Understanding the Equivalence Point in Acid-Base Titrations

In acid-base titrations, the equivalence point is the moment when the amount of acid equals the amount of base in a solution, resulting in a neutralization reaction. This point is crucial for accurately determining the concentration of an unknown solution. Below are three practical examples that illustrate how to determine the equivalence point in different scenarios.

Example 1: Titrating Hydrochloric Acid with Sodium Hydroxide

In a laboratory setting, a student is tasked with determining the concentration of hydrochloric acid (HCl) using a sodium hydroxide (NaOH) solution of known concentration.

The student starts with a 25 mL sample of HCl and titrates it with NaOH until the equivalence point is reached, indicated by a color change of the phenolphthalein indicator used in the titration. The NaOH solution has a concentration of 0.1 M.

After adding 20 mL of NaOH, the indicator changes color, signaling that the equivalence point has been reached. Using the formula for titration:

[
C_1V_1 = C_2V_2
]

Where:

(C_1) = concentration of HCl (unknown)
(V_1) = volume of HCl (25 mL)
(C_2) = concentration of NaOH (0.1 M)
(V_2) = volume of NaOH used (20 mL)

Plugging in the known values:

[
C_1(25) = (0.1)(20)
]

[
C_1 = \frac{(0.1)(20)}{25} = 0.08 M
]

Thus, the concentration of the HCl solution is 0.08 M.

Notes:

The phenolphthalein indicator is colorless in acidic solutions and pink in basic solutions, making it ideal for this titration.
Variations can include using different indicators based on the pH range of the equivalence point.

Example 2: Titrating Acetic Acid with Potassium Hydroxide

In a food chemistry lab, a researcher aims to determine the acetic acid concentration in vinegar by titrating it with a potassium hydroxide (KOH) solution. The KOH solution is 0.15 M, and a 10 mL sample of vinegar is used for the titration process.

Using phenolphthalein as the indicator, the researcher titrates the vinegar, carefully adding KOH until the solution turns pink, indicating that the equivalence point has been reached. It takes 15 mL of KOH to reach this point.

Applying the titration formula:

[
C_1V_1 = C_2V_2
]

Where:

(C_1) = concentration of acetic acid (unknown)
(V_1) = volume of acetic acid (10 mL)
(C_2) = concentration of KOH (0.15 M)
(V_2) = volume of KOH used (15 mL)

Substituting the known values:

[
C_1(10) = (0.15)(15)
]

[
C_1 = \frac{(0.15)(15)}{10} = 0.225 M
]

Thus, the concentration of acetic acid in the vinegar is 0.225 M.

Notes:

Different indicators can be used if titrating weak acids or bases that do not reach equivalence at neutral pH.
The accuracy of the equivalence point can be improved by performing multiple titrations and averaging the results.

Example 3: Titrating Sulfuric Acid with Barium Hydroxide

In an environmental science lab, a student needs to determine the concentration of sulfuric acid (H₂SO₄) in a wastewater sample. The student uses barium hydroxide (Ba(OH)₂), which has a concentration of 0.2 M, for the titration. A 50 mL sample of wastewater is used.

The student adds Ba(OH)₂ gradually while monitoring the pH with a pH meter until the pH reaches 7, indicating that the equivalence point is reached. The total volume of Ba(OH)₂ used is 30 mL.

Using the titration formula:

[
C_1V_1 = C_2V_2
]

Where:

(C_1) = concentration of H₂SO₄ (unknown)
(V_1) = volume of H₂SO₄ (50 mL)
(C_2) = concentration of Ba(OH)₂ (0.2 M)
(V_2) = volume of Ba(OH)₂ used (30 mL)

Substituting the known values:

[
C_1(50) = (0.2)(30)
]

[
C_1 = \frac{(0.2)(30)}{50} = 0.12 M
]

This indicates that the concentration of sulfuric acid in the wastewater is 0.12 M.

Notes:

The use of a pH meter provides a more precise determination of the equivalence point compared to visual indicators.
It’s crucial to consider the stoichiometry of the reaction, especially with diprotic acids like sulfuric acid.