A titration is a laboratory technique used to determine the unknown concentration of an acid or base (the analyte) by reacting it with a precisely known concentration of a base or acid (the titrant). The reaction continues until the Equivalence Point (EP) is reached. This is the theoretical point where the moles of titrant added are chemically equal to the moles of analyte originally present. Determining the pH at this point is fundamental, as the specific pH value depends entirely on the chemical strengths of the acid and base involved.
Understanding Equivalence Point Chemistry
The pH at the equivalence point is not always neutral (7.00). This value is determined by the behavior of the salt formed during the neutralization reaction. When an acid and base react, they produce a salt and water. The ions from this resulting salt may interact with water in a process called hydrolysis. Ions originating from a strong acid or base do not react significantly with water and are considered neutral.
However, ions that are the conjugate of a weak acid or base will hydrolyze water, which shifts the final pH. A conjugate base from a weak acid reacts with water to produce hydroxide ions (\(\text{OH}^-\)), making the solution basic (\(\text{pH} > 7\)). Conversely, a conjugate acid from a weak base reacts with water to produce hydronium ions (\(\text{H}^+\)), making the solution acidic (\(\text{pH} < 7[/latex]).
Calculating pH in Strong Acid-Strong Base Titrations
The calculation for a strong acid-strong base titration, such as [latex]\text{HCl}\) being titrated with \(\text{NaOH}\), represents the simplest case. At the equivalence point, the moles of \(\text{H}^+\) from the acid exactly equal the moles of \(\text{OH}^-\) from the base, reacting completely to form water. The resulting salt, such as \(\text{NaCl}\), is composed of ions that do not hydrolyze water.
Since the salt ions do not affect the \(\text{H}^+\) or \(\text{OH}^-\) concentration, the solution’s \(\text{pH}\) is determined solely by the auto-ionization of water. At \(25^\circ\text{C}\), the concentration of hydronium and hydroxide ions from water is \(1.0 \times 10^{-7}\text{ M}\). Consequently, the calculated \(\text{pH}\) at the equivalence point for any strong acid-strong base titration is always \(7.00\).
Calculating pH in Weak Acid-Strong Base Titrations
The calculation for a weak acid titrated by a strong base, such as acetic acid with \(\text{NaOH}\), is more involved because the equivalence point is basic (\(\text{pH} > 7\)). At this point, the weak acid has been completely converted into its conjugate base. This conjugate base, such as the acetate ion, acts as a weak base that hydrolyzes water to produce \(\text{OH}^-\) ions.
Calculation Steps
The first step requires calculating the concentration of the conjugate base using the total volume and moles of salt formed at the equivalence point. The base dissociation constant (\(\text{K}_b\)) is found using the relationship \(\text{K}_w = \text{K}_a \times \text{K}_b\). Here, \(\text{K}_w\) is the ion product of water (\(1.0 \times 10^{-14}\)) and \(\text{K}_a\) is the acid dissociation constant. This \(\text{K}_b\) value and the conjugate base concentration are used in an equilibrium expression to solve for the hydroxide ion concentration (\(\text{OH}^-\)). The resulting \(\text{[OH}^-]\) is then converted to \(\text{pOH}\) and subtracted from \(14.00\) to yield the final \(\text{pH}\).
Calculating pH in Strong Acid-Weak Base Titrations
When a weak base, such as ammonia (\(\text{NH}_3\)), is titrated with a strong acid, like \(\text{HCl}\), the calculation results in an acidic equivalence point (\(\text{pH} < 7[/latex]). At the equivalence point, the solution contains only the salt, which is the conjugate acid of the weak base (e.g., the ammonium ion, [latex]\text{NH}_4^+[/latex]). This conjugate acid hydrolyzes water to produce hydronium ions ([latex]\text{H}^+[/latex]), making the solution acidic.
Calculation Steps
The process begins by calculating the concentration of the conjugate acid at the equivalence point, accounting for the total volume of the mixed solutions. Its acid dissociation constant ([latex]\text{K}_a\)) is determined from the weak base’s \(\text{K}_b\) using the relationship \(\text{K}_w = \text{K}_a \times \text{K}_b\). The calculated \(\text{K}_a\) value and the conjugate acid concentration are applied in an equilibrium expression to determine the hydronium ion concentration (\(\text{H}^+\)). The final step involves taking the negative logarithm of \(\text{[H}^+]\) to find the acidic \(\text{pH}\).
Experimental Methods for Locating the Equivalence Point
While calculations provide the theoretical \(\text{pH}\), laboratory methods are necessary to practically locate the equivalence point during the titration. One common technique uses a chemical indicator, which is a weak acid or base that changes color over a specific \(\text{pH}\) range. The indicator must be chosen so that its color change, known as the end point, occurs as close as possible to the calculated \(\text{pH}\) of the equivalence point.
A more precise method involves using a \(\text{pH}\) meter to continuously monitor the solution’s \(\text{pH}\) as the titrant is added, generating a titration curve. The equivalence point is visually identified as the steepest part of the curve, where the \(\text{pH}\) changes most rapidly. For the highest accuracy, a first or second derivative plot can be used, which mathematically transforms the titration curve to pinpoint the exact volume of titrant added. The first derivative, \(\Delta(\text{pH})/\Delta\text{V}\), reveals the equivalence point as a sharp peak.