Titration is a fundamental analytical chemistry technique used to determine the molarity (concentration) of an unknown solution (the analyte). This is achieved by precisely reacting the analyte with a solution of known concentration (the titrant) until the chemical reaction is complete. Molarity is defined as the amount of solute, measured in moles, dissolved per liter of solution. Calculating this value requires careful measurement and relies on knowing the exact quantity of the standardized solution needed to react completely with the unknown substance.
Understanding the Core Concepts
Before calculations begin, the chemical relationship between the two substances must be established. The equivalence point is defined as the point where the moles of the added titrant exactly balance the moles of the analyte, based on reaction stoichiometry. This point is often signaled visually by an indicator dye that changes color. A balanced chemical equation provides the mole ratio linking the known quantity of the titrant to the unknown quantity of the analyte.
For instance, in a common acid-base titration, sulfuric acid (\(H_2SO_4\)) reacting with sodium hydroxide (\(NaOH\)) follows the balanced equation: \(H_2SO_4 + 2NaOH \rightarrow Na_2SO_4 + 2H_2O\). This equation shows that one mole of sulfuric acid reacts completely with two moles of sodium hydroxide, establishing a 1:2 mole ratio. This ratio is crucial for translating the measured volume of the standard solution into the amount of substance in the unknown solution.
Determining Moles of the Standard Solution
The first mathematical step is calculating the moles of the titrant delivered from the burette. This uses the standardized molarity of the titrant and the exact volume dispensed to reach the equivalence point. Volume measured in milliliters (mL) must be converted into liters (L) before calculation. This is done by dividing the milliliter measurement by 1,000, aligning the unit with molarity’s “per liter” component.
Once in liters, moles of the standard solution are determined using the relationship: Moles = Molarity \(\times\) Volume. For example, if the titrant had a known concentration of 0.100 M and exactly 25.00 mL (or 0.02500 L) was used, the moles of the titrant would be \(0.100 \text{ mol/L} \times 0.02500 \text{ L}\), which equals \(0.00250 \text{ moles}\). This calculated value establishes the known starting point for determining the concentration of the unknown solution.
Applying Stoichiometry to Find Moles of the Unknown
The moles of the standard solution must now be converted into the corresponding moles of the unknown analyte using the reaction’s stoichiometric coefficients. This step applies the mole ratio established by the balanced chemical equation. The mole ratio translates the quantity of the consumed titrant into the quantity of the analyte originally present. Conversion is achieved by multiplying the moles of the known substance by a fraction derived from the balanced equation’s coefficients.
Returning to the sulfuric acid and sodium hydroxide example, where the mole ratio is 1 mole of \(H_2SO_4\) to 2 moles of \(NaOH\), the calculation is straightforward. If \(0.00250\) moles of the titrant (\(NaOH\)) were used, the amount of the analyte (\(H_2SO_4\)) is determined by multiplying the moles of \(NaOH\) by the ratio \(\frac{1 \text{ mol } H_2SO_4}{2 \text{ mol } NaOH}\). Performing this calculation yields \(0.00250 \text{ moles } NaOH \times \frac{1}{2} = 0.00125 \text{ moles } H_2SO_4\).
Correct application depends on identifying which coefficient corresponds to the known substance and which to the unknown. The unknown substance’s mole is placed in the numerator, and the known substance’s mole is placed in the denominator. This fraction ensures units cancel, yielding the moles of the analyte, which is the final piece of information needed before concentration determination.
Calculating the Final Molarity
The final step is to calculate the analyte’s concentration (molarity) using the determined moles. Molarity is calculated by dividing the moles of the analyte by the initial volume of the analyte solution measured into the flask. The relationship is: Molarity = Moles / Volume. The moles used are the value calculated in the preceding stoichiometric step.
The required volume is the initial, precise volume of the unknown solution placed in the reaction flask. This initial volume, usually measured using a pipette, must also be converted from milliliters to liters. For instance, 10.00 mL of the unknown solution converts to 0.01000 L. Using the calculated \(0.00125\) moles of \(H_2SO_4\) and \(0.01000 \text{ L}\), the final molarity is \(\frac{0.00125 \text{ moles}}{0.01000 \text{ L}}\), resulting in \(0.125 \text{ M}\).