Tabla de constantes Analisis, Apuntes de Arquitectura

¡Descarga Tabla de constantes Analisis y más Apuntes en PDF de Arquitectura solo en Docsity! 725 Appendix 1A Single-Sided Normal Distributiona u 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4365 0.4325 0.4286 0.4247 0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0253 2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 2.3 0.0107 0.0104 0.0102 0.00964 0.00914 0.00866 2.4 0.00820 0.00776 0.00734 0.00695 0.00657 2.5 0.00621 0.00587 0.00554 0.00523 0.00494 2.6 0.00466 0.00440 0.00415 0.00391 0.00368 2.7 0.00347 0.00326 0.00307 0.00289 0.00272 2.8 0.00256 0.00240 0.00226 0.00212 0.00199 2.9 0.00187 0.00175 0.00164 0.00154 0.00144 3.0 0.00135 3.1 0.000968 3.2 0.000687 AppendixAppendix 1 continued 1400-AP1 9/8/99 4:39 PM Page 725 726 Modern Analytical Chemistry Single-Sided Normal Distributiona—continued u 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 3.3 0.000483 3.4 0.000337 3.5 0.000233 3.6 0.000159 3.7 0.000108 3.8 0.0000723 3.9 0.0000481 4.0 0.0000317 4.1 0.0000207 4.2 0.0000133 4.3 0.00000854 4.4 0.00000541 4.5 0.00000340 4.6 0.00000211 4.7 0.00000130 4.8 0.000000793 4.9 0.000000479 5.0 0.000000287 aThis table gives the proportion, P, of the area under a normal distribution curve that lies to the right of the deviation z, where z is defined as z = (X – µ)/σ For example, the proportion of the area under a normal distribution curve that lies to the right of a deviation of 0.04 is 0.4840, or 48.40%. The area to the left of the deviation is given as 1 – P. Thus, 51.60% of the area under the normal distribution curve lies to the left of a deviation of 0.04. When the deviation is negative, the values in the table give the proportion of the area under the normal distribution curve that lies to the left of z; therefore, 48.40% of the area lies to the left, and 51.60% of the area lies to the right of a deviation of –0.04. Appendix 1B t-Tablea Value of t for confidence interval of: 90% 95% 98% 99% Critical value of ötö for α values of: 0.10 0.05 0.02 0.01 Degrees of Freedom 1 6.31 12.71 31.82 63.66 2 2.92 4.30 6.96 9.92 3 2.35 3.18 4.54 5.84 4 2.13 2.78 3.75 4.60 5 2.02 2.57 3.36 4.03 6 1.94 2.45 3.14 3.71 7 1.89 2.36 3.00 3.50 8 1.86 2.31 2.90 3.36 9 1.83 2.26 2.82 3.25 10 1.81 2.23 2.76 3.17 12 1.78 2.18 2.68 3.05 14 1.76 2.14 2.62 2.98 16 1.75 2.12 2.58 2.92 18 1.73 2.10 2.55 2.88 20 1.72 2.09 2.53 2.85 30 1.70 2.04 2.46 2.75 50 1.68 2.01 2.40 2.68 ∞ 1.64 1.96 2.33 2.58 aThe t-values in this table are for a two-tailed test. For a one-tailed test, the α values for each column are half of the stated value. For example, the first column for a one-tailed test is for the 95% confidence level, α = 0.05. 1400-AP1 9/8/99 4:39 PM Page 726 729 FW Element Compound (g/mol) Comments aluminum Al metal 26.982 antimony Sb metal 121.760 KSbOC4H4O6 324.92 compound prepared by drying KSbOC4H4O6 · 1/2H2O at 110 °C and storing in desiccator arsenic As metal 74.922 As2O3 197.84 toxic barium BaCO3 197.35 dry at 200 °C for 4 h bismuth Bi metal 208.980 Bi2O3 465.96 not considered a primary standard boron H3BO3 61.83 do not dry bromine KBr 119.01 cadmium Cd metal 112.411 CdO 128.40 not considered a primary standard calcium CaCO3 100.09 