Chapter 2 Basic Tools of Analytical Chemistry e 2.6 The amount of oxalic acid in a sample of rhubarb was determined by reacting a with Fe+ as outlined in reaction 2. 2. In a typical analysis, the oxalic acid in 10.62 g of rhubarb was extracted with a suitable solvent. The complete oxidation of the oxalic acid to CO2 required 36.44 mL of 0.0130 M Fe3+. What the weight percent of oxalic acid in the sample of rhubarb? SOLUTION We begin by calculating the moles of Fe+ used in the reaction 0. 0130 mol fe3 ×0.03644L=4.737×10- mol fe3+ The moles of oxalic acid reacting with the Fe+, therefore, is 4. x 10- mol Fe3+. I mol C2H2O4 =2.369×10-4molC2H2O4 2 mol Fe3 Converting moles of oxalic acid to grams of oxalic acid 2369×10-4molC2H2O4 0.03gC2H2O nol C2H20,=2.132 x 10-2 g oxalic acid and converting to weight percent gives the concentration of oxalic acid in the sample of rhubarb as 2132×10-2gC2H 10.62 g rhubarb×100=0.201%wwC2H2O4 In the analysis described in Example 2.6 oxalic acid already was present in the desired form. In many analytical methods the compound to be determined must be converted to another form prior to analysis. For example, one method for the quan- titative analysis of tetraethylthiuram disulfide(CloH2oN2S4), the active ingredient in the drug Antabuse(disulfiram), requires oxidizing the s to SO2, bubbling the SO2 through H2O2 to produce H2SO4, followed by an acid-base titration of the H2SO4 with NaOH. Although we can write and balance chemical reactions for each of these steps, it often is easier to apply the principle of the conservation of reaction units A reaction unit is that part of a chemical species involved in a reaction. Con sider, for example, the general unbalanced chemical reaction Conservation of reaction units requires that the number of reaction units associated with the reactant A equal the number of reaction units associated with the reactant B. Translating the previous statement into mathematical form gives Number of reaction units per A x moles A number of reaction units per B X moles B If we know the moles of a and the number of reaction units associated with a and B, then we can calculate the moles of b. note that a conservation of reaction units as defined by equation 2.3, can only be applied between two species. There are five important principles involving a conservation of reaction units: mass, charge, pro- tons, electron pairs, and electrons
Chapter 2 Basic Tools of Analytical Chemistry 21 EXAMPLE 2.6 The amount of oxalic acid in a sample of rhubarb was determined by reacting with Fe3+ as outlined in reaction 2.2. In a typical analysis, the oxalic acid in 10.62 g of rhubarb was extracted with a suitable solvent. The complete oxidation of the oxalic acid to CO2 required 36.44 mL of 0.0130 M Fe3+. What is the weight percent of oxalic acid in the sample of rhubarb? SOLUTION We begin by calculating the moles of Fe3+ used in the reaction The moles of oxalic acid reacting with the Fe3+, therefore, is Converting moles of oxalic acid to grams of oxalic acid and converting to weight percent gives the concentration of oxalic acid in the sample of rhubarb as In the analysis described in Example 2.6 oxalic acid already was present in the desired form. In many analytical methods the compound to be determined must be converted to another form prior to analysis. For example, one method for the quantitative analysis of tetraethylthiuram disulfide (C10H20N2S4), the active ingredient in the drug Antabuse (disulfiram), requires oxidizing the S to SO2, bubbling the SO2 through H2O2 to produce H2SO4, followed by an acid–base titration of the H2SO4 with NaOH. Although we can write and balance chemical reactions for each of these steps, it often is easier to apply the principle of the conservation of reaction units. A reaction unit is that part of a chemical species involved in a reaction. Consider, for example, the general unbalanced chemical reaction A + B → Products Conservation of reaction units requires that the number of reaction units associated with the reactant A equal the number of reaction units associated with the reactant B. Translating the previous statement into mathematical form gives Number of reaction units per A × moles A = number of reaction units per B × moles B 2.3 If we know the moles of A and the number of reaction units associated with A and B, then we can calculate the moles of B. Note that a conservation of reaction units, as defined by equation 2.3, can only be applied between two species. There are five important principles involving a conservation of reaction units: mass, charge, protons, electron pairs, and electrons. 2.132 10 g C C –2 2 2 × × = H O g rhubarb ww H O 2 4 2 4 10 62 100 0 201 . . %/ 2 10 mol C 90.03 g C mol C = 2.132 10 oxalic acid –4 2 2 2 –2 .369 2 4 2 4 2 4 ×× × H O H O H O g 4.737 10 mol Fe 1 mol C mol Fe = 2.369 10 mol C –4 3+ 2 3+ –4 ×× × 2 H O H O 2 4 2 4 2 0 0130 0 03644 . . mol Fe L L = 4.737 10 Fe 3+ –4 3+ × × mol 1400-CH02 9/8/99 3:48 PM Page 21
