In an acid-base titration a solution containing a known concentration of base is slowly added to an acid until the acid is completely neutralized. Alternatively, a known concentration of acid is slowly added to a basic solution until the base is completely neutralized.
A. Strong Acid - Strong Base Titrations
Therefore, when a strong acid is combined with a strong base it produces a salt (anion from acid, cation from base) that has no tendency to affect the pH of a solution
HCl(aq) + NaOH(aq) ® NaCl(aq) + H2O(l)
Here both Cl-(aq) and Na+(aq) are spectator ions.
A.1. What happens when a stoichiometrically equivalent amount of base is added to a solution of acid, i.e. at equivalence point? [H+]0 = [OH-]0
All of the H+ ions present in the acid react with an equivalent amount of OH- ions from the base; and there are no net excess of either H+ or OH- ions (i.e. [H+] = [OH-]). The reaction of the H+ and OH- ions produces H2O(l): H+(aq) + OH-(aq) ® H2O(l) with Kw = 10-14. Also, [Na+] = [Cl-], and we essentially have a solution of NaCl(aq) in water with no effect on pH. When an equivalent amount of a strong base is added to a solution of a strong acid, the solution has a neutral pH (i.e. pH = 7.0)
A.2. What happens if the amount of base present in the solution is less than stoichiometrically equivalent to that of an acid? (Either: less amount of base is added to acidic solution or more than stoichiometrically equivalent amount of acid is added to basic solution), [H+]0 > [OH-]0
For the NaOH that is added, all of it will ionize making [OH-]0, and all of the OH- ions added will react with acid (initially at [H+]0) to produce H2O(l). Since [H+]0 > [OH-]0, when equilibrium is reached there will be remaining H+ ions and Cl- ions. The solution will contain primarily H+, Cl- and Na+ ions (almost no OH- ions, [H+] > [OH-] ). Thus, the solution will be acidic with:
[H+] = [H+]0 - [OH-]0 and pH = -log( [H+]0 - [OH-]0)
A.3. What happens if the amount of acid present in the solution is less than stoichiometrically equivalent to that of a base? (Either: less amount of acid is added to basic solution or more than stoichiometrically equivalent amount of base is added to acidic solution), [H+]0 < [OH-]0
Now all initial [H+]0 is neutralized and solution will be basic with:
[OH-] = [OH-]0 - [H+]0 and pH = 14 + log([OH-]0 - [H+]0)
Here is what a titration curve of a strong-acid/strong-base titration experiment might look like:
As we approach the equivalence point, the concentration of [H+] gets very small, and therefore, small additions of base will make a large relative change in the concentration of [H+].
B. The Addition of a Strong Base to a Weak Acid
The conjugate base of a weak acid will affect the pH of the solution (i.e. it will have some tendency to combine with a proton and produce the weak acid, thus affecting the concentration of H+). Thus, we need to consider the stoichiometry between the acid and the base, and the equilibrium reactions of the species that remain
B.1. What happens before the equivalence point?
The amount of strong base that is added will ionize completely, to produce a stoichiometric amount of OH-(aq) and conjugate acid (e.g. Na+)
HA(aq) + OH-(aq) <==> A-(aq) + H2O(l)
This amount of conjugate base has to be factored into the equilibrium expression to determine the [H+]
The remaining weak acid (after the neutralization) is the concentration for the pH calculation
For example: Calculate the pH of a solution of a monoprotic weak acid (Ka = 1.8 x 10-4) after 10 mL of 0.1M NaOH has been titrated into a 50 mL solution of 0.2M weak acid.
n(AH) = (0.05L * 0.2moles/L) = 0.01moles
n(OH-) = (0.01L * 0.1moles/L) = 0.001moles
n(A-) = n(AH) - n(OH-) = 0.009 moles
[HA] = 0.009moles/0.06L = 0.15M
[A-] = 0.001moles/0.06L = 0.0167M
HA(aq) ó H+(aq) + A-(aq) and Ka = [H+]*[A-] / [HA]
Thus [H+] = Ka * [HA] / [A-] = 1.8 x 10-4 * 0.15 / 0.0167 = 1.62 x 10-3
Resulting pH = 2.79
Titration Curves of Weak Acids with a Strong Base
B.2. What happens at the equivalence point?
At the equivalence point the solution contains only the salt. However, for a weak acid, the salt contains the conjugate base, which is able to recombine with a proton.
Thus, at the equivalence point of the titration of a weak acid with a strong base, the solution is slightly basic
B.3. What happens after the equivalence point?
After the equivalence point, the solution contains salt and excess (i.e. non-neutralized) base (OH-). The pH of the solution after the equivalence point is determined mainly by the excess OH- ions provided by the strong base
The Titration of a Weak Base with a Strong Acid
Similar features are observed for the titration of a weak acid/base with a strong base/acid
Choice of a pH Dye
Often titrations are performed with pH indicator dye which is titrated simaltaneosly with the solution. The neat thing about them is that they have different color in acidic, HA, and basic, A-, form. Different dyes have different pKa (check this out: Acid base indicators) and accordingly are useful for tracking the pH in a titration, usually as a means of detecting the equivalence point of the titration.
Consider the titration of an acid with a base in which a few drops of indicator have been added to the acid being titrated. Initially, the pH of the acid will probably be low enough that the indicator is almost entirely in its acidic (HIn) form. As base is added the pH will increase, causing the indicator to change to its basic (In-) form, causing a visible colour change. The point in the titration at which the colour changes is known as the endpoint of the titration.
The endpoint of a titration is NOT the same thing as the equivalence point:
If an appropriate indicator is chosen such that the endpoint of the titration occurs at the equivalence point, then a colour change in the solution being titrated can be used as a signal that the equivalence point has been reached. The volume of titrant needed to reach the equivalence point can then be read, allowing us to calculate concentrations, volumes, Ka's etc. as described in the previous section.
Intuition may suggest that the endpoint of the titration will occur at the equivalence point if we choose an indicator whose pKa is equal to the pH of the equivalence point. If such an indicator was chosen, the colour change would be half complete at the equivalence point.
Titrations of Polyprotic Acids
Polyprotic acids can potentially donate more than one proton
Try this Virtual Titrator in Java and a neat set of notes and quizzes from UBC: PH tutorial.