cerium Ce metal 140.116 (NH4)2Ce(NO3)6 548.23 not considered a primary standard cesium Cs2CO3 325.82 Cs2SO4 361.87 chlorine NaCl 58.44 chromium Cr metal 51.996 K2Cr2O7 294.19 cobalt Co metal 58.933 copper Cu metal 63.546 CuO 79.54 fluorine NaF 41.99 do not store in glass container iodine KI 166.00 KIO3 214.00 iron Fe metal 55.845 lead Pb metal 207.2 Pb(NO3)2 331.20 approaches primary standard lithium Li2CO3 73.89 AppendixAppendix 2 Recommended Reagents for Preparing Primary Standards continued constant weight at 110 °C. Most compounds can be dissolved in dilute acid (1:1 HCl or 1:1 HNO3), with heating if necessary; some of the compounds are water- soluble. A ll compounds should be of the highest available purity. Metals should be cleaned with dilute acid to remove surface impurities and rinsed with distilled water. Unless otherwise indicated, compounds should be dried to 1400-AP2 9/8/99 4:39 PM Page 729 730 Modern Analytical Chemistry FW Element Compound (g/mol) Comments magnesium Mg metal 24.305 MgO 40.31 not considered a primary standard manganese Mn metal 54.938 MnSO4 • H2O 169.01 not considered a primary standard; may be dried at 110 °C without loss of hydrated water mercury Hg metal 200.59 molybdenum Mo metal 95.94 nickel Ni metal 58.693 phosphorus KH2PO4 136.09 not considered a primary standard potassium KCl 74.56 K2CO3 138.21 K2Cr2O7 294.19 KHC8H4O4 204.23 silicon Si metal 28.085 SiO2 60.08 silver Ag metal 107.868 AgNO3 169.87 approaches primary standard sodium NaCl 58.44 Na2CO3 106.00 Na2C2O4 134.00 strontium SrCO3 147.63 sulfur elemental S 32.066 K2SO4 174.27 Na2SO4 142.04 tin Sn metal 118.710 titanium Ti metal 47.867 tungsten W metal 183.84 uranium U metal 238.029 U3O8 842.09 vanadium V metal 50.942 V2O5 181.88 not considered a primary standard zinc Zn metal 65.39 ZnO 81.37 not considered a primary standard Source: Information compiled from Moody, J. R.; Greenberg, R. R.; Pratt, K. W.; et al. Anal. Chem. 1988, 60, 1203A–1218A; and Smith, B. W.; Parsons, M. L. J. Chem. Educ. 1973, 50, 679–681. 1400-AP2 9/8/99 4:39 PM Page 730 731 Appendix 3A Solubility Products Bromide (Br–) pKsp Ksp CuBr 8.3 5 × 10–9 AgBr 12.30 5.0 × 10–13 Hg2Br2 22.25 5.6 × 10–23 HgBr2(µ = 0.5 M) 18.9 1.3 × 10–19 PbBr2(µ = 4.0 M) 5.68 2.1 × 10–6 Carbonate (CO32–) pKsp Ksp MgCO3 7.46 3.5 × 10–8 CaCO3 (calcite) 8.35 4.5 × 10–9 CaCO3 (aragonite) 8.22 6.0 × 10–9 SrCO3 9.03 9.3 × 10–10 BaCO3 8.30 5.0 × 10–9 MnCO3 9.30 5.0 × 10–10 FeCO3 10.68 2.1 × 10–11 CoCO3 9.98 1.0 × 10–10 NiCO3 6.87 1.3 × 10–7 Ag2CO3 11.09 8.1 × 10–12 Hg2CO3 16.05 8.9 × 10–17 ZnCO3 10.00 1.0 × 10–10 CdCO3 13.74 1.8 × 10–14 PbCO3 13.13 7.4 × 10–14 Chloride (Cl–) pKsp Ksp CuCl 6.73 1.9 × 10–7 AgCl 9.74 1.8 × 10–10 Hg2Cl2 17.91 1.2 × 10–18 PbCl2 4.78 1.7 × 10–5 Chromate (CrO42–) pKsp Ksp BaCrO4 9.67 2.1 × 10–10 CuCrO4 5.44 3.6 × 10–6 Ag2CrO4 11.92 1.2 × 10–12 Hg2CrO4 8.70 2.0 × 10–9 AppendixAppendix 3 Cyanide (CN–) pKsp Ksp AgCN 15.66 2.2 × 10–16 Zn(CN)2 (µ = 3.0 M) 15.5 3 × 10–16 Hg2(CN)2 39.3 5 × 10–40 Ferrocyanide ([Fe(CN)64–]) pKsp Ksp Zn2[Fe(CN)6] 15.68 2.1 × 10–16 Cd2[Fe(CN)6] 17.38 4.2 × 10–18 Pb2[Fe(CN)6] 18.02 9.5 × 10–19 Fluoride (F–) pKsp Ksp MgF2 8.18 6.6 × 10–9 CaF2 10.41 3.9 × 10–11 SrF2 8.54 2.9 × 10–9 BaF2 5.76 1.7 × 10–6 