A titration is a quantitative chemical procedure used to determine the unknown concentration of a substance, called the analyte. This is achieved by reacting the analyte with a precisely known volume and concentration of a solution, called the titrant. The titrant is added until the reaction between the two is considered complete. The moment this reaction achieves theoretical completion is formally defined as the equivalence point.
The Stoichiometric Definition
The equivalence point represents the precise chemical stage where the moles of the added titrant are stoichiometrically equal to the moles of the analyte originally present in the solution. This is a purely theoretical point derived from the balanced chemical equation governing the reaction between the two substances. The stoichiometric ratio dictates the exact molar quantity of titrant required to consume the entirety of the analyte.
For instance, in the simplest acid-base reaction, one mole of acid reacts with one mole of base, establishing a 1:1 molar ratio. Reaching the equivalence point means the amount of base added has exactly matched the initial amount of acid. The reaction is considered complete, and the solution now contains only the products, typically a salt and water.
Prior to this point, the analyte is in excess, and afterward, the titrant becomes the excess substance. The volume of titrant used to reach this specific point is the fundamental measurement needed to calculate the unknown concentration of the analyte.
The equivalence point is determined through calculation and is not a point that can be directly observed in the laboratory. It acts as the conceptual target for any titration experiment, providing the basis for accurate concentration determination.
Distinguishing Equivalence from Endpoint
The terms equivalence point and endpoint are often used interchangeably, but they represent two distinct concepts in a titration. The equivalence point is the theoretical maximum of the chemical reaction based on stoichiometry, marking the moment when the reactants are chemically equivalent. The endpoint, conversely, is the observable event that signals the completion of the titration.
In most titrations, the endpoint is marked by a sudden, visible change in the solution, most commonly a change in color when a chemical indicator is used. The goal of a well-designed experiment is to select a detection method that makes the visually observed endpoint occur as close as possible to the theoretically calculated equivalence point.
A slight difference, referred to as the titration error, exists because the indicator itself must react to change color. If the indicator is poorly chosen, the endpoint may occur significantly after or before the true equivalence point. The equivalence point remains the scientific standard, while the endpoint is the practical, experimental approximation of that standard.
Practical Methods for Detection
Scientists employ two primary methods in the laboratory to determine the practical endpoint, which serves as the best possible proxy for the theoretical equivalence point.
Chemical Indicators
The traditional method involves adding a chemical indicator to the analyte solution before beginning the titration. Indicators are typically weak acids or weak bases that exhibit a different color depending on whether they are in their protonated or deprotonated form. The indicator is chosen so that its color transition range overlaps with the steep, rapid change in pH that occurs around the expected equivalence point. For example, phenolphthalein changes from colorless to pink over a specific pH range, signaling the endpoint.
Titration Curves
A more precise method involves using a pH meter to create a titration curve, which is a graph of the solution’s pH plotted against the volume of titrant added. The equivalence point is identified graphically as the inflection point, which is the steepest part of the resulting S-shaped curve.
By calculating the first or second derivative of the titration curve, the exact volume of titrant at the equivalence point can be pinpointed with high accuracy. This instrumental method eliminates the subjective visual error associated with color indicators, providing a highly reliable measure of the reaction’s completion. The pH meter is preferred when high precision is required.
Why the Equivalence Point pH Varies
A common misconception is that the equivalence point in an acid-base titration always occurs at a neutral pH of 7.0. This is only true for the titration of a strong acid with a strong base, such as hydrochloric acid (HCl) with sodium hydroxide (NaOH). The resulting salt, sodium chloride (NaCl), is neutral because neither the sodium ion nor the chloride ion reacts with water to affect the pH.
The pH at the equivalence point shifts away from 7.0 when one or both of the reactants are weak, due to a chemical process known as salt hydrolysis.
Weak Acid/Strong Base Titration
When a weak acid (like acetic acid) is titrated with a strong base, the resulting salt is sodium acetate. The acetate ion, which is the conjugate base of the weak acid, reacts with water. This hydrolysis reaction produces hydroxide ions (OH-), making the solution slightly basic at the equivalence point, typically resulting in a pH greater than 7.
Strong Acid/Weak Base Titration
Conversely, titrating a strong acid with a weak base (like ammonia) produces an acidic salt. The ammonium ion, the conjugate acid, hydrolyzes water to produce hydrogen ions (H+). This causes the equivalence point to occur at a pH less than 7, making the solution acidic. This variability underscores that the equivalence point is a measure of stoichiometric completion, not necessarily a measure of neutrality.