The Degree of Ionization, usually denoted with a greek lower case alpha, is the
ratio of the advancement of the dissociative ionization of the acid or base to the number
of moles of undissociated species if no dissociation is allowed to take place. If one
starts with only undissociated acid (or base) this ratio is the advancement over the
initial concentration
The Dilution of a Strong Acid is trivial:
| Initial Concentration |
% dissociation () |
pH |
| 0.10 M HCl |
100% |
1.00 |
| 0.010 M HCl |
100% |
2.00 |
| 0.0010 M HCl |
100% |
3.00 |
The Dilution of a Concentrated Weak Acid is also trivial:
| Initial Concentration |
% dissociation () |
pH |
| 0.10 M HAc |
1.3% |
2.88 |
| 0.010 M HAc |
4.2% |
3.37 |
| 0.0010 M HAc |
12% |
3.90 |
Note: A factor of ten dilution of a strong acid changes the
[H+(aq)] by a factor of 10
and thus the pH by one unit. The Dilution of a weak acid by a factor of 10 changes the
[H+(aq)] by (10)1/2 and the pH by 1/2 unit.
The Neutralization of an Acid: Titration
Titration is the reaction of a known volume of an unknown concentration of an
acid(base) with a known concentration of a base(acid). The pH of the mixture is
observed as a function of the volume of added stock reagent. In addition to dilution of
the unknown, acid/base neutralization occurs.
Let's Calculate a Titration Curve:
Strong Acid / Strong base titrations are easy to understand because the degree
of ionization of both the acid and base is 100% at all concentrations. Consider the
titration of 25.00 mL of 0.100 M HCl with 0.100 NaOH. (in this case
the "unknown's" concentration is known). The Net Ionic equation for this
neutralization is the classic one:
| Vol. NaOH
Added [mL] |
Total Volume
[mL] |
% Diss
Acid |
n[H+]e
mmol |
n[OH-]e
mmol |
pH |
| 0 |
25 |
100% |
2.5 |
2.5 x 10-12 |
1.00 |
| 10 |
35 |
100% |
1.5 |
8.2 x 10-12 |
1.37 |
| 20 |
45 |
100% |
0.5 |
4.0 x 10-11 |
1.95 |
| 22 |
47 |
100% |
0.3 |
7.3 x 10-11 |
2.19 |
| 24 |
49 |
100% |
0.1 |
2.5 x 10-10 |
2.70 |
| 25 |
50 |
100% |
5.0 x 10-6 |
5.0 x 10-6 |
7.00 |
| 26 |
51 |
100% |
2.6 x 10-10 |
0.1 |
11.30 |
| 28 |
53 |
100% |
9.4 x 10-11 |
0.3 |
11.75 |
| 30 |
55 |
100% |
6.0 x 10-11 |
0.5 |
11.96 |
| 40 |
65 |
100% |
2.8 x 10-11 |
1.5 |
12.36 |
| 50 |
75 |
100% |
2.3 x 10-11 |
2.5 |
12.52 |
- The point at which the same number of moles of acid and base are present in
solution is called the equivalence point.
- For a Strong Acid / Strong Base titration, the equivalence point is at neutral pH
(pH=7)
- At all times the water self ionization equilibrium is maintained, i.e.
Test Your Knowledge: At this point, you should have all the tricks needed to
calculate a titration curve for the neutralization of a weak acid by a
strong base. (You may use a spreadsheet or MathCad type computer program or
simply graph paper and a calculator) Assume 25.00 mL of 0.100 M of the
hypothetical acid HA (Ka = 1.0 x 10-5) is titrated with 0.100 M NaOH. Fill in the table
below and graph the results in the form: (pH) vs (volume base added)
| Vol. NaOH
Added [mL] |
Total Volume
[mL] |
% Diss
Acid |
n[H+]e
mmol |
n[OH-]e
mmol |
pH |
| 0 |
25 |
|
|
|
|
| 10 |
35 |
|
|
|
|
| 20 |
45 |
|
|
|
|
| 22 |
47 |
|
|
|
|
| 24 |
49 |
|
|
|
|
| 25 |
50 |
|
|
|
|
| 26 |
51 |
|
|
|
|
| 28 |
53 |
|
|
|
|
| 30 |
55 |
|
|
|
|
| 40 |
65 |
|
|
|
|
| 50 |
75 |
|
|
|
|
Bonus Question: What, in general, is the pH at the equivalence point for this type of
titration?
TOP