4.6.A.1 Titration and Equivalence Point:

1.Basic Principles of Titration:

i. Definition and Purpose of Titration:

Titration is a laboratory technique used to determine the concentration of a substance (an analyte) in a solution by adding a volume of a solution of known concentration (the titrant) until the reaction between the two substances is complete. The purpose of titration is to determine the unknown concentration of the analyte by reaching a specific endpoint, which indicates that the amount of titrant added is stoichiometrically equivalent to the analyte.

ii. Steps in Titration:
a. Preparation: A measured volume of the analyte is taken and transferred to a flask, sometimes along with an indicator.
b. Titration: The titrant is slowly added to the analyte until an endpoint is attained. The endpoint may be defined by a change in color or other easily perceived phenomenon.
c. Calculation: From the amount of titrant used and the known concentration, the analyte’s concentration is calculated by relating stoichiometry.

iii. Types of Titrations:

There are various types of titrations depending on the nature of the chemical reaction:

 a. Acid-Base Titration:

Purpose: It is used to determine the concentration of an acid or a base.
How it Works: A solution of acid is titrated with a solution of a base (or vice versa), and the endpoint is often indicated by a color change of a pH indicator.
Example: Titrating hydrochloric acid (HCl) with sodium hydroxide (NaOH).
Equation:     HCl(aq)+NaOH(aq)→NaCl(aq)+H2​O(l)
Indicator: Common indicators include phenolphthalein (for strong acid/strong base) and methyl orange (for weak acid/strong base).

b. Redox Titration:
Principle: To find out the concentration of an oxidizing or reducing agent.
How it Works: A redox reaction, where the titrant either donates or accepts electrons from the analyte. The endpoint can be identified by a color change in the solution or a potentiometer measuring voltage changes.
Example: Titration of a solution containing iron(II) ions (Fe²⁺) with potassium permanganate (KMnO₄), a strong oxidizing agent.
Equation:       5Fe2+(aq)+MnO4−​(aq)+8H+(aq)→5Fe3+(aq)+Mn2+(aq)+4H2​O(l)
Indicator: The titrant, such as KMnO₄, often acts as its own indicator because it changes color at the endpoint.

c. Complexometric Titration:
Purpose: To find the concentration of metal ions in a solution.
How it Works: A chelating agent (ligand) is used to form a complex with the metal ions. The titration is usually carried out in the presence of a pH buffer and an indicator that changes color when all the metal ions have reacted.
Example: Titrating calcium or magnesium ions in water using ethylenediaminetetraacetic acid (EDTA).
Equation:        Ca2+(aq)+EDTA4−(aq)→CaEDTA2−(aq)
Indicator: Eriochrome Black T is often applied for calcium or magnesium determinations.

These are the basic principles of titration and the common types used in chemical analysis. Each type of titration has its own specific methods and applications based on the nature of the substances involved and the desired outcome.

2. Equivalence Point and Endpoint:

• Equivalence Point

i. Definition and Importance of the Equivalence Point:

The equivalence point is that point in the titration where the amount of titrant added is chemically equivalent to the amount of analyte in the solution. It is the point at which the reaction between the titrant and analyte is complete with no excess of either reactant. Equivalence point, therefore, represents that exact point where stoichiometric amounts of both the two reactants reacted as per the balanced equation.

Importance: This is important because at the equivalence point, one can tell how much titrant is needed to fully neutralize or react with the analyte. All this becomes possible at the equivalence point. This is very important for accurate calculations in quantitative analysis.

ii. How to Know When the Equivalence Point Has Been Reached:

a. pH Measurements: In acid-base titrations, the equivalence point can often be determined by measuring the pH of the solution as the titrant is added. The pH typically undergoes a sharp change at the equivalence point. For strong acid-strong base titrations, this is usually a very steep pH rise. For weak acids or bases, the change may not be as sharp, and other methods may be used.
b. Graphical Method: By plotting the pH of the solution versus the volume of titrant added (a titration curve), the equivalence point is where the graph shows the most rapid change in pH.

c. Stoichiometric Calculation: In some cases, you can calculate the equivalence point based on the known concentration of the titrant and the volume added, using stoichiometry to determine when the titrant has completely reacted with the analyte.

