Titration is a fundamental technique in chemistry designed to determine the concentration of a substance in a solution. This quantitative chemical analysis method reacts a solution of unknown concentration (the analyte) with a precisely measured solution of known concentration (the titrant). The underlying principle is a complete and known chemical reaction between the two substances. By measuring the volume of the titrant required to complete the reaction, one can mathematically deduce the concentration of the unknown analyte.
Essential Variables and Terminology
Concentration is most commonly expressed as Molarity (M), defined as the number of moles of solute dissolved per liter of solution (mol/L). All titration calculations rely on determining the number of moles of each reactant.
The second primary measurement is Volume (V), the precise amount of liquid used for both the titrant and the analyte. While volume is often measured in milliliters (mL) during the experiment, it must always be converted to liters (L) for accurate Molarity calculations. This conversion is achieved by dividing the milliliter volume by 1,000.
The final concept is the Equivalence Point, which is the theoretical moment when the moles of titrant added exactly equal the moles of analyte, based on the specific molar ratio of their balanced chemical reaction. This point signals the completion of the reaction. Although the experimental endpoint is physically observed (often marked by an indicator color change), the equivalence point is the value used for the calculation. The equivalence point links the measured volume of the known solution to the unknown quantity of the analyte.
Applying Stoichiometry to Find Moles
The calculation begins by determining the moles (n) of the titrant that reacted at the equivalence point. This utilizes the relationship n = M × V, where V is the volume in liters. Calculating the moles of the known substance provides the first numerical value derived from the experiment. For instance, a 0.100 M titrant where 0.0250 L was added contains 0.00250 moles of the titrant.
The next step integrates stoichiometry, the study of quantitative relationships between reactants and products in a chemical reaction. This requires a correctly balanced chemical equation, which reveals the molar ratio. This ratio connects the known moles of the titrant to the unknown moles of the analyte.
If the reaction is a simple 1:1 ratio (e.g., hydrochloric acid (HCl) and sodium hydroxide (NaOH)), the moles of the titrant directly equal the moles of the analyte. For non-1:1 ratios, the moles of the titrant must be adjusted by the appropriate ratio to find the moles of the analyte. Applying this stoichiometric factor yields the exact quantity, in moles, of the unknown substance.
Calculating the Final Concentration of the Unknown
With the moles of the analyte now determined, the final step is to calculate its original concentration. This involves rearranging the Molarity formula: M = n/V. The moles (n) used are the moles of the analyte derived from the stoichiometry step. The volume (V) is the precisely measured initial volume of the unknown solution placed in the titration flask.
Consider an example where sulfuric acid (H₂SO₄), the analyte, is titrated with sodium hydroxide (NaOH), the titrant, which is a reaction with a 1:2 molar ratio. Suppose the initial sample volume of H₂SO₄ was 20.0 mL (0.0200 L). If the previous calculation determined that 0.00500 moles of H₂SO₄ were present in that sample, the concentration calculation becomes straightforward.
The original Molarity of the unknown H₂SO₄ solution is calculated by dividing the 0.00500 moles by the 0.0200 L initial volume. This results in a final concentration of 0.250 M for the sulfuric acid. This entire process links the precise volume and known concentration of the titrant to the volume of the unknown sample, using stoichiometry as the necessary link, to yield the final concentration of the analyte.