Modern Analytical Chemistry 2C. I Conservation of mass The easiest principle to appreciate is conservation of mass. Except for nuclear reac- tions, an element's total mass at the end of a reaction must be the same as that pres- ent at the beginning of the reaction; thus, an element serves as the most fundamen- tal reaction unit. Consider, for example, the combustion of butane to produce CO, and H,o. for which the unbalanced reaction CAHlo(g)+O2(g)-)CO2(g)+ H2o(g) All the carbon in CO2 comes from the butane, thus we can select carbon as a tion unit. Since there are four carbon atoms in butane, and one carbon ator CO,, we write 4× moles c4H1o=1× moles co Hydrogen also can be selected as a unit since all the hydrogen in butane ends up in the H2O produced during combustion. Thus, we can write 10× moles c4H10=2× moles h2O Although the mass of oxygen is conserved during the reaction, we cannot apply equation 2.3 because the O2 used during combustion does not end up in a single Conservation of mass also can, with care, be applied to groups of atoms. For example, the ammonium ion, NH+, can be precipitated as Fe(NH4)2(SO4)26H2O Selecting NH4* as the reaction unit gives 2× moles Fe(NH4)2(SO4)2·6H2O=1× moles nh4 2C. 2 Conservation of Charge The stoichiometry between two reactants in a precipitation reaction is governed by a conservation of charge, requiring that the total cation charge and the total anion harge in the precipitate be equal. The reaction units in a precipitation reaction, therefore, are the absolute values of the charges on the cation and anion that make up the precipitate. Applying equation 2. 3 to a precipitate of Ca3(PO4)2 formed from the reaction of Ca t and Po4, we write 2× moles Ca2+=3× moles pc43 2C. 3 Conservation of Protons In an acid-base reaction, the reaction unit is the proton. For an acid, the num- ber of reaction units is given by the number of protons that can be donated to the base: and for a base, the number of reaction units is the number of protons that the base can accept from the acid. In the reaction between H3PO4 and NaOH, for example, the weak acid H3 PO4 can donate all three of its pro tons to NaoH, whereas the strong base NaoH can accept one proton. Thus, we write 3× moles h3PO4=1× moles naOH Care must be exercised in determining the number of reaction units ated with the acid and base. The number of reaction units for an acid. for in stance, depends not on how many acidic protons are present, but on how many
22 Modern Analytical Chemistry 2C.1 Conservation of Mass The easiest principle to appreciate is conservation of mass. Except for nuclear reactions, an element’s total mass at the end of a reaction must be the same as that present at the beginning of the reaction; thus, an element serves as the most fundamental reaction unit. Consider, for example, the combustion of butane to produce CO2 and H2O, for which the unbalanced reaction is C4H10(g) + O2(g) → CO2(g) + H2O(g) All the carbon in CO2 comes from the butane, thus we can select carbon as a reaction unit. Since there are four carbon atoms in butane, and one carbon atom in CO2, we write 4 × moles C4H10 = 1 × moles CO2 Hydrogen also can be selected as a reaction unit since all the hydrogen in butane ends up in the H2O produced during combustion. Thus, we can write 10 × moles C4H10 = 2 × moles H2O Although the mass of oxygen is conserved during the reaction, we cannot apply equation 2.3 because the O2 used during combustion does not end up in a single product. Conservation of mass also can, with care, be applied to groups of atoms. For example, the ammonium ion, NH4 +, can be precipitated as Fe(NH4)2(SO4)2 ⋅ 6H2O. Selecting NH4 + as the reaction unit gives 2 × moles Fe(NH4)2(SO4)2 · 6H2O = 1 × moles NH4 + 2C.2 Conservation of Charge The stoichiometry between two reactants in a precipitation reaction is governed by a conservation of charge, requiring that the total cation charge and the total anion charge in the precipitate be equal. The reaction units in a precipitation