Titration Methods in Analytical Chemistry

Overview: Titrations in Analytical Chemistry

• Titration involves determining the quantity of a substance (analyte) by reacting it with a known quantity of another substance (reagent).
• The process includes an introduction to titration, methodology and common titrimetry terms.

Introduction to Titration Methods

• Gravimetric methods quantitatively determine the mass of a pure compound chemically related to the analyte.
• Titration methods quantitatively determine the amount of a reagent with a known concentration (titrant) needed to react completely with the analyte (titrand).
• A titrant can be a chemical standard solution or an electric current of known magnitude.
• Volumetric titrations use the volume of a standard reagent as the measured quantity.
• Gravimetric titrations measure the mass of the reagent instead of its volume.
• Coulometric titrations measure the quantity of charge required for a complete reaction with the analyte.
• Redox titrations use volumetric methods involving electron transfer in analytical reactions.
• Additional titration methods include amperometric titrations and spectrophotometric titrations.

Terms used in Volumetric Titrations

• A standard solution (or standard titrant) is a reagent with a precisely known concentration.

• Titration entails slowly adding a standard solution to the analyte until the reaction is complete.

• The volume or mass of the reagent required to complete the titration is the difference between the initial and final readings.

• The equivalence point is the point in a titration when the amount of added standard reagent is equivalent to the amount of analyte.

• The end point refers to when a physical change indicates that the chemical equivalence condition is achieved.

• Indicators produce a physical change at or near the equivalence point during a titration.

• Titration error (E) is the difference in volume or mass between the equivalence point and the end point.

• E₁ = Vep - Vea : Vep is the actual volume of reagent to reach the end point, and Veo is the theoretical volume to reach the equivalence point

• See "Figure 11-1" to view a typical titration process

Standard Solutions: Qualities and Types

• An ideal standard solution remains stable, reacts rapidly and completely with the analyte, and undergoes a selective reaction quantitatively described by a balanced equation.
• A primary standard is a highly purified compound used as a reference material of high purity, atmospheric stability, absence of hydrate water, modest cost, reasonable solubility in the titration medium, and reasonably large molar mass.
• Secondary standards are less pure compounds often used when primary standards are unavailable.
• Standardization involves determining the concentration of a volumetric solution by titrating it against a carefully measured quantity of a primary or secondary standard, or a known volume of another standard solution.

Titration Methods: Direct vs. Back Titration

• Direct titration involves the titrant reacting directly with the analyte.
• Back-titration occurs when an excess of a standard solution consumes the analyte, and the excess is then titrated with a second standard solution.
• Back-titrations are necessary when the reaction rate is slow or when the standard solution lacks stability.

Volumetric Calculations

• Molar concentration (c) and normal concentration (CN) express concentrations for standard solutions in titrations.

• Molar concentration represents the number of moles of reagent in 1 liter of solution.

• Normal concentration represents the number of equivalents of reagent in 1 liter of solution.

• Key relationships for volumetric calculations:

• amount A (mol) = mass A (g) / molar mass A(g/mol)

• amount A (mmol) = mass A (g) / millimolar mass A (g/mmol)

• amount A (mol) = V(L) x CA (mol A / L)

• amount A (mmol) = V(mL) x CA (mmol A / mL)

• Examples 11-4 and 11-5 demonstrate determining the concentration of a solution standardized against a primary standard or another standard solution

• Example 11-5 demonstrates calculating the amount of analyte in a sample using titration data

• The calculations rely on three algebraic relationships: Equations 11-2 and 11-4, and the stoichiometric ratio of millimoles of analyte to millimoles of titrant.

Titration Curves

• Titration curves are plots that show a concentration-related variable against titrant volume.
• End points are detected by changes in color in the reagent (titrant), analyte or an indicator.
• End points are also detected a change in potential of an electrode that responds to the titrant concentration or the analyte concentration.

Types of Titration Curves

• Sigmoidal curves plot the p-function of the analyte (or sometimes the titrant) as a function of titrant volume.
• Linear segment curves measure readings on both sides of, but away from, the equivalence point, where the vertical axis is an instrument reading directly proportional to the analyte or titrant concentration.
• Sigmoidal curves offer speed and convenience.
• Linear segment curves are advantageous for reactions complete only in the presence of considerable excess reagent or analyte.

Understanding Concentration Changes During Titrations

• Table 11-1 shows the major changes in reagent and analyte concentrations during titration and the equivalence point.
• Figure 11-3 illustrates the large changes in relative equivalence using data from the fourth and fifth columns of Table 11-1.

Neutralization Titrations

• Focuses on acid-base titrations

Standard Solutions for Neutralization Titrations

• Standard solutions used in neutralization titrations involve strong acids or strong bases because they react more completely with an analyte.
• Standard solutions of acids include diluted hydrochloric, perchloric, or sulfuric acid.
• Nitric acid is rarely utilized.
• Standard solutions of bases usually consist of solid sodium, potassium, or barium hydroxides.

Acid-Base Indicators

• An acid-base indicator is a weak organic acid or base with different colors in its undissociated and conjugate forms.

• Figure 12-1 provides examples of 12 common indicators, including their colors and transition ranges.

• Equilibrium for an acid-type indicator is: HIn + H2O = In + H3O+

• (acid color) + (base color)

• Equation 12-1 is the equilibrium-constant expression for the dissociation of an acid-type indicator.

• K = [H₂O⁺ ] [In²] / [HIn]

• Equation 12-1 can be rearranged to give Equation 12-2.

• [H₂O+] = K [HIn] / [In]

• Equation 12-3 is derived from the negative logarithms of the expressions for the pH of acid color and the pH of basic color.

• indicator pH range=pK ±1 -Figure 12-3 displays indicator pH as a function of pH (pK = 5.0).

Errors in Acid-Base Titrations

• Determinate error occurs when the color change of the indicator differs from the pH at the equivalence point and is minimized by choosing the indicator.