Simple Titration

Titration is a common laboratory method of quantitative chemical analysis used to determine the concentration of an identified analyte (a substance to be determined). A simple titration involves the gradual addition of a solution of known concentration (the titrant) to a known volume of a solution with an unknown concentration (the analyte) until the reaction reaches the endpoint, which is often indicated by a color change.

Basic Principles of Titration

In a titration, the reaction between the titrant and the analyte must be known and should be rapid and complete. The point at which the reaction is complete is called the equivalence point. The endpoint of a titration is the point at which the indicator changes color, which should be as close as possible to the equivalence point.

The most common type of titration is the acid-base titration, where the reaction involves a proton transfer. However, titrations can also be used for redox reactions, precipitation reactions, and complex formation reactions.

Steps in a Simple Titration

Preparation of Solutions: Prepare the analyte solution and standardize the titrant solution.
Setup: Rinse the burette with the titrant and fill it. Place the analyte in a flask along with a few drops of indicator.
Titration: Add the titrant to the analyte solution until the endpoint is reached.
Calculation: Calculate the concentration of the analyte using the volume of titrant added.

Titration Formula

The titration formula is based on the stoichiometry of the reaction. For a simple acid-base titration, the formula is:

$$ n_{\text{acid}} \cdot M_{\text{acid}} \cdot V_{\text{acid}} = n_{\text{base}} \cdot M_{\text{base}} \cdot V_{\text{base}} $$

Where:

$n_{\text{acid}}$ and $n_{\text{base}}$ are the stoichiometric coefficients of the acid and base in the balanced chemical equation.
$M_{\text{acid}}$ and $M_{\text{base}}$ are the molar concentrations of the acid and base.
$V_{\text{acid}}$ and $V_{\text{base}}$ are the volumes of the acid and base solutions.

Differences Between Endpoint and Equivalence Point

Endpoint	Equivalence Point
The point at which the indicator changes color.	The point at which the amount of titrant added is stoichiometrically equivalent to the amount of analyte in solution.
May not exactly coincide with the equivalence point.	Theoretical point where the reaction is complete.
Observable and practical measure during titration.	Determined by stoichiometry, not directly observable.

Example of a Simple Titration

Problem: You are titrating a 25.0 mL sample of hydrochloric acid (HCl) with 0.100 M sodium hydroxide (NaOH). It takes 30.0 mL of NaOH to reach the endpoint. What is the concentration of the HCl solution?

Solution: The balanced chemical equation for the reaction is:

$$ \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} $$

From the equation, we see that the stoichiometric coefficients ($n_{\text{acid}}$ and $n_{\text{base}}$) are both 1.

Using the titration formula:

$$ M_{\text{acid}} \cdot V_{\text{acid}} = M_{\text{base}} \cdot V_{\text{base}} $$

Substitute the known values:

$$ M_{\text{acid}} \cdot 25.0\ \text{mL} = 0.100\ \text{M} \cdot 30.0\ \text{mL} $$

Solve for $M_{\text{acid}}$:

$$ M_{\text{acid}} = \frac{0.100\ \text{M} \cdot 30.0\ \text{mL}}{25.0\ \text{mL}} $$

$$ M_{\text{acid}} = 0.120\ \text{M} $$

Therefore, the concentration of the HCl solution is 0.120 M.

Conclusion

Simple titration is a fundamental technique in chemistry for determining the concentration of a solution. It requires a well-understood reaction, a standardized titrant, and an appropriate indicator to signal the endpoint. By carefully performing the titration and applying the stoichiometric principles, one can accurately calculate the concentration of an unknown analyte.