PbF2 7.44 3.6 × 10–8 Hydroxide (OH–) pKsp Ksp Mg(OH)2 11.15 7.1 × 10–12 Ca(OH)2 5.19 6.5 × 10–6 Ba(OH)2 ⋅ 8H2O 3.6 3 × 10–4 La(OH)3 20.7 2 × 10–21 Mn(OH)2 12.8 1.6 × 10–13 Fe(OH)2 15.1 8 × 10–16 Co(OH)2 14.9 1.3 × 10–15 Ni(OH)2 15.2 6 × 10–16 Cu(OH)2 19.32 4.8 × 10–20 Fe(OH)3 38.8 1.6 × 10–39 Co(OH)3 (T = 19 °C) 44.5 3 × 10–45 Ag2O (+H2O t 2Ag+ + 2OH–) 15.42 3.8 × 10–16 Cu2O (+ H2O t 2Cu+ + 2OH–) 29.4 4 × 10–30 Zn(OH)2 (amorphous) 15.52 3.0 × 10–16 Cd(OH)2 (β) 14.35 4.5 × 10–15 continued 1400-AP3 9/8/99 4:40 PM Page 731 Acid Dissociation Constants—continued Compound Conjugate Acid pKa Ka chloroacetic acid ClCH2COOH 2.865 1.36 × 10–3 chromic acid H2CrO4 –0.2; (T = 20 °C) 1.6 6.51 3.1 × 10–7 citric acid 3.128 (COOH) 7.45 × 10–4 4.761 (COOH) 1.73 × 10–5 6.396 (COOH) 4.02 × 10–7 cupferron 4.16; (µ = 0.1 M) 6.9 × 10–5 cysteine (1.71) (COOH) 1.9 × 10–2 8.36 (SH) 4.4 × 10–9 10.77 (NH3) 1.7 × 10–11 dichloroacetic acid Cl2CHCOOH 1.30 5.0 × 10–2 diethylamine (CH3CH2)2NH2+ 10.933 1.17 × 10–11 dimethylamine (CH3)2NH2+ 10.774 1.68 × 10–11 dimethylgloxime 10.66 2.2 × 10–11 12.0 1 × 10–12 ethylamine CH3CH2NH3+ 10.636 2.31 × 10–11 ethylenediamine +H3NCH2CH2NH3+ 6.848 1.42 × 10–7 9.928 1.18 × 10–10 ethylenediaminetetraacetic acid (EDTA) 0.0 (COOH); (µ = 1.0 M) 1.0 1.5 (COOH); (µ = 0.1 M) 3.2 × 10–2 2.0 (COOH); (µ = 0.1 M) 1.0 × 10–2 2.68 (COOH); (µ = 0.1 M) 2.1 × 10–3 6.11 (NH); (µ = 0.1 M) 7.8 × 10–7 10.17 (NH); (µ = 0.1 M) 6.8 × 10–11 formic acid HCOOH 3.745 1.80 × 10–4 fumaric acid 3.053 8.85 × 10–4 4.494 3.21 × 10–5 glutamic acid 2.23 (α-COOH) 5.9 × 10–3 4.42 (λ-COOH) 3.8 × 10–5 9.95 (NH3) 1.12 × 10–10 734 Modern Analytical Chemistry OH C CH2COOHHOOCH2C COOH N NO OH NH3 + CHCH2SH COOH NOHHON CH3H3C CH2COOHHOOCH2C HOOCH2C CH2COOH +HNCH2CH2NH + HOOC COOH NH3 + CHCH2CH2COOH COOH 1400-AP3 9/8/99 4:40 PM Page 734 Compound Conjugate Acid pKa Ka glutamine 2.17 (COOH); (µ = 0.1 M) 6.8 × 10–3 9.01 (NH3); (µ = 0.1 M) 9.8 × 10–10 glycine +H3NCH2COOH 2.350 (COOH) 4.47 × 10–3 9.778 (NH3) 1.67 × 10–10 glycolic acid HOCH2COOH 3.831 (COOH) 1.48 × 10–4 histidine 1.7 (COOH); (µ = 0.1 M) 2 × 10–2 6.02 (NH); (µ = 0.1 M) 9.5 × 10–7 9.08 (NH3); (µ = 0.1 M) 8.3 × 10–10 hydrogen cyanide HCN 9.21 6.2 × 10–10 hydrogen fluoride HF 3.17 6.8 × 10–4 hydrogen peroxide H2O2 11.65 2.2 × 10–12 hydrogen sulfide H2S 7.02 9.5 × 10–8 13.9 1.3 × 10–14 hydrogen thiocyanate HSCN 0.9 1.3 × 10–1 8-hydroxyquinoline 4.91 (NH) 1.23 × 10–5 9.81 (OH) 1.55 × 10–10 hydroxylamine HONH3+ 5.96 1.1 × 10–6 hypobromous HOBr 8.63 2.3 × 10–9 hypochlorous HOCl 7.53 3.0 × 10–8 hypoiodous HOI 10.64 2.3 × 10–11 iodic acid HIO3 0.77 1.7 × 10–1 isoleucine 2.319 (COOH) 4.80 × 10–3 9.754 (NH3) 1.76 × 10–10 leucine 2.329 (COOH) 4.69 × 10–3 9.747 (NH3) 1.79 × 10–10 lysine 2.04 (COOH); (µ = 0.1 M) 9.1 × 10–3 9.08 (α-NH3); (µ = 0.1 M) 8.3 × 10–10 10.69 (ε-NH3);(µ = 0.1 M) 2.0 × 10–11 Appendix 3 735 NH3 + O CHCH2CH2CNH2 COOH CHCH2 COOH NH3 + H N H+ N OH H+ N NH3 + CHCH(CH3)CH2CH3 COOH NH3 + CHCH2CH(CH3)2 COOH NH3 + CHCH2CH2CH2CH2NH3 + COOH continued 1400-AP3 9/8/99 4:40 PM Page 735 Acid Dissociation Constants—continued Compound Conjugate Acid pKa Ka maleic acid 1.910 1.23 × 10–2 6.332 4.66 × 10–7 malic acid 3.459 (COOH) 3.48 × 10–4 5.097 (COOH) 8.00 × 10–6 malonic