Acid-Base Titrations

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.

• The equivalence point is the point at which a stoichiometrically equivalent amount of base has been added to the acid
• This situation can be identified by noting an appropriate (pH-induced) color change in an indicator dye that is added to the solution. Or a pH meter can be used to measure the pH of the solution as a function of added base
• A graph or plot of the pH as a function of added titrant (e.g. base solution) is called a titration curve
• A titration curve can help to figure out when the equivalence point occurs, and also the value of the acid or base dissociation constant (i.e. K_a, or K_b). The titration curve can also help identify what type of indicator dye would be most useful in following the acid-base neutralization reaction

• A strong acid ionizes completely in solution. Likewise, a strong base.
• The conjugate base of the strong acid has no tendency to combine with a H⁺. Likewise, the conjugate acid of the strong base has no tendency to combine with OH^- to produce a H₂O.

Example:

HCl(aq) + NaOH(aq) ® NaCl(aq) + H₂O(l)

What happens when a stoichiometrically equivalent amount of strong base is added to a solution of a strong acid?

• 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 H⁺ or OH^- ions left over (i.e. [H⁺] = [OH^-]). The reaction of the H⁺ and OH^- ions produces H₂O(l)
• Also, [Na⁺] = [Cl^-], and we essentially have a solution of H₂O and NaCl(aq)
• Since the NaCl produced has no effect upon pH, when an equivalent amount of NaOH is added to a solution of HCl the solution has a neutral pH (i.e. pH = 7.0)

What happens if a less-than-stoichiometrically equivalent amount of strong base is added to the strong acid solution?

• For the NaOH that is added, all of it will ionize, and all of the OH^- ions added will react with acid (to produce Na⁺ and H₂O(l))
• Since the NaOH that was added is less than the concentration of HCl acid, there will be remaining H⁺ ions and Cl^- ions

• The [Cl^-] will be greater than [Na⁺] in this case, but who cares? We have already determined that they don't affect the pH anyway. Thus, the solution will be acidic if less-than-stoichiometrically equivalent amount of base is added
• The concentration of [H⁺] ion will be equal to the starting concentration minus the amount that is neutralized. The amount that is neutralized is equal to the concentration of added base. The pH of the solution will be determined by the amount of [H⁺] remaining after this neutralization

What happens if a greater-than-stoichiometrically equivalent amount of base is added to the acid solution?

• All H⁺ from the acid are neutralized (essentially no H⁺ from the acid remains)
• There will be Cl^- ions, Na⁺ ions and OH^- ions in solution. Thus, the solution will be basic.
• The [Na⁺] will be greater than [Cl^-], but who cares? These ions don't affect pH. Thus, the pH will depend upon the concentration of the OH^- ions in solution.
• The concentration of OH^- ions will be equal to the amount of basic solution added minus the amount that is neutralized. The amount neutralized is equal to the concentration of acid in the original sample.

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⁺].

• Because of this, there is a large change in pH near the equivalence point
• This behavior also means that we can use an indicator dye to show when we are very close to the equivalence point, even though the indicator may change color at a pH that is not exactly equal to pH 7.0

This gets a little complicated because the conjugate base of the 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
• 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⁺)
• The stoichiometric amount of OH^-(aq) will react completely with an equivalent amount of H⁺ ion released by the weak acid
• Therefore, a stoichiometric amount of weak acid will ionize and be neutralized.
• This will also result in the production of a stoichiometric amount of conjugate base:

HA(aq) + OH^-(aq) ® A^-(aq) + H₂O(l)

For example: Calculate the pH of a solution of a weak acid with K_a = 1.8 x 10^-4 after 10ml of 0.1M NaOH has been titrated into a 50ml solution of 0.2M weak acid.

• First of all, how many total moles of weak acid do we have?

HA(aq) ó H⁺(aq) + A^-(aq)

• 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.

• 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
• Notice that after one-half of the acid has been stoichiometrically titrated the [HA] = [A-]. At this point the pH = pKa. If you look at the above curves you will notice that the titration profile is relatively flat around the pH = pK_a point. This means that within this region the pH is not changing much upon the addition of small amounts of base. This is the definition of a "buffered" solution, and explains why the most effective buffering is at a pH value equal to the pKa.
• Notice also that the transition is sharp at the equivalence point. This is the opposite property that we would want for a buffered solution. It means that the pH changes a lot with small changes of added base. At the equivalence point all the acid has been titrated and essentially none of the [HA] form remains. Thus, there is no longer any ability to neutralize added base (and so, the solution can no longer buffer against such changes)

Similar features are observed for the titration of a weak acid/base with a strong base/acid

• In the case of a weak base titrated with a strong acid, the pH after the equivalence point is determined by the excess [H⁺] from the strong acid
• At the equivalence point, the solution contains conjugate base of the strong acid (e.g. Cl-; does not affect pH) and conjugate acid (e.g. NH₄⁺ which will affect pH - i.e. has some tendency to release H+ ions). The conjugate acid can donate a proton, thus, at the equivalence point the pH is lower than neutral (pH 7.0)

Polyprotic acids can potentially donate more than one proton

• Each proton will have an associated K_a value
• The titration curve will reflect the separate K_a values
• There will be two unique equivalence points, associated with the separate K_a values