Introduction to Analytical Chemistry Chapter 2 Important Chemical Concepts and a Basic Approach to Chemical Equilibrium

2A Some Important Units of Measurement 2A-1 SI Units Scientists throughout the world are adopting a standardized system of units known as the International System of Units (SI). This system is based on the seven fundamental base units shown in Table 2-1. Numerous other useful units, such as volts, hertz, coulombs, and joules, are derived from these base units. 2-2

Table 2-1 2-3

Table 2-2 2-4

2A-1 SI Units SI is the acronym for the French “Système International d’Unités.” The ångstrom unit, Å, is a non-SI unit of length that is widely used to express the wavelength of very short radiation such as X-rays (1 Å = 0.1 nm = 10-10 m). Typical X-radiation lies in the range of 0.1 to 10 Å. 2-5

2A-2 The Mole The mole (mol) is the SI unit for the amount of a chemical species. It is always associated with a chemical formula and represents Avogadro’s number (6.022 × 1023) of particles represented by that formula. The molar mass (M) of a substance is the mass in grams of one mole of the substance. 2-6

Feature 2-1 Distinguishing between Mass and Weight Photo of Edwin “Buzz” Aldrin taken by Neil Armstrong in July 1969. Armstrong’s reflection may be seen in Aldrin’s visor. The suits worn by Armstrong and Aldrin during the Apollo 11 mission to the Moon appear to be quite massive. But because the mass of the Moon is only 1/81 that of Earth and the acceleration due to gravity is only 1/6 that on Earth, the weight of the suits on the Moon was only 1/6 of their weight on Earth. The mass of the suits, however, was identical in both locations. Photo courtesy of the National Aeronautics and Space Administration. 2-7

Feature 2-2 Atomic Mass Units and the Mole The masses for the elements listed in the table inside the back cover of this text are relative masses in terms of atomic mass units (amu), or daltons. The atomic mass unit is based on a relative scale in which the reference is the 12C carbon isotope, which is assigned a mass of exactly 12 amu. 2-8

Feature 2-2 Atomic Mass Units and the Mole The molar mass M of 12C is defined as the mass in grams of 6.022 × 1023 atoms of the carbon-12 isotope, or exactly 12 g. The molar mass of any other element is the mass in grams of 6.022 × 1023 atoms of that element and is numerically equal to the atomic mass of the element in amu units. Thus, the atomic mass of naturally occurring oxygen is 15.9994 amu; its molar mass is 15.9994 g. 2-9

2B Solutions and Their Concentrations 2B-1 Expressing Solution Concentrations Molar Concentration The molar concentration (cx) of a solution of a chemical species X is the number of moles of the solute species that is contained in one liter of the solution (not one liter of the solvent). Molar concentration, or molarity M, has the dimensions of mol L-1. 2-10

2B-1 Expressing Solution Concentrations Analytical Molarity The analytical molarity of a solution gives the total number of moles of a solute in 1 L of the solution, or alternatively, the total number of millimoles in 1 mL. For example, a sulfuric acid solution that has an analytical concentration of 1.0 M can be prepared by dissolving 1.0 mol, or 98 g, of H2SO4 in water and diluting to exactly 1.0 L. 2-11

2B-1 Expressing Solution Concentrations Equilibrium Molarity The equilibrium molarity, or species molarity, expresses the molar concentration of a particular species in a solution at equilibrium. For example, the species molarity of H2SO4 in a solution with an analytical concentration of 1.0 M is 0.0 M because the sulfuric acid is entirely dissociated into a mixture of H3O+, HSO4-, and SO42-, ions; there are essentially no H2SO4 molecules as such in this solution. The equilibrium concentrations and thus the species molarities of these three ions are 1.01, 0.99, and 0.01 M, respectively. 2-12

2B-1 Expressing Solution Concentrations Equilibrium molar concentrations are usually symbolized by placing square brackets around the chemical formula for the species, so for our solution of H2SO4 with an analytical concentration of 1.0 M, we can write 2-13