acid HOOCCH2COOH 2.847 1.42 × 10–3 5.696 2.01 × 10–6 methionine 2.20 (COOH); (µ = 0.1 M) 6.3 × 10–3 9.05 (NH3); (µ = 0.1 M) 8.9 × 10–10 methylamine CH3NH3+ 10.64 2.3 × 10–11 2-methylaniline 4.447 3.57 × 10–5 4-methylaniline 5.084 8.24 × 10–6 2-methylphenol 10.28 5.2 × 10–11 4-methylphenol 10.26 5.5 × 10–11 nitrilotriacetic acid 1.1 (COOH); (T = 20 °C , µ = 1.0 M) 8 × 10–2 1.650 (COOH); (T = 20 °C) 2.24 × 10–2 2.940 (COOH); (T = 20 °C) 1.15 × 10–3 10.334 (NH3); (T = 20 °C) 4.63 × 10–11 2-nitrobenzoic acid 2.179 6.62 × 10–3 3-nitrobenzoic acid 3.449 3.56 × 10–4 736 Modern Analytical Chemistry HOOC COOH CHCOOHHOOCH2C OH NH3 + CHCH2CH2SCH3 COOH CH3 NH3 + NH3 +H3C CH3 OH OHH3C CH2COOH +HN CH2COOH CH2COOH COOH NO2 COOH NO2 1400-AP3 9/8/99 4:40 PM Page 736 Compound Conjugate Acid pKa Ka trimethylamine (CH3)3NH+ 9.800 1.58 × 10–10 tris(hydroxymethyl)- aminomethane (TRIS or THAM) (HOCH2)3CNH3+ 8.075 8.41 × 10–9 tryptophan 2.35 (COOH); (µ = 0.1 M) 4.5 × 10–3 9.33 (NH3); (µ = 0.1 M) 4.7 × 10–10 tyrosine 2.17 (COOH); (µ = 0.1 M) 6.8 × 10–3 9.19 (NH3) 6.5 × 10–10 10.47 (OH) 3.4 × 10–11 valine 2.286 (COOH) 5.18 × 10–3 9.718 (OH) 1.91 × 10–10 Source: All values are from Martell, A. E.; Smith, R. M. Critical Stability Constants, Vol. 1–4. Plenum Press: New York, 1976. Unless otherwise stated, values are for 25 °C and zero ionic strength. Values in parentheses are considered less reliable. Appendix 3C Metal–Ligand Formation Constants Acetate CH3COO– log K1 log K2 log K3 log K4 log K5 log K6 Mg2+ 1.27 Ca2+ 1.18 Ba2+ 1.07 Mn2+ 1.40 Fe2+ 1.40 Co2+ 1.46 Ni2+ 1.43 Cu2+ 2.22 1.41 Ag+ 0.73 –0.09 Zn2+ 1.57 Cd2+ 1.93 1.22 –0.89 Pb2+ 2.68 1.40 Appendix 3 739 CHCH2 COOH NH3 + H N OHCHCH2 COOH NH3 + NH3 + CHCH(CH3)2 COOH continued 1400-AP3 9/8/99 4:40 PM Page 739 Metal–Ligand Formation Constants—continued Ammonia NH3 log K1 log K2 log K3 log K4 log K5 log K6 Ag+ 3.31 3.91 Co2+ (T = 20 °C) 1.99 1.51 0.93 0.64 0.06 –0.74 Ni2+ 2.72 2.17 1.66 1.12 0.67 –0.03 Cu2+ 4.04 3.43 2.80 1.48 Zn2+ 2.21 2.29 2.36 2.03 Cd2+ 2.55 2.01 1.34 0.84 Chloride Cl– log K1 log K2 log K3 log K4 log K5 log K6 Cu2+ 0.40 Fe3+ 1.48 0.65 Ag+ (µ = 5.0 M) 3.70 1.92 0.78 –0.3 Zn2+ 0.43 0.18 –0.11 –0.3 Cd2+ 1.98 1.62 –0.2 –0.7 Pb2+ 1.59 0.21 –0.1 –0.3 Cyanide CN– log K1 log K2 log K3 log K4 log K5 log K6 Fe2+ 35.4 (β6) Fe3+ 43.6 (β6) Ag+ 20.48 (β2) 0.92 Zn2+ 11.07 (β2) 4.98 3.57 Cd2+ 6.01 5.11 4.53 2.27 Hg2+ 17.00 15.75 3.56 2.66 Ni2+ 30.22 (β4) Ethylenediamine H2NCH2CH2NH2 log K1 log K2 log K3 log K4 log K5 log K6 Ni2+ 7.38 6.18 4.11 Cu2+ 10.48 9.07 Ag+ (T = 20 °C , µ = 0.1 M) 4.70 3.00 Zn2+ 5.66 4.98 3.25 Cd2+ 5.41 4.50 2.78 EDTA log K1 log K2 log K3 log K4 log K5 log K6 Mg2+ (T = 20 °C, µ = 0.1 M) 8.79 Ca2+ (T = 20 °C, µ = 0.1 M) 10.69 Ba2+ (T = 20 °C, µ = 0.1 M) 7.86 Bi3+ (T = 20 °C, µ = 0.1 M) 27.8 Co2+ (T = 20 °C, µ = 0.1 M) 16.31 Ni2+ (T = 20 °C, µ = 0.1 M) 18.62 Cu2+ (T = 20 °C, µ = 0.1 M) 18.80 740 Modern Analytical Chemistry NCH2CH2N CH2COO – CH2COO – –OOCH2C –OOCH2C 1400-AP3 9/8/99 4:40 PM Page 740 EDTA log K1 log K2 log K3 log K4 log K5 log K6 Cr3+ (T = 20 °C, µ = 0.1 M) (23.4) Fe3+ (T = 20 °C, µ = 0.1 M) 25.1 Ag+ (T = 20 °C, µ = 0.1 M) 7.32 Zn2+ (T = 20 °C, µ = 0.1 M) 16.50 Cd2+ (T = 20 °C, µ = 0.1 M) 16.46 Hg2+ (T = 20 °C, µ = 