reaction, therefore, are the absolute values of the charges on the cation and anion that make up the precipitate. Applying equation 2.3 to a precipitate of Ca3(PO4)2 formed from the reaction of Ca2+ and PO4 3–, we write 2 × moles Ca2+ = 3 × moles PO4 3– 2C.3 Conservation of Protons In an acid–base reaction, the reaction unit is the proton. For an acid, the number of reaction units is given by the number of protons that can be donated to the base; and for a base, the number of reaction units is the number of protons that the base can accept from the acid. In the reaction between H3PO4 and NaOH, for example, the weak acid H3PO4 can donate all three of its protons to NaOH, whereas the strong base NaOH can accept one proton. Thus, we write 3 × moles H3PO4 = 1 × moles NaOH Care must be exercised in determining the number of reaction units associated with the acid and base. The number of reaction units for an acid, for instance, depends not on how many acidic protons are present, but on how many 1400-CH02 9/8/99 3:48 PM Page 22
Chapter 2 Basic Tools of Analytical Chemistry 23 of the protons are capable of reacting with the chosen base. In the reaction b tween H3PO4 and NH3 H3PO4(ag)+ 2NH3(aq)e HPO4(ag)+ 2NH4*(aq) a conservation of protons requires that 2 x moles H3PO4= moles of NH3 2C.4 Conservation of Electron Pairs In a complexation reaction, the reaction unit is an electron pair. For the metal, the number of reaction units is the number of coordination sites available for binding ligands. For the ligand, the number of reaction units is equivalent to the number of electron pairs that can be donated to the metal. One of the most important analyti- al complexation reactions is that between the ligand ethylenediaminetetracetic acid (EDTA), which can donate 6 electron pairs and 6 coordinate metal ions, such as Cutt; thus 6× mole cu2+=6× moles edta 2C.5 Conservation of Electrons a redox reaction, the reaction unit is an electron transferred from a reducing agent to an oxidizing agent. The number of reaction units for a reducing agent is equal to the number of electrons released during its oxidation. For an oxidizing agent, the number of reaction units is given by the number of electrons needed to cause its reduction. In the reaction between Fe+ and oxalic acid(reaction 2. 2),for example, Fe3+ undergoes a 1-electron reduction. Each carbon atom in oxalic acid is initially present in a +3 oxidation state, whereas the carbon atom in CO2 is in a +4 dation state. Thus, we can write 1× moles fe-+=2× moles ofh2C2O4 Note that the moles of oxalic acid are multiplied by 2 since there are two carbon atoms, each of which undergoes a l-electron oxidation. 2C.6 Using Conservation Principles in Stoichiometry Problems As shown in the following examples, the application of conservation principles sim- plifies stoichiometric calculations EXAMPLE 2.7 Rework Example 2.6 using conservation principles SOLUTION Conservation of electrons redox reaction requires that moles Fe+=2 x moles H2C2O4 hich can be transformed by writing moles as the product of molarity and olume or as grams per formula weight. 2×gH2C204 FWH2C2O
Chapter 2 Basic Tools of Analytical Chemistry 23 of the protons are capable of reacting with the chosen base. In the reaction between H3PO4 and NH3 H3PO4(aq) + 2NH3(aq) t HPO4 –(aq) + 2NH4 +(aq) a conservation of protons requires that 2 × moles H3PO4 = moles of NH3 2C.4 Conservation of Electron Pairs In a complexation reaction, the reaction unit is an electron pair. For the metal, the number of reaction units is the number of coordination sites available for binding ligands. For the ligand, the number of reaction units is equivalent to the number of electron pairs that can be donated to the metal. One of the most important analytical complexation reactions is that between the ligand ethylenediaminetetracetic acid (EDTA), which can donate 6 electron pairs and 6 coordinate metal ions, such as Cu2+; thus 6 × mole Cu2+ = 6 × moles EDTA 2C.5 Conservation of Electrons In a redox reaction, the reaction unit is an electron transferred from a reducing agent to an oxidizing agent. The number of reaction units for a reducing agent is equal to the number of electrons released during its oxidation. For an oxidizing agent, the number of reaction units is given by the number of electrons needed to cause its reduction. In the reaction between Fe3+ and oxalic acid (reaction 2.2), for example, Fe3+ undergoes a 1-electron reduction. Each carbon atom in oxalic acid is initially present in a +3 oxidation state, whereas the carbon atom in CO2 is in a +4 oxidation state. Thus, we can write 1 × moles Fe3+ = 2 × moles of H2C2O4 Note that the moles of oxalic acid are multiplied by 2 since there are two carbon atoms, each of which undergoes a 1-electron oxidation. 