The equivalence point in a titration is the exact moment when the substance being added (the titrant) has completely reacted with the substance being analyzed (the analyte). At this point, neither reactant is in excess. In an acid-base titration, this means the moles of acid equal the moles of base, and the solution contains only salt and water. IUPAC, the international authority on chemical terminology, defines it as the stage where “the titrant has completely reacted with the titrand according to the stoichiometry of the reaction.”
Why the Equivalence Point Matters
Titration is fundamentally a measuring technique. You slowly add a solution of known concentration to a solution of unknown concentration, and by finding the exact volume needed to complete the reaction, you can calculate how much of the unknown substance was present. The equivalence point is the linchpin of that calculation.
The core math is straightforward: at the equivalence point, moles of titrant equal moles of analyte (adjusted for stoichiometry). If you know the concentration of your titrant and measure how much volume you added, you can calculate the moles delivered. Those moles equal the moles of the unknown substance in your original sample. From there, you can work backward to find its concentration. For example, if 150 mL of 0.1 M base is needed to reach the equivalence point, that means 0.015 moles of base were added, which reacted with exactly 0.015 moles of acid in the original solution.
Equivalence Point vs. End Point
These two terms sound interchangeable, but they refer to different things. The equivalence point is the theoretical, exact moment of complete reaction. You can’t directly observe it with your eyes. The end point is the moment you actually detect a change, usually a color shift caused by an indicator dye added to the solution.
An indicator is a weak acid or base that changes color at a specific pH. When the reaction nears completion and the pH shifts dramatically, the indicator responds with a visible color change. In a well-designed titration, the end point and equivalence point are extremely close together, but they’re rarely identical. The tiny gap between them is a small, accepted source of error.
pH at the Equivalence Point
A common misconception is that the equivalence point always occurs at pH 7. That’s only true for one specific combination: a strong acid titrated with a strong base (or vice versa). In that case, the salt produced doesn’t affect the pH, so the solution is neutral.
When a weak acid is titrated with a strong base, the equivalence point pH is above 7. That’s because the reaction produces a salt whose negative ion is slightly basic, pulling the solution to the alkaline side. Titrating acetic acid (vinegar) with sodium hydroxide, for instance, gives an equivalence point around pH 8.7.
The reverse is also true. When a strong acid is used to titrate a weak base, the equivalence point falls below 7, because the resulting salt is slightly acidic. Knowing which scenario you’re in determines everything from the indicator you choose to how you interpret your titration curve.
Reading a Titration Curve
If you plot pH on the vertical axis against the volume of titrant added on the horizontal axis, you get a characteristic S-shaped curve. The equivalence point sits right at the steepest part of that curve, where the pH changes most rapidly with each tiny drop of titrant added. Before and after that steep region, the pH changes gradually.
There are three mathematical approaches to pinpoint the equivalence point from measured data:
- The pH curve itself: Find the point where the slope is steepest, which corresponds to the inflection point of the S-curve.
- The first derivative: Plot how quickly pH is changing at each step. The equivalence point is where this first derivative reaches its maximum value.
- The second derivative: Plot how the rate of pH change is itself changing. The equivalence point is where the second derivative crosses zero, shifting from positive to negative. This method gives the most precise reading because a zero-crossing is easier to identify than a peak.
In practice, if your data shows the second derivative switching from positive to negative between 29.7 mL and 29.75 mL of titrant added, you can narrow the equivalence point to that narrow window with high confidence.
Choosing the Right Indicator
Since you need the indicator’s color change to match the pH at the equivalence point, picking the right one depends on what type of titration you’re running. Each indicator changes color over a specific pH range, centered roughly around its own characteristic value (called its pKa). Here are some common options:
- Thymol blue (pKa 1.6): changes from red to yellow between pH 1.2 and 2.8
- Methyl orange (pKa 4.2): changes from red to orange between pH 3.1 and 4.4
- Methyl red (pKa 5.0): changes from red to yellow between pH 4.2 and 6.2
- Bromothymol blue (pKa 7.1): changes from yellow to blue between pH 6.0 and 7.8
- Phenolphthalein (pKa 9.5): changes from colorless to pink/red between pH 8.3 and 10.0
- Alizarin yellow (pKa 11.0): changes from yellow to red between pH 10.1 and 12.4
For a strong acid/strong base titration with an equivalence point at pH 7, bromothymol blue is a natural fit. For a weak acid/strong base titration where the equivalence point lands above pH 7, phenolphthalein works well because its color change range (8.3 to 10.0) overlaps with that higher pH. For a strong acid/weak base titration with an equivalence point below 7, methyl orange or methyl red is the better choice.
Picking the wrong indicator means its color change happens at a pH that doesn’t correspond to the true equivalence point, and your calculated concentration will be off. The general rule: match the indicator’s transition range to the expected equivalence point pH, not just to pH 7.
Multiple Equivalence Points
Some substances can donate or accept more than one unit of acid or base. Phosphoric acid, for example, has three acidic protons, so titrating it with a strong base produces up to three equivalence points. Each one appears as its own steep jump on the titration curve. The second derivative method is especially useful here, because you’re looking for the specific zero-crossing that corresponds to each reaction stage. In the data, the equivalence point of interest is typically where the second derivative changes sign for the second time, not the first.
Polyprotic acids like this are common in biochemistry and environmental chemistry, so recognizing multiple equivalence points on a single curve is a practical skill, not just a textbook exercise.