0.1 M) 21.7 Pb2+ (T = 20 °C, µ = 0.1 M) 18.04 Al3+ (T = 20 °C, µ = 0.1 M) 16.3 Fluoride F– log K1 log K2 log K3 log K4 log K5 log K6 Al3+ (µ = 0.5 M) 6.11 5.01 3.88 3.0 1.4 0.4 Hydroxide OH– log K1 log K2 log K3 log K4 log K5 log K6 Al3+ 9.01 (9.69) (8.3) 6.0 Co2+ 4.3 4.1 1.3 0.5 Fe2+ 4.5 (2.9) 2.6 –0.4 Fe3+ 11.81 10.5 12.1 Ni2+ 4.1 3.9 3 Pb2+ 6.3 4.6 3.0 Zn2+ 5.0 (6.1) 2.5 (1.2) Iodide I– log K1 log K2 log K3 log K4 log K5 log K6 Ag+ (T = 18 °C) 6.58 (5.12) (1.4) Cd2+ 2.28 1.64 1.08 1.0 Pb2+ 1.92 1.28 0.7 0.6 Nitriloacetate log K1 log K2 log K3 logK4 log K5 log K6 Mg2+ (T = 20 °C, µ = 0.1 M) 5.41 Ca2+ (T = 20 °C, µ = 0.1 M) 6.41 Ba2+ (T = 20 °C, µ = 0.1 M) 4.82 Mn2+ (T = 20 °C, µ = 0.1 M) 7.44 Fe2+ (T = 20 °C, µ = 0.1 M) 8.33 Co2+ (T = 20 °C, µ = 0.1 M) 10.38 Ni2+ (T = 20 °C, µ = 0.1 M) 11.53 Cu2+ (T = 20 °C, µ = 0.1 M) 12.96 Fe3+ (T = 20 °C, µ = 0.1 M) 15.9 Zn2+ (T = 20 °C, µ = 0.1 M) 10.67 Cd2+ (T = 20 °C, µ = 0.1 M) 9.83 Pb2+ (T = 20 °C, µ = 0.1 M) 11.39 Appendix 3 741 NCH2CH2N CH2COO – CH2COO – –OOCH2C –OOCH2C N CH2COO – CH2COO – CH2COO – continued 1400-AP3 9/8/99 4:40 PM Page 741 E° E°′ Chromium (V) (V) Cr3+ + e– t Cr2+ –0.424 Cr2+ + 2e– t Cr(s) –0.90 Cr2O72– + 14H+ + 6e– t 2Cr3+ + 7H2O 1.36 CrO42– + 4H2O + 3e– t Cr(OH)4– + 4OH– –0.13 1 M NaOH E° E°′ Cobalt (V) (V) Co2+ + 2e– t Co(s) –0.277 Co3+ + e– t Co2+ 1.92 Co(NH3)63+ + e– t Co(NH3)62+ 0.1 Co(OH)3(s) + e– t Co(OH)2(s) + OH– 0.17 Co(OH)2(s) + 2e– t Co(s) + 2OH– –0.746 E° E°′ Copper (V) (V) Cu+ + e– t Cu(s) 0.520 Cu2+ + e– t Cu+ 0.159 Cu2+ + 2e– t Cu(s) 0.3419 Cu2+ + I– + e– t CuI(s) 0.86 Cu2+ + Cl– + e– t CuCl(s) 0.559 E° E°′ Fluorine (V) (V) F2(g) + 2H+ + 2e– t 2HF 3.053 F2(g) + 2e– t 2F– 2.87 E° E°′ Gallium (V) (V) Ga3+ + 3e– t Ga(s) –0.529 E° E°′ Gold (V) (V) Au+ + e– t Au(s) 1.83 Au3+ + 2e– t Au+ 1.36 Au3+ + 3e– t Au(s) 1.52 AuCl4– + 3e– t Au(s) + 4Cl– 1.002 E° E°′ Hydrogen (V) (V) 2H+ + 2e– t H2(g) 0.00000 H2O + e– t 1⁄2H2(g) + OH– –0.828 E° E°′ Iodine (V) (V) I2(s) + 2e– t 2I– 0.5355 I3– + 2e– t 3I– 0.536 HIO + H+ + 2e– t I– + H2O 0.985 IO3– + 6H+ + 5e– t 1⁄2I2(s) + 3H2O 1.195 IO3– + 3H2O + 6e– t I– + 6OH– 0.257 E° E°′ Iron (V) (V) Fe2+ + 2e– t Fe(s) –0.44 Fe3+ + 3e– t Fe(s) –0.037 Fe3+ + e– t Fe2+ 0.771 0.70 1 M HCl 0.767 1 M HClO4 0.746 1 M HNO3 0.68 1 M H2SO4 0.44 0.3 M H3PO4 Fe(CN)63– + e– t Fe(CN)64– 0.356 0.71 1 M HCl Fe(phen)33+ + e– t Fe(phen)32+ 1.147 Fe(CN)63– + e– t Fe(CN)64– 0.356 E° E°′ Ianthanum (V) (V) La3+ + 3e– t La(s) –2.38 E° E°′ Lead (V) (V) Pb2+ + 2e– t Pb(s) –0.126 PbO2(s) + 4H+ + 2e– t Pb2+ + 2H2O 1.46 PbO2(s) + SO42– + 4H+ + 2e– t PbSO4(s) + 2H2O 1.690 PbSO4(s)+ 2e– t Pb(s) + SO42– –0.356 E° E°′ Lithium (V) (V) Li+ + e– t Li(s) –3.040 E° E°′ Magnesium (V) (V) Mg2+ + 2e– t Mg(s) –2.356 Mg(OH)2(s) + 2e– t Mg(s) + 2OH– –2.687 E° E°′ Manganese (V) (V) Mn2+ + 2e– t Mn(s) –1.17 M3+ + e– t Mn2+ 1.5 MnO2(s) + 4H+ + 2e– t Mn2+ + 2H2O 1.23 MnO4– + 4H+ + 3e– t MnO2(s) + 2H2O 1.70 MnO4– + 8H+ + 5e– t Mn2+ + 4H2O 1.51 MnO4– + 2H2O + 3e– t MnO2(s) + 4OH– 0.60 E° E°′ Mercury (V) (V) Hg2+ + 2e– t Hg(l) 0.8535 2Hg2+ + 2e– t Hg22+ 0.911 Hg22+ + 2e– t 2Hg(l) 0.7960 Hg2Cl2(s) + 2e– t 2Hg(l) + 2Cl– 0.2682 HgO(s) + 2H+ + 2e– t Hg(l) + H2O 0.926 Hg2Br2(s) + 2e– t 2Hg(l) + 2Br– 0.1392 Hg2I2(s) + 2e– t 2Hg(l) + 