# Acid-Base Titrations

### Acid-Base Indicators

Acid-base indicators are weak acids or weak bases that can be used to detect changes in pH during a titration.

A titration is quantitative method that relies on measuring the volume of a solution of a known concentration necessary to neutralize a given volume of acid or base. In acid-base titration, strong acid or strong base is added to the unknown solution up to the point of neutralization. The concentration of acid or base in the unknown solution can then be calculated from the known amount of acid or base added.

An important aspect of acid-base titrations is being able to detect changes in pH as a volume of acid or base is being added to the solution of unknown concentration. An acid-base indicator is a weak acid or base that is different colors in the dissociated and nondissociated states. As the amount of dissociated acid or base increases, the solution changes color, making the change in pH visible.

Often an acid-base titration is used to determine the concentration of a solution of acid or base. This is done by adding acid or base of a known concentration (the titrant) to the unknown solution (the analyte). At the equivalence point all the acid or base molecules in the acidic or basic solution have been neutralized. At this point, the number of molecules added to the solution is stoichiometrically equal to the number originally present. In other words, if the ratio of acid to base in the balanced equation is 1:1, then the number of molecules added equals the number originally present. If the balanced equation calls for two molecules of acid to neutralize every molecule of base, the ratio of acid added to base neutralized will be 2:1.

Like the analyte, the indicator used in an acid-base titration also absorbs acid or base ions and will also reach an equivalence point. Ideally, this will occur at the pH at which the acid-base indicator changes color, called the end point.

Because the indicator is a weak acid or base, the end point can be expressed as an equilibrium:
$K_{\rm a}=\frac{\lbrack\rm H^+\rbrack\lbrack\rm{Ind}^-\rbrack}{\lbrack\rm{HInd}\rbrack}$
where [HInd] is the concentration of the indicator, a weak acid in this case, and [Ind] is the concentration of its conjugate base. An acid-base indicator works because HInd and Ind are different colors. The solution will be one color for most of the pH range below the end point and another color for most of the pH range above the end point. The color of the solution will change from the first to the second as the titration takes the pH through and past the end point.

The Henderson-Hasselbalch equation relates pH and pKa by the concentrations of the acid and its conjugate base. If $\frac{\lbrack\rm{Ind}^-\rbrack}{\lbrack\rm{HInd}\rbrack}$ is greater than 1, then pH will be greater than pKa, and the solution will be more basic than before. If $\frac{\lbrack\rm{Ind}^-\rbrack}{\lbrack\rm{HInd}\rbrack}$ is less than 1, then pH will be less than pKa, and the solution will be more acidic than before.

Many indicators will begin to change color when they get within one pH point of their end point and will continue to change until they are about one pH point past the end point.

### Titration Curves

Titration curves show changes in pH as titrant is added to the analyte.

During titration, as more and more titrant is added to an analyte solution, the pH of the solution changes. A titration curve is a graph showing the change in pH of an analyte solution as titrant is added. Initially, the pH changes slowly, until the solution approaches its equivalence point. At that point the pH rises rapidly and then levels off.

Titration curves are similar, with slight differences, in different titration scenarios.

When a strong acid analyte, such as hydrochloric acid (HCl), is titrated against a strong base titrant, such as sodium hydroxide (NaOH), the titration curve will typically be steep.

#### Titration Curve for Strong Acid-Strong Base Titration

Since the hydrochloric acid (HCl) completely dissociates, the analyte solution initially contains a high concentration of hydrogen (H+) ions, giving it a low pH. The sodium hydroxide (NaOH) that is added also completely dissociates. As the titration begins, the hydroxide (OH) ions entering solution will neutralize the H+ ions, and the pH slowly rises. Eventually, so many of the H+ ions are neutralized that the concentration of OH ions begins to increase. At that point the pH rises sharply, and the slope of the curve becomes nearly vertical. The equivalence point occurs midway along this vertical portion of the curve, at pH 7. As more titrant is added, very few H+ ions remain, and the solution is dominated by OH ions. Once this happens, the pH levels off at a high pH.

To calculate the pH after titrating an acid with a base, follow these steps:

1. Calculate the number of moles of titrant added. This is used to determine the amount of OH ions that have been added and therefore the amount of H+ ions that have been neutralized.

2. Calculate the number of moles of H+ initially, and subtract the number of neutralized ions to find the number of moles remaining.

3. Calculate the total volume, and determine the concentration of protons (H+), which can be used to calculate pH.

Step-By-Step Example
Calculation of pH for a Known Amount of Titrant
Suppose 200.0 mL of 1.0 M HCl is titrated with 2.0 M NaOH. What is the pH when 80.0 mL of NaOH has been added?
Step 1
Determine the moles of HCl present at the start of the titration.
$(200.0\;\rm{mL}\;\rm{HCl}\;)\left(\frac{1\;\rm L}{1{,}000\;\rm{mL}}\right)\!\left(\frac{1.0\;\rm{mol}}{\rm L}\right)=0.20\;\rm{mol}\;\rm{HCl}$
Step 2
Determine the moles of NaOH that have been added.
$(0.0800\;\rm L\;\rm{NaOH})\!\left(\frac{2.0\;\rm{mol}}{\rm L}\right)=0.16\;\rm{mol}\;\rm{NaOH}$
Solution
Because HCl is a strong acid and NaOH is a strong base, assume all 0.16 mol NaOH reacts with 0.16 mol HCl, leaving 0.04 mol H3O+. The total volume is now 280.0 mL of solution containing 0.04 mol H3O+.
$\left[{\rm H}_3\rm O^+\right]=\frac{0.04\;\rm{mol}}{0.2800\;\rm L}=\;0.14\;\rm M$
$\rm{pH}=-\log\left[{\rm H}_3\rm O^+\right]=-\log \;(0.14)=0.85$

A similar approach can be used to calculate pH anywhere along the curve in any of the three titration scenarios.

When a weak base is titrated with a strong acid titrant, a slightly different curve forms. The initial pH is moderately high because the solution is basic but not strongly so. The presence of some undissociated base in the analyte solution will act as a buffer, able to accept the added protons. Therefore, although the pH falls, it does so more slowly than it would if the base were strong. Once nearing the equivalence point, the curve slopes steeply, and once again the equivalence point is in the middle of the steep region. The curve then levels out again at a low pH because the solution is acidic. Note that the solution at the equivalence point is not neutral but slightly acidic. This means the best indicator for this type of titration would be one that reaches its end point in slightly acidic conditions.

#### Titration Curve for Weak Base-Strong Acid Titration

When a weak acid is titrated with a strong base titrant, the initial pH is moderately low. The pH rises slowly. Near the equivalence point, the curve slopes steeply. It then levels out again at a high pH because the solution is basic. When a strong base is titrated with a weak acid titrant, the initial pH is very high, given the total dissociation of the base. Addition of the titrant lowers the pH slowly, until nearing the equivalence point. The curve then levels out at a moderately low pH because the solution is weakly acidic.

#### Titration Curve for Strong Base-Weak Acid Titration

When a strong acid is titrated with a weak base, the shape of the curve is opposite the shape of a strong base titrated with a weak acid. In this case, the initial pH is very low, with total dissociation of the acid. Addition of the titrant slowly increases the pH, until near the equivalence point. The curve then levels out at a moderately high pH because the solution is weakly basic.