• Endpoint
  Equivalence Point vs Endpoint:

  Equivalence Point: The point in the titration curve where the amount of titrant added is stoichiometrically equivalent to the amount of analyte present. Thus, at the equivalence point, there is a complete reaction.
  Endpoint: This is the point at which a visible change in the titration occurs; usually, it’s indicated by a color change brought about by an indicator. It is the experimental or practical endpoint for the titration, but it doesn’t necessarily coincide with the equivalence point.

Ideal conditions make the endpoint and equivalence point close, though they are very rarely the same. The endpoint tends to overshoot or fall a little short of the equivalence point. This is true because the sensitivity of the experiment is very minimal, and most indicators tend to have some limitation.

How Indicators Are Used to Detect the Endpoint:

Indicators are substances that change color at a specific pH or chemical condition, signaling the endpoint of a titration. The choice of indicator depends on the type of titration and the expected pH or chemical environment at the equivalence point.

Acid-Base Titration: Common acid-base indicators (such as phenolphthalein, methyl orange, or bromothymol blue) change color when the pH of the solution reaches a certain value. For example:
Phenolphthalein: Colorless turns pink with solution changing from acidic to slightly basic.
Methyl orange: Changes red to yellow in the transition from acidic to neutral or slightly basic.
Redox Titration: In redox titrations, indicators may change color based on the oxidation state of the substance. For example, in the titration of iron(II) with potassium permanganate, the permanganate itself acts as the indicator because it changes color from purple to colorless as it is reduced to Mn²⁺.

Complexometric Titration: Indicators such as Eriochrome Black T change color upon complete chelation of metal ions with an EDTA-type complexing agent. The indicator’s color often shifts from red to blue once a metal ion is complexed.

3. Stoichiometry of Titration:

Stoichiometry in titration is used to relate the amount of titrant, the known solution, to the amount of analyte, the unknown solution, through the balanced chemical equation of the titration reaction. This way, you will be able to determine the concentration of the analyte after performing the titration.

i. Application of Balanced Chemical Equations in Titrant and Analyte Amount Relationship

This is by making use of the balanced chemical equation that describes their reaction. Coefficients in the balanced equation provide a molar ratio of titrant to analyte. As such, this provides one basis to calculate the amount of analyte existing based on the amount of titrant used.

ii. Example Acid-Base Titration:

We have here an acid-base titration between hydrochloric acid (HCl) and sodium hydroxide (NaOH): HCl (aq) + NaOH (aq) → NaCl (aq) + H2O (l)
The balanced equation shows that the molar ratio of HCl and NaOH is 1:1.
This means that for every mole of HCl, one mole of NaOH is needed to neutralize it.

iii. Step-by-Step Process to Relate Titrant and Analyte:

1. Identify the reaction: Write the balanced chemical equation.
2. Determine the volume and concentration of the titrant: The concentration and volume of the titrant are usually known from the experiment.
3. Use stoichiometry: The mole ratio from the balanced equation enables one to relate the volume of titrant used to the volume of analyte.

Once the titration is completed, you can use the volume of titrant required to reach the endpoint and its concentration to calculate the concentration of the analyte.

iv. Steps for Calculation:

1. Write the balanced chemical equation to determine the molar relationship between titrant and analyte.
2. Calculate moles of titrant: Use the volume (in liters) and the concentration (in moles per liter) of the titrant to find the number of moles of titrant used.

                                                                                                             moles of titrant=Concentration of titrant (M)×Volume of titrant (L)

3. Use the mole ratio from the balanced equation to calculate the moles of the analyte, based on the moles of the titrant.

                                                                                            moles of analyte=moles of titrant×(mole ratio of titrant mole ratio of analyte​)

4. Determine the concentration of analyte: Once you know the moles of analyte, divide by the volume of the analyte in L to get its concentration.

                                                                                                    Concentration of analyte (M)=Volume of analyte (L)moles of analyte​