Honors Chemistry
Name: _________________________________________ Date: ______________ Mods: _________
Calculating pH, Ka and % Ionization for WEAK Acids
Weak Acids:
Most acidic substances are weak acids. Unlike strong acids, weak acids are only partially ionized in
aqueous solution. We can use the equilibrium constant for the ionization reaction to express the
extent to which a weak acid ionizes.
If we represent a general weak acid as HA, we can write the equation for its ionization below:
We can then use this equation to write an equilibrium-constant expression for this reaction:
*Ka is called the acid-dissociation constant.
The magnitude of Ka indicates the tendency of the acid to ionize in water. If the value of Ka is greater
than one, the equilibrium lies to the right, and we are dealing with a ____________ acid. If the value
of Ka is less than one, the equilibrium lies to the left, and we are dealing with a ______________ acid.
Therefore, the higher the value of Ka, the ________________ the acid.
Because weak acids only partially ionize in aqueous solution, we must use our skills for solving
equilibrium problems (ICE tables) from Chapter 15 in order to calculate either the Ka value for a weak
acid or the pH of its solutions.
Percent Ionization:
Weak acids will only partially ionize. That means that typically less than 1% of the weak acid
molecules present in a reaction will break up into H+ and A-.
% ionization =
Polyprotic Acids & Ka values:
Many acids have more than one ionizable H atom. These acids are known as polyprotic acids. For
example, each of the H atoms in sulfurous acid can ionize in successive steps. Write these steps
below.
The acid-dissociation constants for these equilibria are labeled Ka1 and Ka2. The numbers on the
constants refer to the particular proton of the acid that is ionizing. Thus, Ka2 always refers to the
equilibrium involving removal of the second proton of a polyprotic acid.
By viewing the Ka values listed above for the successive ionizations of the H atoms in sulfurous acid, it
is obvious that it is always _____________ to remove the first proton from a polyprotic acid than to
remove the second. For an acid with three ionizable protons, it is easier to remove the second proton
than the third. Thus, Ka values become successively ______________ as successive protons are
removed.
ICE Table (1st type) Instructional Notes:
1) Make sure you have a balanced chemical reaction (in this case, the ionization of the acid).
2) Transfer the initial concentration of the weak acid given in the problem into the “I” row of the
ice table. [Note that the initial concentrations of all products in a reaction will always be
zero!!!]
3) Calculate the [H+] from the given pH value. This value is the change in [H+] so it is entered
into the “C” row. The numerical value of all reactants and products will be the same because
every weak acid molecule that ionizes will produce equal quantities of both product ions. [Note
that the change in REACTANTS must always be subtracted because we are using up
the reactants to form products. Similarly, the change in PRODUCTS must always be
added because we are forming more products.]
4) For the “E” row in the ice table, the equilibrium concentration is equal to the initial
concentration plus or minus (depending if it is a product or reactant, respectively).
*** For the weak acid, since the change in the concentration of the acid is so tiny in
comparison to the initial concentration, it is ignored (initial acid concentration = equilibrium acid
concentration)
5) Write the equilibrium expression. All the equilibrium concentrations from the ice table may be
plugged into the expression to solve for the acid-dissociation constant, Ka.
Calculating Ka and Percent Ionization from Measured pH:
1. A student prepared a 0.10 M solution of formic acid (HCHO2) and measured its pH using a pH
meter. The pH at 25°C was found to be 2.38.
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(a) Calculate Ka for formic acid at this temperature.
(b) What percentage of the acid is ionized in this 0.10 M solution?
ICE Table (2nd type) Instructional Notes:
6) Make sure you have a balanced chemical reaction (in this case, the ionization of the acid).
7) Transfer the given initial concentration of the weak acid given in the problem into the “I” row of
the ice table. [Note that the initial concentrations of all products in a reaction will always
be zero!!!]
8) In these kinds of problems will give the value of the Ka in the problem, but the pH will not be
given so the change in the reactant and product concentrations will be unknown. Therefore, in
the “C” row of the ice table, changes in concentration will be given in terms of the variable “x”.
[Note that the change in REACTANTS must always be subtracted because we are using
up the reactants to form products. Similarly, the change in PRODUCTS must always be
added because we are forming more products.]
