4.2 Acid-base titrations and indicators

Acid-Base Titrations

Process of acid-base titration

An acid-base titration is a quantitative method for finding the concentration of an unknown acid or base. You do this by slowly adding a solution of known concentration (the titrant) to the unknown solution (the analyte) until the reaction is complete.

The equivalence point is the moment when the titrant has completely neutralized the analyte. Every mole of acid has reacted with every mole of base, with no excess of either. This is the target of the whole procedure.

Titrations show up in a wide range of practical settings:

• Determining the acetic acid concentration in vinegar or citric acid in fruit juice
• Quality control in food, beverage, and pharmaceutical production
• Environmental monitoring, such as measuring the acidity of rainwater or soil samples

Indicators for acid-base titrations

Indicators are themselves weak acids or weak bases. They change color over a specific pH range because their molecular structure shifts between a protonated form ($HIn$) and a deprotonated form ($In^-$), and each form absorbs different wavelengths of light. The color you see depends on which form dominates in solution.

When choosing an indicator, follow two rules:

1. The indicator's $pK_a$ should be close to the pH at the equivalence point. If the equivalence point pH is around 9, phenolphthalein works well. If it's around 4, methyl orange is a better fit.
2. The color change should be sharp and easy to see. A subtle shift from light yellow to slightly darker yellow is harder to call than colorless to pink.

Common indicators and their useful pH ranges:

For a strong acid–strong base titration, the equivalence point pH is 7, and several indicators work (including bromocresol green or phenolphthalein). For a weak acid–strong base titration, the equivalence point pH is above 7 because the conjugate base of the weak acid hydrolyzes in water, so phenolphthalein is the better choice. For a strong acid–weak base titration, the equivalence point pH is below 7 because the conjugate acid of the weak base hydrolyzes, making methyl orange more appropriate.

Calculations and Interpretation

Concentration calculations from titration data

For a monoprotic acid reacting with a monoprotic base in a 1:1 mole ratio, the key equation is:

$M_a \times V_a = M_b \times V_b$

• $M_a$ = molarity of the acid
• $V_a$ = volume of the acid
• $M_b$ = molarity of the base
• $V_b$ = volume of the base

This works because at the equivalence point, moles of acid equal moles of base. Since moles = molarity × volume, the equation follows directly.

For polyprotic acids or bases with different stoichiometries, you need to account for the mole ratio. For example, $H_2SO_4$ reacting with $NaOH$ has a 1:2 ratio, so the relationship becomes $2 \times M_a \times V_a = M_b \times V_b$.

Steps to find the unknown concentration:

1. Record the initial buret reading before you begin adding titrant.

2. Add titrant until the indicator signals the equivalence point (a persistent color change that lasts at least 30 seconds).

3. Record the final buret reading.

4. Calculate the volume of titrant used: $V_{titrant} = V_{final} - V_{initial}$.

5. Plug the known values into $M_a \times V_a = M_b \times V_b$ and solve for the unknown molarity.

Example: You titrate 25.00 mL of an unknown $HCl$ solution with 0.150 M $NaOH$. The equivalence point is reached after adding 18.30 mL of $NaOH$.

$M_a \times 25.00 \text{ mL} = 0.150 \text{ M} \times 18.30 \text{ mL}$

$M_a = \frac{0.150 \times 18.30}{25.00} = 0.110 \text{ M}$

Color changes vs. pH in titrations

As you add titrant to the analyte, the pH of the solution changes, and the titration curve has three distinct regions:

Before the equivalence point: The pH changes slowly with each addition of titrant. Most of the analyte hasn't reacted yet, so it dominates the solution's pH. The indicator stays in the color of its protonated form (for example, phenolphthalein remains colorless in acidic solution).

At the equivalence point: A very small addition of titrant causes a dramatic pH jump. This steep, nearly vertical region of the curve is where the indicator undergoes its color change. You'll see an intermediate shade briefly, then the color of the deprotonated form takes over. The steeper this region, the more precisely you can identify the equivalence point.

After the equivalence point: Excess titrant is now being added, so the pH levels off and changes slowly again. The indicator stays in the color of its deprotonated form (phenolphthalein stays pink).

One thing to watch: the endpoint (where the indicator actually changes color) and the equivalence point (where neutralization is chemically complete) are not always exactly the same. A well-chosen indicator keeps the difference negligibly small, but a poorly chosen one can introduce real error into your results. For example, using methyl orange for a weak acid–strong base titration would cause the color change to happen well before the true equivalence point, leading you to underestimate the concentration of the acid.