Titration is a common laboratory method used to determine the concentration of an unknown chemical solution, called the analyte, by reacting it with a solution of known concentration, called the titrant. During an acid-base titration, a pH meter monitors the acidity or basicity of the analyte as the titrant is slowly added. A titration curve is the resulting visual representation, a graph that plots the continuous change in the analyte’s pH against the volume of titrant introduced. Analyzing this curve allows chemists to track the reaction’s progress and determine when the two substances have completely reacted with each other.
Understanding the Curve’s Layout
The horizontal x-axis measures the cumulative volume of the titrant added, typically in milliliters. The vertical y-axis represents the pH of the analyte solution. Because the pH scale is logarithmic, small changes in hydrogen ion concentration near the middle of the scale result in a substantial change in the curve’s height.
Most titration curves display four general regions that reflect the chemical state of the solution. The initial pH is determined solely by the analyte before any titrant is added. This is followed by a region of gradual change, where the pH shifts slowly as the titrant begins to react with the analyte. The third region is a sharp, nearly vertical slope where a minute addition of titrant causes a dramatic change in pH.
The curve levels off again in the fourth region as the solution becomes dominated by the excess titrant, and the pH approaches the value of the pure titrant. The slow changes in the initial and final regions occur because the solution resists changes to its pH, while the rapid change in the middle signifies the completion of the reaction.
Identifying the Equivalence Point
The equivalence point represents the exact volume of titrant required to stoichiometrically neutralize the analyte. This point is always located at the midpoint of the steep, vertical section of the curve.
A simple geometric method to locate this point involves drawing tangent lines parallel to the flat regions before and after the steep slope. A third line is then drawn to bisect the vertical distance between the two parallel tangents. The point where this bisection line intersects the curve marks the equivalence point.
For greater accuracy, derivative methods are often employed, particularly with digital data. The first derivative of the curve, which plots the change in pH divided by the change in volume, produces a graph with a distinct peak. The volume corresponding to the apex of this peak is the exact volume of the titrant at the equivalence point.
The second derivative method offers finer precision by plotting the change of the first derivative. This yields a curve that crosses the x-axis precisely at the equivalence point volume. Once the volume is determined, tracing horizontally to the y-axis reveals the pH at the equivalence point, a value governed by the strength of the acid and base used.
Interpreting Curve Shapes
The overall shape of the titration curve provides information about the strengths of the acid and base involved in the reaction. A titration involving a strong acid and a strong base, such as hydrochloric acid and sodium hydroxide, produces a curve with a sharp vertical rise. The equivalence point is found exactly at a pH of 7.0, because the resulting salt is neutral and does not react with water.
When a weak acid is titrated with a strong base, the curve begins at a higher initial pH than a strong acid of the same concentration. The shape features a relatively flat section before the steep rise, known as the buffer region, where the solution resists changes in pH. The equivalence point for this combination is always basic, occurring at a pH greater than 7.0, due to the hydrolysis of the conjugate base formed.
Conversely, titrating a weak base with a strong acid results in a curve that starts at a high, basic pH and drops toward the acidic region. This curve also exhibits a buffering region. The equivalence point for a weak base/strong acid titration is acidic, with a pH less than 7.0, because the conjugate acid reacts with water to release hydrogen ions.
The half-equivalence point is a key feature on weak acid or weak base titration curves. This point is located halfway through the buffering region, where half of the weak analyte has been neutralized. At the half-equivalence point, the concentration of the weak acid equals the concentration of its conjugate base. This simplifies the calculation such that the pH of the solution equals the acid’s pKa value, or the pOH equals the pKb for a weak base. This relationship allows the pKa or pKb, a measure of the analyte’s chemical strength, to be determined directly from the curve.