2B-1 Expressing Solution Concentrations Percent Concentration Chemists frequently express concentrations in terms of percent (parts per hundred). Three common methods are 2-14

2B-1 Expressing Solution Concentrations Parts Per Million and Parts Per Billion parts per billion (ppb) parts per thousand (ppt) 2-15

2B-1 Expressing Solution Concentrations Parts Per Million and Parts Per Billion 2-16

2B-1 Expressing Solution Concentrations p-Functions Scientists frequently express the concentration of a species in terms of its p-function, or p-value. The p-value is the negative base-10 logarithm (log) of the molar concentration of that species. 2-17

2B-2 Density and Specific Gravity of Solutions Density is the mass of a substance per unit volume. In SI units, density is expressed in units of kg / L or alternatively g/mL. Specific gravity is the ratio of the mass of a substance to the mass of an equal volume of water. 2-18

2C Chemical Stoichiometry Stoichiometry is defined as the mass relationships among reacting chemical species. This section provides a brief review of stoichiometry and its applications to chemical calculations. 2-19

2C-1 Empirical Formulas and Molecular Formulas An empirical formula gives the simplest whole-number ratio of atoms in a chemical compound. In contrast, a molecular formula specifies the number of atoms in a molecule. Two or more substances may have the same empirical formula but different molecular formulas. 2-20

2C-1 Empirical Formulas and Molecular Formulas For example, CH2O is both the empirical and the molecular formula for formaldehyde. It is also the empirical formula for such diverse substances as acetic acid (C2H4O2), glyceraldehyde (C3H6O3), and glucose (C6H12O6). The empirical formula is obtained from the percent composition of a compound. In addition, the molecular formula requires a knowledge of the molar mass of the species. 2-21

2C-1 Empirical Formulas and Molecular Formulas A structural formula provides additional information. For example, structural formulas of C2H5OH and CH3OCH3 reveal structural differences between these compounds that are not discernible in the molecular that they are share. 2-22

Example 2-12 (a) What mass of AgNO3 (169.9 g/mol) is needed to convert 2.33 g of Na2CO3 (106.0 g/mol) to Ag2CO3 ? 2-23

Example 2-12 (a) Na2CO3(aq) 2AgNO3(aq): Ag2CO3(s) 2NaNO3(aq) Step 1: Step 2: The balanced equation reveals that 2-24

Example 2-12 Here, the stoichiometric factor is (2 mol AgNO3)/(1 mol Na2CO3). Step 3: 2-25

Example 2-12 (b) What mass of Ag2CO3 (275.7 g/mol) will be formed? (b) 2-26

2D The Chemical Composition of Aqueous Solutions 2D-1 Classifying Solutions of Electrolytes Most of the solutes we discuss are electrolytes, which form ions when dissolved in water (or certain other solvents) and thus produce solutions that conduct electricity. In a solvent, strong electrolytes ionize essentially completely, whereas weak electrolytes ionize only partially. Table 2-3 is a compilation of solutes that act as strong and weak electrolytes in water. 2-27

Table 2-3 2-28

2D-2 Describing Acids and Bases Brønsted and Lowry proposed independently a theory of acid / base behavior that is particularly useful in analytical chemistry. According to the Brønsted –Lowry theory, an acid is a proton donor and a base is a proton acceptor. 2-29

2D-2 Describing Acids and Bases Conjugate base Conjugate acid Neutralization 2-30

2D-2 Describing Acids and Bases (2-4) (2-5) 2-31

2D-2 Describing Acids and Bases Some species have both acidic and basic properties and are called amphiprotic solutes, as illustrated in Feature 2-4. 2-32

Feature 2-4 Amphiprotic Species A zwitterion is an ion that bears both a positive and a negative charge. 2-33

