Analytical Chemistry Chapter 10

Volumetric Methods

Objectives

• Explain the basic principles of volumetric methods in analytical chemistry
• State the chemical basis of titrimetric analysis
• Construct and evaluate titration curves and their applications in quantitative analysis
• Apply concept of acid-base chemistry in volumetric and titrimetric methods
• Perform analysis of systems involving neutralization titrations

Introduction to Titration Methods

• Titration methods are based on determining the quantity of a reagent of known concentration required to react completely with the analyte
• Types of titration methods: volumetric, gravimetric, coulometric, redox, amperometric, and spectrophotometric

Terms Used in Volumetric Titrations

• Standard solution: a reagent of known concentration
• Standard titrant: a reagent of known concentration used to titrate the analyte
• Back-titration: a process in which the excess of a standard solution is determined by titrating it with a second standard solution

Equivalence Points and End Points

• Equivalence point: the point in a titration when the amount of added standard reagent is equivalent to the amount of analyte
• End point: the point in a titration when a physical change occurs that is associated with the condition of chemical equivalence
• Indicators produce an observable physical change at or near the equivalence point

Primary Standards

• A primary standard is a highly purified compound that serves as a reference material
• Criteria for a primary standard: high purity, atmospheric stability, absence of hydrate water, modest cost, and reasonable solubility in the titration medium

Standard Solutions

• Ideal standard solution: stable, reacts rapidly with the analyte, reacts more or less completely with the analyte, and undergoes a selective reaction with the analyte
• Two methods to establish the concentrations of standard solutions: direct method and standardization

Volumetric Calculations

• Molar concentration: the number of moles of reagent in 1 liter of solution
• Normal concentration: the number of equivalents of reagent in 1 liter of solution
• Calculations based on two pairs of equations: Equation 11-2 and Equation 11-4

Titration Curves

• Plots of a concentration-related variable versus titrant volume
• Two types of titration curves: sigmoidal curves and linear segment curves
• Advantages of sigmoidal curves: speed and convenience
• Advantages of linear segment curves: reactions that are complete only in the presence of a considerable excess of the reagent or analyte

Concentration Changes During Titrations

• Major changes in the relative concentrations of reagent and analyte that characterize the equivalence point in a titration
• Calculations of the concentration of unreacted HCl and NaOH added during the titration### Titration of a Strong Base with a Strong Acid
• Calculate the pH during the titration of 50.00 mL of 0.0500 M NaOH with 0.1000 M HCl at 25°C after the addition of various volumes of reagent.
• The titration curves for NaOH with HCl are shown in Figure 12-5, which can be used to select an indicator for the titration.

Titration Curves for Weak Acids

• Four types of calculations are needed to compute values for a weak acid or weak base titration curve:
  • Initially, only a weak acid or weak base is present, and the pH is calculated from the concentration of that solute and its dissociation constant.
  • After various increments of titrant have been added (up to, but not including, the equivalence point), the solution consists of a series of buffers, and the pH of each buffer can be calculated from the analytical concentrations of the conjugate base or acid and the concentrations of the weak acid or base that remains.
  • At the equivalence point, the solution contains only the conjugate of the weak acid or base being titrated, and the pH is calculated from the concentration of this product.
  • Beyond the equivalence point, the excess of strong acid or base titrant suppresses the acidic or basic character of the reaction product, and the pH is governed largely by the concentration of the excess titrant.

Example of Titration of a Weak Acid with a Strong Base

• Calculate the pH during the titration of 50.00 mL of 0.1000 M acetic acid (HOAc) with 0.1000 M sodium hydroxide at 25°C.
• The initial pH, pH after the addition of 10.00 mL and 25.00 mL of reagent, and the equivalence-point pH can be calculated using the dissociation-constant expression for acetic acid.
• The pH values calculated for this example are compared with a more dilute titration in Table 12-3 and Figure 12-6.

Characteristics of Titration Curves

• At the half-titration point in a weak-acid titration, the hydronium ion concentration equals the dissociation constant of the acid.
• At the half-titration point in a weak-base titration, the hydroxide ion concentration equals the dissociation constant of the base.
• The buffer capacities of each of the solutions are at a maximum at this point.
• The pH of buffers is largely independent of dilution, as shown in Figure 12-6.
• The effect of acid strength (dissociation constant) on titration curves is shown in Figure 12-7, which illustrates that the pH change in the equivalence-point region becomes smaller as the acid becomes weaker and the reaction becomes less complete.

Choosing an Indicator

• The choice of indicator is more limited for the titration of a weak acid than the titration of a strong acid.
• When there is a small change in end-point pH associated with the titration of a solution, there is likely to be a significant titration error regardless of indicator.
• Similar problems occur as the strength of the acid being titrated decreases.
• With more concentrated solutions, the titration can be performed with reasonable precision.