Titration is a fundamental method in quantitative chemical analysis used to determine the unknown concentration of a substance, called the analyte, by reacting it with a solution of known concentration, the titrant. The equivalence point (EP) of an acid-base titration is the moment when the moles of the added titrant have exactly reacted with and neutralized the moles of the analyte present. Determining the pH at this stoichiometric point is crucial for understanding the reaction’s chemistry and calculating the analyte’s initial concentration.
The Chemistry of the Equivalence Point
The common assumption that the pH at the equivalence point must be 7.0 is often incorrect; this is only true for the reaction between a strong acid and a strong base. At the equivalence point, the acid and base have completely reacted, leaving only the salt formed from the neutralization reaction and water. The final pH depends entirely on whether the ions of this salt react with water, a process known as hydrolysis.
If the salt is formed from a weak acid, its conjugate base will react with water, generating hydroxide ions (OH-). The presence of these ions causes the solution’s pH to become basic, meaning it will be greater than 7.0. Conversely, the conjugate acid of a weak base will donate a proton to water, resulting in the formation of hydronium ions (H3O+). This increase in H3O+ concentration leads to an acidic solution, and the pH at the equivalence point will be less than 7.0.
Determining pH Experimentally
Two main experimental approaches are used to find the pH corresponding to the equivalence point. The most precise method uses an electronic pH meter to monitor the reaction and generate a titration curve. Small, measured volumes of the titrant are added sequentially, and the pH of the analyte solution is recorded after each addition.
Plotting the collected pH values against the total volume of titrant added produces a characteristic S-shaped curve. The equivalence point is visually identified as the center of the vertical, steepest portion of this curve. More accurately, the exact volume of the equivalence point is found by calculating the first or second derivative of the curve, locating the inflection point with high precision.
The second, more traditional method uses a chemical indicator, a substance that changes color over a specific, narrow pH range. The point at which the indicator visibly changes color is called the endpoint. For the endpoint to accurately estimate the equivalence point, the indicator must be carefully selected. The indicator’s pKa value must align closely with the expected pH of the equivalence point. For example, phenolphthalein is appropriate for titrations with a basic equivalence point because its color change range is between pH 8.2 and 10.0.
Calculating pH Based on Titration Type
The method for calculating the pH at the equivalence point relies on the chemical species present in the solution after the complete neutralization reaction. This calculation varies significantly depending on the strength of the acid and base involved in the titration.
Strong Acid/Strong Base
When a strong acid and a strong base react, such as hydrochloric acid (HCl) and sodium hydroxide (NaOH), the resulting salt, like sodium chloride (NaCl), consists of ions that do not hydrolyze in water. The chloride ion (Cl-) is the conjugate base of a strong acid and is too weak to react with water. Similarly, the sodium ion (Na+) is the conjugate acid of a strong base and does not react. Consequently, the pH of the solution is determined solely by the autoionization of water, resulting in a neutral equivalence point pH of 7.0 (at 25 degrees Celsius).
Weak Acid/Strong Base
Titrating a weak acid, like acetic acid (CH3COOH), with a strong base yields a solution at the equivalence point containing the conjugate base of the weak acid. This conjugate base hydrolyzes water, producing hydroxide ions (OH-) and making the solution basic (pH greater than 7.0).
The calculation begins by determining the concentration of the conjugate base anion at the equivalence point. This concentration is used in an equilibrium expression for the hydrolysis reaction, often set up using an ICE (Initial, Change, Equilibrium) table. To find the concentration of OH- and the final pH, the base dissociation constant (Kb) for the conjugate base is required. This Kb value is derived from the weak acid’s dissociation constant (Ka) and the ion product of water (Kw = 1.0 x 10^-14) using the relationship Kw = Ka x Kb. Once the OH- concentration is found, the pOH is calculated and subtracted from 14 to determine the final pH.
Strong Acid/Weak Base
The titration of a strong acid with a weak base, such as hydrochloric acid (HCl) and ammonia (NH3), leaves the conjugate acid of the weak base, the ammonium ion (NH4+), at the equivalence point. This conjugate acid donates a proton to water, forming hydronium ions (H3O+) and making the solution acidic (pH less than 7.0).
The first step is to calculate the concentration of the conjugate acid cation at the equivalence point. The acid dissociation constant (Ka) for the conjugate acid is necessary for the equilibrium calculation. This Ka is found from the weak base’s dissociation constant (Kb) and Kw using the relationship Kw = Ka x Kb. An ICE table is then used to model the hydrolysis reaction of the conjugate acid with water, allowing for the determination of the H3O+ concentration. Calculating the negative logarithm of this concentration directly yields the pH of the solution at the equivalence point.