2D-2 Describing Acids and Bases Amphiprotic Solvents Amphiprotic solvents behave as acids in the presence of basic solutes and bases in the presence of acidic solutes. (2-6) (2-7) 2-34

2D-3 Solvents and Autoprotolysis 2-35

2D-3 Solvents and Autoprotolysis The hydronium ion is the hydrated proton formed when water reacts with an acid. It is usually formulated as H3O, although several higher hydrates exist. In this text we use the symbol H3O+ in the chapters that deal with acid / base equilibria and acid / base equilibrium calculations. In other chapters, we simplify to the more convenient H+. We should keep in mind, however, that this symbol represents the hydrated proton. 2-36

2D-4 Strong and Weak Acids and Bases Figure 2-3 shows the dissociation reaction of a few common acids in water. Strong acids react with water so completely that no undissociated solute molecules remain. The others are weak acids, which react incompletely with water to give solutions that contain significant amounts of both the parent acid and its conjugate base. 2-37

Figure 2-3 Figure 2-3 Dissociation reactions and relative strengths of some common acids and their conjugate bases. Note that HCl and HClO4 are completely dissociated in water. 2-38

2D-4 Strong and Weak Acids and Bases In a differentiating solvent, various acids dissociate to different degrees and thus have different strengths. In a leveling solvent, several acids are completely dissociated and are thus of the same strength. 2-39

2E Chemical Equilibrium Equilibrium-constant expressions are algebraic equations that describe the concentration relationships that exist among reactants and products at equilibrium. Among other things, equilibrium-constant expressions permit us to calculate the error that results from any unreacted analyte remaining when equilibrium has been reached. 2-40

2E-1 Describing the Equilibrium State The rate of this reaction and the extent to which it proceeds to the right can be readily monitored by observing the orange-red color of the triiodide ion I3– (the other participants in the reaction are colorless) as it increases with time. If, for example, we add 1 mmol of arsenic acid H3AsO4 to 100 mL of a solution containing 3 mmol of potassium iodide, the red color of the triiodide ion appears almost immediately, and within a few seconds the intensity of the color becomes constant, which shows that the triiodide concentration has become constant (see color plate 1b). 2-41

2E-1 Describing the Equilibrium State The concentration relationship at chemical equilibrium (that is, the position of equilibrium) is independent of the route by which the equilibrium state is achieved. 2-42

2E-1 Describing the Equilibrium State The Le Châtelier principle states that the position of an equilibrium always shifts in such a direction as to relieve a stress that is applied to the system. Mass-action effect The mass-action effect is a shift in the position of an equilibrium caused by adding one of the reactants or products to a system. 2-43

2E-1 Describing the Equilibrium State Chemical reactions do not cease at equilibrium. Instead, the amounts of reactants and products are constant because the rates of the forward and reverse processes are identical. Equilibrium-constant expressions provide no information as to whether a chemical reaction is fast enough to be useful in an analytical procedure. 2-44

2E-2 Writing Equilibrium Constants (2-9) (2-10) Equilibrium constant 2-45

Table 2-4 2-46

2E-3 Important Equilibrium Constants in Analytical Chemistry If one (or more) of the species in Equation 2-10 is a pure liquid, a pure solid, or the solvent present in excess, no term for this species appears in the equilibrium constant expression. The constant K in Equation 2-10 is a temperature- dependent numerical quantity called the equilibrium constant. 2-47

2E-3 Important Equilibrium Constants in Analytical Chemistry [Z]Z in Equation 2-10 is replaced with pz in atmospheres if Z is a gas. No term for Z is included in the equation if this species is a pure solid, a pure liquid, or the solvent of a dilute solution. Remember: Equation 2-10 is only an approximate form of an equilibrium-constant expression. The exact expression takes the form where aY , aZ , aW, and aX are the activities of species Y, Z,W, and X (see Section 5B). 2-48