2I– –0.0405 744 Modern Analytical Chemistry Standard Reduction Potentialsa—continued 1400-AP3 9/8/99 4:40 PM Page 744 E° E°′ Molybdenum (V) (V) Mo3+ + 3e– t Mo(s) –0.2 MoO2(s) + 4H+ + 4e– t Mo(s) + 2H2O –0.152 MoO42– + 4H2O + 6e– t Mo(s) + 8OH– –0.913 E° E°′ Nickel (V) (V) Ni2+ + 2e– t Ni(s) –0.257 Ni(OH)2(s) + 2e– t Ni(s) + 2OH– –0.72 Ni(NH3)62+ + 2e– t Ni(s) + 6NH3 –0.49 E° E°′ Nitrogen (V) (V) N2(g) + 5H+ + 4e– t N2H5+ –0.23 N2O(g) + 2H+ + 2e– t N2(g) + H2O 1.77 2NO(g) + 2H+ + 2e– t N2O(g) + H2O 1.59 HNO2 + H+ + e– t NO(g) + H2O 0.996 2HNO2 + 4H+ + 4e– t N2O(g) + 3H2O 1.297 NO3– + 3H+ + 2e– t HNO2 + H2O 0.94 E° E°′ Oxygen (V) (V) O2(g) + 2H+ + 2e– t H2O2 0.695 O2(g) + 4H+ + 4e– t 2H2O 1.229 H2O2 + 2H+ + 2e– t 2H2O 1.763 O2(g) + 2H2O + 4e– t 4OH– 0.401 O3(g) + 2H+ + 2e– t O2(g) + H2O 2.07 E° E°′ Phosphorus (V) (V) P(s, white) +3H+ + 3e– t PH3(g) –0.063 H3PO3 + 2H+ + 2e– t H3PO2 + H2O –0.499 H3PO4 + 2H+ + 2e– t H3PO3 + H2O –0.276 E° E°′ Platinum (V) (V) Pt2+ + 2e– t Pt(s) 1.188 PtCl42– + 2e– t Pt(s) + 4Cl– 0.758 E° E°′ Potassium (V) (V) K+ + e– t K(s) –2.924 E° E°′ Ruthenium (V) (V) Ru3+ + e– t Ru2+ 0.249 RuO2(s) + 4H+ + 4e– t Ru(s) + 2H2O 0.68 Ru(NH3)63+ + e– t Ru(NH3)62+ 0.10 Ru(CN)63– + e– t Ru(CN)64– 0.86 E° E°′ Selenium (V) (V) Se(s) + 2e– t Se2– –0.670 1 M NaOH Se(s) + 2H+ + 2e– t H2Se(g) –0.115 H2SeO3 + 4H+ + 4e– t Se(s) + 3H2O 0.74 SeO43– + 4H+ + e– t H2SeO3 + H2O 1.151 E° E°′ Silicon (V) (V) SiF62– + 4e– t Si(s) + 6F– –1.37 SiO2(s) + 4H+ + 4e– t Si(s) + 2H2O –0.909 SiO2(s) + 8H+ + 8e– t SiH4(g) + 2H2O –0.516 E° E°′ Silver (V) (V) Ag+ + e– t Ag(s) 0.7996 AgBr(s) + e– t Ag(s) + Br– 0.071 Ag2C2O4(s) + 2e– t 2Ag(s) + C2O42– 0.47 AgCl(s) + e– t Ag(s) + Cl– 0.2223 AgI(s) + e– t Ag(s) + I– –0.152 Ag2S(s) + 2e– t 2Ag(s) + S2– –0.71 Ag(NH3)2+ + e– t Ag(s) + 2NH3 0.373 E° E°′ Sodium (V) (V) Na+ + e– t Na(s) –2.713 E° E°′ Strontium (V) (V) Sr2+ + 2e– t Sr(s) –2.89 E° E°′ Sulfur (V) (V) S(s) + 2e– t S2– –0.407 S(s) + 2H+ + 2e– t H2S 0.144 S2O62– + 4H+ + 2e– t 2H2SO3 0.569 S2O82– + 2e– t 2SO42– 1.96 S4O62– + 2e– t 2S2O32– 0.080 2SO32– + 2H2O + 2e– t S2O42– + 4OH– –1.13 2SO32– + 3H2O + 4e– t S2O32– + 6OH– –0.576 1 M NaOH 2SO42– + 4H+ + 2e– t S2O62– + 2H2O –0.25 SO42– + H2O + 2e– t SO32– + 2OH– –0.936 SO42– + 4H+ + 2e– t H2SO3 + H2O +0.172 E° E°′ Thallium (V) (V) Tl3+ + 2e– t Tl+ 1.25 1 M HClO4 0.77 1 M HCL Tl3 + 3e– t Tl(s) 0.742 Appendix 3 745 continued 1400-AP3 9/8/99 4:40 PM Page 745 E° E°′ Tin (V) (V) Sn2+ + 2e– t Sn(s) –0.19 1 M HCl Sn4+ + 2e– t Sn2+ 0.154 0.139 1 M HCl E° E°′ Titanium (V) (V) Ti2+ + 2e– t Ti(s) –1.63 Ti3+ + e– t Ti2+ –0.37 E° E°′ Tungsten (V) (V) WO2(s) + 4H+ + 4e– t W(s) + 2H2O –0.119 WO3(s) + 6H+ + 6e– t W(s) + 3H2O –0.090 E° E°′ Uranium (V) (V) U3+ + 3e– t U(s) –1.66 U4+ +e– t U3+ –0.52 UO2+ + 4H+ + e– t U4+ + 2H2O 0.27 UO22+ + e– t UO2+ 0.16 UO22+ + 4H+ + 2e– t U4+ + 2H2O 0.327 E° E°′ Vanadium (V) (V) V2+ + 2e– t V(s) –1.13 V3+ + e– t V2+ –0.255 VO2+ + 2H+ + e– t V3+ + H2O 0.337 VO2+ + 2H+ + e– t VO2+ + H2O 1.000 E° E°′ Zinc (V) (V) Zn2+ + 2e– t Zn(s) –0.7618 Zn(OH)42– + 2e– t Zn(s) + 4OH– –1.285 Zn(NH3)42+ + 2e– t Zn(s) + 4NH3 –1.04 Zn(CN)42– + 2e– t Zn(s) + 4CN– –1.34 746 Modern Analytical Chemistry Source: Values are compiled from the following sources: