
neutralizing added acid or added base. A buffer contains
either:
•
significant amounts of a weak acid and its conjugate base or
•
significant amounts of a weak base and its conjugate acid.
• For example, the buffer in blood is composed of carbonic
acid (H2CO3) and its conjugate base, the bicarbonate ion
_
(HCO3 ).
• When additional base is added to a buffer, the weak acid
reacts with the base, neutralizing it.
• When additional acid is added to a buffer, the conjugate
base reacts with the acid, neutralizing it.
• In this way, a buffer can maintain a nearly constant pH.
A weak acid by itself, even though it partially ionizes to form some of its conjugate base, does not contain sufficient base to
•
be a buffer. Similarly, a weak base by itself, even though it partially ionizes water to form some of its conjugate acid, does
not contain sufficient acid to be a buffer.
•
A buffer must contain significant amounts of both a weak acid and its conjugate base.
•
Consider the simple buffer made by dissolving acetic acid (HC2H3O2) and sodium acetate (NaC2H3O2) in water.
•
With addition of a strong base, such as NaOH, to this solution. The acetic acid neutralizes the base:
As long as the amount of added NaOH is less than the amount of HC2H3O2 in solution, the buffer
neutralizes the added NaOH and the resulting pH change is small.
With addition of strong acid, such as HCl, to the solution. In this case, the conjugate base, NaC2H3O2, neutralizes the added HCl:
As long as the amount of added HCl is less than the amount of NaC2H3O2 in solution, the buffer neutralizes the added HCl and the
resulting pH change is small.
Common Ion Effect
How do we calculate the pH of a buffer—a solution containing both a weak
acid or its conjugate base?
Consider a solution that initially contains HC2H3O2 and NaC2H3O2, each at a
concentration of 0.100 M. The acetic acid ionizes according to the reaction:
However, the ionization of HC2H3O2 in the solution is suppressed
compared to its ionization in a solution that does not initially contain any
C2H3O2- , because the presence of C2H3O2 shifts the equilibrium to the
left (as we would expect from Le Châtelier’s principle).
In other words, the presence of the C2H3O2- (aq) ion causes the acid to ionize even less than it normally would, resulting in a less acidic
solution (higher pH). This effect is known as the common ion effect, so named because the solution contains two substances (HC2H3O2 and
NaC2H3O2) that share a common ion (C2H3O2-). To find the pH of a buffer solution containing common ions, we work an equilibrium problem
in which the initial concentrations include both the acid and its conjugate base.
Calculate the pH of a buffer solution that is 0.1 M in HC2H3O2 and 0.1 M in NaC2H3O2?
The Henderson–Hasselbalch Equation
We can derive an equation that relates the pH of a buffer solution to the initial concentration of the buffer components.
Consider a buffer containing weak acid HA and its conjugate base A- . The acid ionizes as follows:
To find the [H3O+ ] of the buffer (a solution that is 0.100 M in HC2H3O2 and 0.100 M in NaC2H3O2), we substitute the
_
concentrations of HC2H3O2 and C2H3O2 :
In this buffer solution, as in any in which the acid and conjugate base
concentrations are equal, [H3O+ ] is equal to Ka.
The Henderson–Hasselbalch Equation
We can derive an equation for the pH of a buffer by
taking the negative logarithm of both sides:
where the base is the conjugate base of the acid or the acid is the conjugate acid of the base. This equation,
known as the Henderson–Hasselbalch equation, allows us to quickly calculate the pH of a buffer solution from
the initial concentrations of the buffer components as long as the x is small approximation is valid.
Calculate the pH of a buffer solution that is 0.050 M in benzoic acid (HC7H5O2) and 0.150 M in sodium benzoate (NaC7H5O2).
-5
For benzoic acid, Ka = 6.5 x 10 .
Buffers Containing a Base and Its Conjugate Acid
•
A buffer can also be composed of a base and its conjugate acid (where the conjugate acid is an
ion). For example, a solution containing significant amounts of both NH3 and NH4Cl acts as a
+
buffer. The NH3 is a weak base that neutralizes small amounts of added acid, and the NH4 ion
is the conjugate acid that neutralizes small amounts of added base.
•
We calculate the pH of a solution like this in the same way that we calculated the pH of a
buffer containing a weak acid and its conjugate base.
•
When using the Henderson– Hasselbalch equation, however, we must first calculate pKa for
the conjugate acid of the weak base.
•
Ka x Kb = Kw
and
pKa + pKb = 14
Consequently, we can find pKa of the conjugate acid by subtracting pKb of the weak base from
14.
Use the Henderson equation to calculate the pH of a buffer solution that is 0.50 M in NH3 and 0.20 M in NH4Cl. For
ammonia, pKb = 4.75
Buffer Effectiveness: Buffer Range and Buffer Capacity
An effective buffer neutralizes small to moderate amounts of added acid or base. However, that a buffer can be destroyed by the addition of too
much acid or too much base. What factors influence the effectiveness of a buffer?
the relative amounts of the acid and conjugate base
the absolute concentrations of the acid and conjugate base
We then define the capacity of a buffer (how much added acid or base it can effectively neutralize) and the range of a buffer (the pH range over
which a particular acid and its conjugate base can be effective).
Relative Amounts of Acid and Base
A buffer is most effective (most resistant to pH changes) when the concentrations of acid and conjugate base are equal.
As you can see, the buffer with equal amounts of acid and
conjugate base is more resistant to pH change and is therefore
the more effective buffer. A buffer becomes less effective as the
difference in the relative amounts of acid and conjugate base
increases. As a guideline, we can say that an effective buffer
must have a [base]>[acid] ratio in the range of 0.10 to 10. In
order for a buffer to be reasonably effective, the relative
concentrations of acid and conjugate base should not differ by
more than a factor of 10.
Absolute Concentrations of the Acid and Conjugate Base
A buffer is most effective (most resistant to pH changes) when
the concentrations of acid and conjugate base are high.
The buffer with greater amounts of acid and conjugate base is
more resistant to pH changes and therefore is the more effective
buffer. The more dilute the buffer components, the less effective
the buffer.
Buffer Range
In light of the guideline that the relative concentrations of acid and conjugate base should not differ by
more than a factor of 10 in order for a buffer to be reasonably effective, we can calculate the pH range
over which a particular acid and its conjugate base make an effective buffer.