In a dilute aqueous solution, the molar concentration of water is Feature 2-6 Why [H2O] Does Not Appear in Equilibrium- Constant Expressions for Aqueous Solutions In a dilute aqueous solution, the molar concentration of water is Let us suppose we have 0.1 mol of HCl in 1 L of water. The presence of this acid will shift the equilibrium shown in Equation 2-12 to the left. Originally, however, there were only 107 mol/L OH to consume the added protons. 2-49

water concentration will increase only to Feature 2-6 Why [H2O] Does Not Appear in Equilibrium- Constant Expressions for Aqueous Solutions Thus, even if all the OH ions are converted to H2O, the water concentration will increase only to The percent change in water concentration is which is inconsequential. Thus, K[H2O]2 in Equation 2-13 is, for all practical purposes, a constant. That is, 2-50

2E-3 Important Equilibrium Constants in Analytical Chemistry The Ion-Product Constant for Water (2-12) (2-13) 2-51

2E-3 Important Equilibrium Constants in Analytical Chemistry The Ion-Product Constant for Water (2-14) 2-52

Example 2-15 Calculate the hydronium and hydroxide ion concentrations of pure water at 25°C and 100°C. 2-53

Example 2-15 Because OH and H3O+ are formed only from the dissociation of water, their concentrations must be equal: Substitution into Equation 2-14 gives 2-54

Example 2-15 At 25°C, At 100°C, from Table 2-5, 2-55

Table 2-5 2-56

2E-3 Important Equilibrium Constants in Analytical Chemistry What are Solubility-Products? 2-57

2E-3 Important Equilibrium Constants in Analytical Chemistry What are Solubility-Products? Solubility-product constant or the solubility product For Equation 2-15 to apply, it is necessary only that some solid be present. In the absence of Ba(IO3)(s), Equation 2-15 is not valid. (2-15) 2-58

Example 2-17 What mass of Ba(IO3)2 (487 g/mol) can be dissolved in 500.0 mL of water at 25°C? 2-59

Example 2-17 2-60

Example 2-17 Note that the molar solubility is equal to [Ba2+] or to . 2-61

Example 2-17 2-62

Example 2-17 2-63

2E-3 Important Equilibrium Constants in Analytical Chemistry How Does a Common Ion Affect the Solubility of a Precipitate? The commonion effect is a mass-action effect predicted from the Le Châtelier principle. The common-ion effect is responsible for the reduction in solubility of an ionic precipitate when a soluble compound combining one of the ions of the precipitate is added to the solution in equilibrium with the precipitate. 2-64

Example 2-18 Calculate the molar solubility of Ba(IO3)2 in a solution that is 0.0200 M in Ba(NO3)2 . 2-65

Example 2-18 The assumption that does not appear to cause serious error 2-66

Example 2-18 Ordinarily, we consider an assumption of this type to be satisfactory if the discrepancy is less than 10%. Finally, then, 2-67

Example 2-19 Calculate the solubility of Ba(IO3)2 in a solution prepared by mixing 200 mL of 0.0100 M Ba(NO3)2 with 100 mL of 0.100 M NaIO3 . 2-68

Example 2-19 2-69

Example 2-19 where 2[Ba2+] represents the iodate contributed by the sparingly soluble Ba(IO3)2 . 2-70

Example 2-19 A 0.02 M excess of Ba2+ decreases the solubility of Ba(IO3)2 by a factor of about five; this same excess of IO3- lowers the solubility by a factor of about 200. 2-71

2E-3 Important Equilibrium Constants in Analytical Chemistry Writing Dissociation Constants for Acids and Bases where Ka is the acid dissociation constant Kb for nitrous acid. 2-72

2E-3 Important Equilibrium Constants in Analytical Chemistry Writing Dissociation Constants for Acids and Bases In an analogous way, the base dissociation constant Kb for ammonia is 2-73

2E-3 Important Equilibrium Constants in Analytical Chemistry Dissociation Constants for Conjugate Acid/Base Pairs (2-16) 2-74