2C.6 Using Conservation Principles in Stoichiometry Problems As shown in the following examples, the application of conservation principles simplifies stoichiometric calculations. EXAMPLE 2.7 Rework Example 2.6 using conservation principles. SOLUTION Conservation of electrons for this redox reaction requires that moles Fe3+ = 2 × moles H2C2O4 which can be transformed by writing moles as the product of molarity and volume or as grams per formula weight. M g CO FW C O Fe Fe 3 3 2 2 4 2 4 + + × = × V H H 2 2 1400-CH02 9/8/99 3:48 PM Page 23
Mode Sol MFe+×Vc+xFWH2C2O4(0.0130M)0.03644L)(90.03g/mole) =2132×10-2gH2C2O4 and the weight percent oxalic acid is 2132×1028c2H104×100=020%wwC2H2O One quantitative analytical method for tetramethylthiuram disulfide, CIoH2oN2S d(Antabuse), requires oxidizing the sulfur to SOz, and bubbling the resulting a SO2 through H202 to produce H2SO4. The H2SO, is then reacted with NaOH cording to the react H2SO(aq)+ 2NaoH(aq)- Na2SO,(aq)+ 2H2O(e) Using appropriate conservation principles, derive an equation relating the moles of C1oH20N2S to the moles of NaOH. What is the weight percent Cloh2o N2S4 in a sample of Antabuse if the H2SO4 produced from a 0.4613-g portion reacts with 34.85 mL of 0.02500 M NaOH? SOLUTION The unbalanced reactions converting C1oH20N2S4 to H2SO4 are C10H20N2S4→SO2 SO2→H2SO4 Using a conservation of mass we have 4x moles Cloh20N2S4=moles SO,=moles H,SO4 A conservation of protons for the reaction of H2SO, with NaoH gives 2 x moles H, SO4= moles of NaOH Combining the two conservation equations gives the following stoichiometric equation between CloHzoN2S4 and Naoh 8 x moles CloH2oN2S4= moles NaOH Now we are ready to finish the problem Making appropriate substitutions for moles of CioH2o N2S4 and moles of NaOH gives 8×gC0H20N2S4 mNaoH×VaOH FW CIoH20N2S4 Solving for g CloHzoN2S4 gives gC1oH20N2S4=x× mNaoH× VNaOH X FWO1oH (0.02500M)0.03485L)(296.54gmol)=0.032295gC10H20N2S4
24 Modern Analytical Chemistry Solving for g H2C2O4 gives and the weight percent oxalic acid is EXAMPLE 2.8 One quantitative analytical method for tetraethylthiuram disulfide, C10H20N2S4 (Antabuse), requires oxidizing the sulfur to SO2, and bubbling the resulting SO2 through H2O2 to produce H2SO4. The H2SO4 is then reacted with NaOH according to the reaction H2SO4(aq) + 2NaOH(aq) → Na2SO4(aq) + 2H2O(l) Using appropriate conservation principles, derive an equation relating the moles of C10H20N2S4 to the moles of NaOH. What is the weight percent C10H20N2S4 in a sample of Antabuse if the H2SO4 produced from a 0.4613-g portion reacts with 34.85 mL of 0.02500 M NaOH? SOLUTION The unbalanced reactions converting C10H20N2S4 to H2SO4 are C10H20N2S4 → SO2 SO2 → H2SO4 Using a conservation of mass we have 4 × moles C10H20N2S4 = moles SO2 = moles H2SO4 A conservation of protons for the reaction of H2SO4 with NaOH gives 2 × moles H2SO4 = moles of NaOH Combining the two conservation equations gives the following stoichiometric equation between C10H20N2S4 and NaOH 8 × moles C10H20N2S4 = moles NaOH Now we are ready to finish the problem. Making appropriate substitutions for moles of C10H20N2S4 and moles of NaOH gives Solving for g C10H20N2S4 gives 1 8 ( . M)(0.03485 L)(296.54 g/mol) = 0.032295 g C 0 02500 10H NS 20 2 4 g C W C 10 10 H NS M F H NS 20 2 4 20 2 4 NaOH NaOH 1 8 =× × × V 8 20 2 4 20 2 4 × = × g C W C 10 10 H NS F H NS MNaOH NaOH V 2 132 10 10 62 100 0 201 2 2 4 2 4 . . . %/ – × × = g C C 2 2 H O g rhubarb ww H O M FW C O C O Fe Fe 3 3 2 4 2 2 4 2 0 0130 2 2 132 10 + + × × = = × V H M)(0.03644 L)(90.03 g/mole) g H 2 2 ( . . – 1400-CH02 9/8/99 3:48 PM Page 24