9) For the “E” row in the ice table, the equilibrium concentration is equal to the initial
concentration plus or minus the “x” change in concentration.
*** For the weak acid, since the change in the concentration of the acid is so tiny in
comparison to the initial concentration, it is ignored (initial acid concentration = equilibrium acid
concentration)
10) Write the equilibrium expression for the reaction and set in equal to the known Ka value given
in the problem. With the equilibrium concentrations known in terms of “x”, plug these values
into the equilibrium expression and solve it for the value of “x”. [Note that, yet again, the
“change” in concentration of the original acid in typically ignored so that initial and
equilibrium concentrations are the same (we assume that the amount of H+ ionized by a
weak acid is insignificant in comparison to the acid’s initial concentration).]
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Using Ka to Calculate pH:
2. Calculate the pH of a 0.30 M solution of acetic acid (HC2H3O2), the weak acid responsible for
the characteristic odor and acidity of vinegar, at 25°C. What percentage of the acid is ionized
in this 0.30 M solution? The Ka for acetic acid is 1.8 x 10-5.
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Calculating pH, Kb and % Dissociation for WEAK Bases
Weak Bases:
Many substances behave as weak bases in water. Weak bases react with water, removing protons
from H2O to form the conjugate acid of the base and OH- ions. If we represent a general weak base
as B, we can write the equation the represent the acid/base reaction in the space below.
The most commonly encountered weak base is ammonia. Write the equation for its acid/base
reaction with water:
We can then use this equation to write an equilibrium-constant expression for this reaction:
*Kb is called the base-dissociation constant.
Calculating Kb and Percent Ionization from Measured pH:
1. Ephedrine, a central nervous system stimulant, is used in nasal sprays as a decongestant.
This compound is a weak organic base:
C10H15ON (aq) + H2O (l)  C10H15ONH+ (aq) + OH- (aq)
A 0.035 M solution of ephedrine has a pH of 11.33.
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(a) Calculate Kb for ephedrine.
(b) What percentage of the base is ionized in this solution?
Using Kb to Calculate pH
2. Calculate the pH of a 0.15 M solution of NH3. The Kb for ammonia is 1.8 x 10-5. What
percentage of the base is ionized in this solution?
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The Relationship Between Ka and Kb:
The product of the acid-dissociation constant for an acid and the base-dissociation constant for its
conjugate base is equal to the ion-product constant for water as seen below:
Therefore, as the strength of an acid _________________ (larger Ka), the strength of its conjugate
base must ____________________ (smaller Ka) and vice versa so that the product Ka x Kb always
equals 1.0 x 10-14 at 25°C.
Example: The acid dissociation constant for hydrofluoric acid (HF) is 6.8 x 10-4. What is the basedissociation constant, Kb, for the fluoride ion (F-)?
This equation can also be written in terms of pKa and pKb by taking the negative log of both sides as
seen below.
More ICE Table Practice Problems!
1) Lactic acid (HC3H5O3) has one acidic hydrogen. A 0.10 M solution of lactic acid has a pH of
2.44. Calculate Ka and the percentage of the acid that is ionized.
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2) Phenylacetic acid (HC8H7O2) is one of the substances that accumulates in blood of people with
phenylketonuria, an inherited disorder that can cause mental retardation or even death. A
0.085 M solution of HC8H7O2 is found to have a pH of 2.68. Calculate Ka and the percentage
of the acid that is ionized.
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3) Calculate the pH of a 0.20 M solution of HCN. What percentage of the acid is ionized in this
solution? The Ka for hydrocyanic acid is 4.9 x 10-10.
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4) Calculate the pH of a 0.50 M solution of benzoic acid (HC7H5O2). What percentage of the acid
is ionized in this solution? The Ka for benzoic acid is 6.3 x 10-5.
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5) Codeine (C18H21NO3) is a weak organic base. A 5.0 x 10-3 M solution of codeine has a pH of
9.95. (a) Calculate the value of Kb for this substance. (b) What percentage of the base is
ionized in this solution?
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6) Calculate the pH of a 0.075 M solution of ethylamine (C2H5NH2), a weak base. The Kb for
ethylamine is 6.4 x 10-4. What percentage of the base is ionized in this solution?
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