2E-3 Important Equilibrium Constants in Analytical Chemistry Dissociation Constants for Conjugate Acid/Base Pairs 2-75

Example 2-20 What is Kb for the equilibrium 2-76

2E-3 Important Equilibrium Constants in Analytical Chemistry Calculating the Hydronium Ion Concentration in Solutions of Weak Acids 2-77

2E-3 Important Equilibrium Constants in Analytical Chemistry Calculating the Hydronium Ion Concentration in Solutions of Weak Acids One H3O+ ion is formed for each A- ion, and we write (2-17) (2-18) 2-78

2E-3 Important Equilibrium Constants in Analytical Chemistry Calculating the Hydronium Ion Concentration in Solutions of Weak Acids (2-19) 2-79

2E-3 Important Equilibrium Constants in Analytical Chemistry Calculating the Hydronium Ion Concentration in Solutions of Weak Acids (2-20) (2-21) (2-22) 2-80

2E-3 Important Equilibrium Constants in Analytical Chemistry Calculating the Hydronium Ion Concentration in Solutions of Weak Acids Equation simplified (2-23) (2-24) 2-81

2E-3 Important Equilibrium Constants in Analytical Chemistry Calculating the Hydronium Ion Concentration in Solutions of Weak Acids The magnitude of the error introduced by the assumption that [H3O+] << cHA increases as the molar concentration of acid becomes smaller and its dissociation constant becomes larger. 2-82

2E-3 Important Equilibrium Constants in Analytical Chemistry Calculating the Hydronium Ion Concentration in Solutions of Weak Acids Note that the error introduced by the assumption is about 0.5% when the ratio cHA/Ka is 104. The error increases to about 1.6% when the ratio is 103, to about 5% when it is 102, and to about 17% when it is 10. 2-83

2E-3 Important Equilibrium Constants in Analytical Chemistry Calculating the Hydronium Ion Concentration in Solutions of Weak Acids It is noteworthy that the hydronium ion concentration computed with the approximation becomes equal to or greater than the molar concentration of the acid when the ratio is unity or smaller, which is clearly a meaningless result. 2-84

Table 2-6 2-85

Figure 2-4 Figure 2-4 Relative error resulting from the assumption that [H3O+] << cHA in Equation 2-19. 2-86

Example 2-21 Calculate the hydronium ion concentration in 0.120 M nitrous acid. 2-87

Example 2-21 2-88

Example 2-21 [H3O+] << 0.120 We now examine the assumption that 0.120 0.0092 0.120 and see that the error is about 8%. The relative error in [H3O] is actually smaller than this figure, however, as we can see by calculating log (cHA/Ka) = 2.2, which, from Figure 2-4, suggests an error of about 4%. If a more accurate figure is needed, solution of the quadratic equation yields 8.9 × 103 M for the hydronium ion concentration. 2-89

Example 2-22 Calculate the hydronium ion concentration in a solution that is 2.0 × 10-4 M in anilinium hydrochloride, C6H5NH3Cl. 2-90

Example 2-22 The weak acid C6H5NH3+ dissociates as follows: 2-91

Example 2-22 Assume that [H3O+] << 2.0 × 10-4 Comparison of 7.09 × 10-5 with 2.0 × 10-4 , (Figure 2-4 indicates that this error is about 20%). 2-92

Example 2-22 2-93

2E-3 Important Equilibrium Constants in Analytical Chemistry Finding the Hydronium Ion Concentration in Solutions of Weak Bases 2-94

Example 2-23 Calculate the hydroxide ion concentration of a 0.0750 M NH3 solution. 2-95

Example 2-23 2-96

Example 2-23 [OH-] << 7.50 × 10-2 the error in [OH-] is less than 2%. 2-97

Example 2-24 Calculate the hydroxide ion concentration in a 0.0100 M sodium hypochlorite solution. 2-98

Example 2-24 2-99

Example 2-24 2-100

THE END 2-101