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. It does not mean that pH will be necessarily 7.
• 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 - Strong Base Titrations

• A strong acid dissociates completely in solution (HA(aq) ® A^-(aq) + H⁺(l)). Likewise, a strong base (BOH(aq) ® B⁺(aq) + OH^-(aq)).
• 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 a H₂O to produce an OH^- ion. The net ionic equation is H⁺(aq) + OH^-(aq) ® H₂O(l)

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

Example:

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 K_w = 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⁺].

• 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

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⁺)

• 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 which is strong thus we have an equilibrium:

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 (K_a = 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.

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

n(AH) = (0.05L * 0.2moles/L) = 0.01moles

• How many moles of strong base were added?

n(OH^-) = (0.01L * 0.1moles/L) = 0.001moles

• Since 0.001moles of base were added, 0.001moles of acid were neutralized (leaving 0.009 moles of weak acid), and 0.001moles of conjugate base were produced

n(A^-) = n(AH) - n(OH^-) = 0.009 moles

• The volume of the sample after addition of the base is now (0.05 + 0.01L) = 0.06L. Therefore, we have the following concentrations of weak acid and conjugate base:

[HA] = 0.009moles/0.06L = 0.15M

[A^-] = 0.001moles/0.06L = 0.0167M

• The balanced equation and equilibrium expression are:

HA(aq) ó H⁺(aq) + A^-(aq) and K_a = [H⁺]*[A^-] / [HA]

Thus [H⁺] = K_a * [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

• 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 salt and conjugate acid (NH₄⁺). The conjugate acid can donate a proton, thus, at the equivalence point the pH is slightly acidic

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 pK_a (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:

• The equivalence point is a single point defined by the reaction stoichiometry as the point at which the base (or acid) added exactly neutralizes the acid (or base) being titrated.
• The endpoint is defined by the choice of indicator as the point at which the colour changes. Depending on how quickly the colour changes, the endpoint can occur almost instantaneously or be quite wide.

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, K_a'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 pK_a 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.

• Thus for titrating a weak acid with a strong base where, at equivalence point the solution is slightly acidic, an optimum indicator should have a pKa > 7, for example Thymol Blue (pK_a = 8.9) or Phenolphthalein (pK_a = 9.4)
• For titrating a weak base with a strong acid at equivalence point encounters a slightly basic solution. Thus an optimum indicator should have a pKa < 7, for example Bromocresol Green (pK_a = 4.7) or Methyl Red (pK_a = 5.1)
• For titration involving strong base and a strong acid an optimum indicator should have a pKa ~ 7, for example Bromothymol Blue (pK_a = 7.0) or Phenol Red (pK_a = 7.9)

Titrations of Polyprotic Acids

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

Try this Virtual Titrator in Java and a neat set of notes and quizzes from UBC: PH tutorial.