Bard, A. J.; Parsons, R.; Jordon, J., eds. Standard Potentials in Aqueous Solutions. Dekker: New York, 1985; Milazzo, G.; Caroli, S.; Sharma, V. K. Tables of Standard Electrode Potentials. Wiley: London, 1978; Swift, E. H.; Butler, E. A. Quantitative Measurements and Chemical Equilibria. Freeman: New York, 1972. aSolids, gases, and liquids are identified; all other species are aqueous. Reduction reactions in acidic solution are written using H+ instead of H3O+. Reactions may be rewritten by replacing H+ with H3O+ and adding one molecule of H2O to the opposite side of the reaction for each H+; thus H3AsO4 + 2H+ + 2e– t HAsO2 + 2H2O becomes H3AsO4 + 2H3O++ 2e– t HAsO2 + 4H2O Conditions for formal potentials (E°′) are listed next to the potential. Standard Reduction Potentialsa—continued 1400-AP3 9/8/99 4:40 PM Page 746 n t.005 Los Lor Los L90 tao tos to so Ls 1 63.66 381.82 12.71 6.31 3.08 1.376 1.000 7 325 .158 2 9.92 6.96 4,50 2.92 1.89 1.061 816 617 .289 .142 3 5.84 4.54 3,18 2.35 1.64 978 165 584 277 «137 4 4,60 3.75 2.78 2.13 1,53 «JAL 741 569 271 «134 5 4.03 3.36 2.57 2.02 1.48 .920 MET 559 267 .132 6 3.71 3.14 2.45 1,94 1.44 906 118 -553 .265 .131 7 3.50 3,00 2.36 1.90 1.42 -896 311 549 .263 .130 8 3.36 2.90 2.31 1.88 1.40 ,889 .706 546 .262 .130 9 3,25 2.82 2,26 1.83 1.38 .883 703 543 261 .129 10 3,17 2.78 2,23 181 1.37 879 700 042 .260 .129 11 3,11 2.72 2.20 1.80 1.36 876 697 540 .260 .129 12 2.06 2.68 2.18 1.78 1.36 .873 695 539 ,259 128 13 3,01 2,65 2.16 1.77 1.35 .870 694 538 259 .128 14 2.98 2.62 2.14 1.76 1.34 -868 .692 587 258 .128 15 2.95 2.60 2,13 1.75 1.34 866 691 536 .258 .128 16 2.92 2.58 2.12 1.75 1,34 .865 -690 535 258 .128 17 2.90 2.57 2.11 1.74 1.33 .863 .689 534 257 -128 18 2.88 2.55 2.10 1.73 1.33 .862 688 534 257 .127 19 2,86 2.54 2.09 1,73 1.33 861 .688 533 257 .127 20 2.84 2.53 2,09 1.72 1.22 860 «687 533 257 127 21 2.83 2.52 2.08 1.72 1,32 859 686 532 257 127 22 2.82 2.51 2.07 1,72 1.32 .858 .686 532 256 127 23 2.81 2.50 2.07 1.71 1.32 .858 685 532 256 127 24 2.30 2,49 2.06 1.71 1.32 857 ,685 531 256 127 25 2.79 2,48 2.06 171 1.32 856 ,684 531 256 .127 26 2.78 2.48 2.06 1.71 1.32 .856 634 .531 256 .127 27 2,77 2,47 2.05 1.70 1.31 -855 +,684 531 256 127 23 2.76 2,47 2.05 1.70 1.31 855 -683 530 256 127 29 2.76 2.46 2,04 1.70 1.31 .854 683 .530 256 127 30 2.75 2.46 2.04 1,70 131 854 ,683 530 256 127 40 2.70 2.42 2.02 1.68 1.30 851 -681 529 255 «126 50 2.66 2.39 2,00 1.67 1.30 848 .679 527 254 .126 120 2.62 2.36 1,98 1.66 1.29 845 677 526 254 .126 e 2.58 2.33 1.96 1.645 1.28 842 .674 524 .253 .126 Source: R. A. Fisher and F. Yates, Statistical Tables for Biological, Agricultural and Medical Research (6th edition, 1963), Table III, Oliver and Boyd Ltd., Edin- burgh, by permission of the authors and publishers. 