Chapter 2 Basic Tools of Analytical Chemistry The weight percent C1oH2oN2S4 in the sample, therefore, 0.32295gC10H20N2S4 0.4613 g sample 100=7.001%w/wC10H20N2S4 o Basic Equipment and Instrumentation Measurements are made using appropriate equipment or instruments. The array equipment and instrumentation used in analytical chemistry is impressive, ranging from the simple and inexpensive, to the complex and costly. with two exceptions, we will postpone the discussion of equipment and instrumentation to those chap- ters where they are used. The instrumentation used to measure mass and much of the equipment used to measure volume are important to all analytical techniques and are therefore discussed in this section 2D.I Instrumentation for Measuring Mass An objects mass is measured using a balance. The most common type of balance is an electronic balance in which the balance pan is placed over an electromagne An apparatus used to measure mass. (Figure 2.2). The sample to be weighed is placed on the sample pan, displacing the pan downward by a force equal to the product of the sample's mass and the acceler- ation due to gravity. The balance detects this downward movement and generates a counterbalancing force using an electromagnet. The current needed to produce this force is proportional to the objects mass. A typical electronic balance has a capacity of 100-200 g and can measure mass to the nearest +0.0l to +l mg Another type of balance is the single-pan, unequal arm balance(Figure 2.3). In this mechanical balance the balance pan and a set of removable standard weights on one side of a beam are balanced against a fixed counterweight on the beams other side. The beam itself is balanced on a fulcrum consisting of a sharp knife edge. Adding a sample to the balance pan tilts the beam away from its balance point. Selected stan dard weights are then removed until the beam is brought back into balance. The com- bined mass of the removed weights equals the sample's mass. The capacities and mea- surement limits of these balances are comparable to an electronic balance. Detector Balance (a)Photo of a typical electronic balance Control (b)Schematic diagram of electronic balance adding a sample moves the balance pa down, allowing more light to reach the electromagnetic servomotor to generate an opposing force, raising the sample up until the original intensity of light at the detector is restored b) Photo courtesy of Fisher Scientific
Chapter 2 Basic Tools of Analytical Chemistry 25 The weight percent C10H20N2S4 in the sample, therefore, is 2D Basic Equipment and Instrumentation Measurements are made using appropriate equipment or instruments. The array of equipment and instrumentation used in analytical chemistry is impressive, ranging from the simple and inexpensive, to the complex and costly. With two exceptions, we will postpone the discussion of equipment and instrumentation to those chapters where they are used. The instrumentation used to measure mass and much of the equipment used to measure volume are important to all analytical techniques and are therefore discussed in this section. 2D.1 Instrumentation for Measuring Mass An object’s mass is measured using a balance. The most common type of balance is an electronic balance in which the balance pan is placed over an electromagnet (Figure 2.2). The sample to be weighed is placed on the sample pan, displacing the pan downward by a force equal to the product of the sample’s mass and the acceleration due to gravity. The balance detects this downward movement and generates a counterbalancing force using an electromagnet. The current needed to produce this force is proportional to the object’s mass. A typical electronic balance has a capacity of 100–200 g and can measure mass to the nearest ±0.01 to ±1 mg. Another type of balance is the single-pan, unequal arm balance (Figure 2.3). In this mechanical balance the balance pan and a set of removable standard weights on one side of a beam are balanced against a fixed counterweight on the beam’s other side. The beam itself is balanced on a fulcrum consisting of a sharp knife edge. Adding a sample to the balance pan tilts the beam away from its balance point. Selected standard weights are then removed until the beam is brought back into balance. The combined mass of the removed weights equals the sample’s mass. The capacities and measurement limits of these balances are comparable to an electronic balance. 0 32295 0 100 7 001 20 2 4 20 2 4 . . % g C .4613 sample w/w C 10 10 H NS g × = H NS Detector Light source N S S Balance pan Electromagnetic servomotor Control circuitry Figure 2.2 (a) Photo of a typical electronic balance. (b) Schematic diagram of electronic balance; adding a sample moves the balance pan down, allowing more light to reach the detector. The control circuitry directs the electromagnetic servomotor to generate an opposing force, raising the sample up until the original intensity of light at the detector is restored. Photo courtesy of Fisher Scientific. (a) (b) balance An apparatus used to measure mass. 1400-CH02 9/8/99 3:48 PM Page 25