258  TABLE 49 md ados o sos o a ss a aos 1 7.88 6.63 5.02 3,84 2.711 1,32 455 »102 .0158 .0089 0010 .0002 .0000 2] 106 921 738 599 46L 27 189 575 211 108 0506 0201 0100 3 12.8 11.3 9,35 71.81 6,25 4,11 2.37 1.21 584 352 216 115 072 4| 149 183 111 949 7.TO 589 3836 192 106 711 484 297 207 5| 167 151 128 111 92% 663 485 267 16 115 881 554 412 6 18.5 16.8 14,4 12.6 10.6 7,84 5.35 3.45 2,20 1.64 1,24 .872 678 7 20.3 18.5 16.0 1.1 12.0 9.04 6.35 4.25 2,82 2.17 1.69 1.24 .989 3 22.0 20.1 17.5 15.5 13.4 10,2 7,34 5.07 3.49 2.73 2.18 1.65 1,34 2 23.6 217 19.0 16.9 14.7 11.4 8.34 5.90 4.17 8.33 2.70 2.09 173 10 25,2 23.2 20,5 18.3 16.0 125 9,34 6.74 4.87 3.94 3.25 2.56 2.16 11 26.8 247 21.9 19.7 17.3 13.7 10.3 7.58 5.58 4.57 3,82 3.05 2.60 12 28,3 26.2 23.3 21.0 18.5 14.8 11.3 8,44 6.30 5,23 4.40 3.57 3,07 13 29.8 277 24.7 22.4 19.3 16.0 12.3 9.30 7.04 5.89 5.01 4.11 3.57 14 31.3 29.1 26.1 23.7 21,1 171 13.3 10.2 7.79 6.57 5.63 4.66 4.07 15 32.8 30.6 27.5 25.0 22.8 18,2 14.3 11.0 8.55 7.26 6.26 5,23 4.50 16 | 343 320 288 268 28.5 194 158 119 2981 796 69 681 514 17 35.7 33,4 30.2 27.6 24.8 20.5 16.3 12.8 10.1 8,67 7.56 6.41 5.70 18 37.2 34,8 31.5 23.9 26.0 21.6 17.3 13.7 10.9 9.39 3.23 7.01 6,26 19 38.6 36.2 32,9 30.1 27.2 22.7 18.3 14.6 11.7 10,1 8.91 7.63 6,84 20 400 37.6 34.2 31.4 28.4 23.8 19.8 15.5 12.4 10.9 9.59 3.26 7.43 21 41.4 38.9 35.5 32.7 29.6 24.9 20.3 16.3 13.2 11.6 10.3 38,90 8.03 22 42.8 40.3 36.8 33.9 30.8 26,0 21.3 17.2 14.0 12.3 11.0 9,54 8.64 23 44,2 41.6 38.1 35.2 32.0 271 22.3 18.1 14.8 13.1 11.7 10,2 9.26 24 45.6 43.0 39.4 36.4 33.2 23.2 23.38 19.0 15.7 12,8 12.4 10.9 9,89 25 46.9 44.3 40.6 77 34.4 29.3 24,3 19.9 16.5 14,6 13,1 11.5 10.5 26 48.8 45.6 41.9 38.9 35.5 30.4 25.3 20.8 17.3 15,4 13.8 12,2 11.2 27| 496 470 432 401 36.7 315 268 217 181 162 146 129 118 23 51.0 48,3 44.5 41.3 37.9 32.6 27.3 22.7 18.9 16.9 15.3 13.6 12.5 29 52.3 49.5 45.7 42.6 39.1 33.7 28.8 23.6 19.8 17.7 16.0 14.3 13.1 30 53.7 50.9 47.0 43,8 40,3 34.8 29.3 24.5 20.6 18.5 16.8 15.0 13,8 40 66.8 63.7 59.8 55.8 51.8 45.6 39.3 33.7 29.1 26.5 24.4 22,2 20.7 50 79.5 76.2 TL4 67.5 63.2 56,3 49.3 42.9 377 34.8 32.4 29.7 28.0 60 92.0 88,4 383.3 79.1 74.4 67.0 52.3 465 43.2 40.5 37.5 35.5 70 | 1042 100.4 95.0 90.5 85.5 776 69.3 61.7 55.3 51.7 48.8 45.4 43.3 80 | 116.3 1123 106,6 101.9 96.6 88.1 79,3 mi 64.3 60.4 57.2 53.5 51.2 90 | 123.3 124,1 1181 1131 1076 98,6 89.3 30.6 73.3 69.1 65.6 61.3 59,2 100 | 140.2 135.8 129.6 124.3 118.5 109.1 99,3 90.1 82.4 aa 74,2 70.1 87.3 Source: Catherine M. Thompson, Table of percentage points of the x? distribution, Biometrika, Vol, 32 (1941), by permission of the author and publisher. 2 9  '951h: PERCENTILE VALUES FOR: - Ñ THE-F DISTRIBUTION -- 5 Ar degrees of freedom for numerator nz = degrees of freedom:for denominator (sháded area = 95) TABLE al 1 2 3 4 5 6 8 12 16 20 30 40 50 100 «o 1|161.4 199.5 215,7 224.6 230.2 234,0 238.9 243.9 246,3 248.0 250,1 251.1 2522 253.0 254.3 218,51 19.00 19.16 19.25 19,30 19.83 19,87 19.41 19.48 19.45 19.46 19146 19.47 19.49 19.50 3[10.13 955 928 912 901 894 885 8,74 8.69 8.66 8.62 8.60 8.58 856 8,53 4| 7.71 6,94 6.59 639 626 6.16 604 591 584 580 575 5.71 5.70 566 5.63 5| 6.61 5.79 541 5.19 505 495 482 468 4.60 4.56 4.50 446 444 440 4.36 6] 5.99 5.14 4.76 453 439 4,28 415 400 3.92 3.87 281 38.77 375 3.11 3,67 TP 558 4.74 435 4.12 8.97 387 3.73 3.57 3,49 3.44 2.38 834 332 3.28 3,23 8/1 532 446 407 3.84 3.69 358 3.44 3,28 320 315 3.08 3.0% 3.03 298 2.093 9 512 426 3.86 3.63 348 3.37 3,23 3.07 298 293 286 282 280 2.76 2.71 0| 496 410 371 348 233 3.22 3.07 291 282 2.77 2.70 267 2.64 259 254 11[ 484 2398 359 3,36 3.20 3.09 295 2.79 2.70 265 257 253 250 245 240 12| 4.76 3,89 349 326 3.11 3.00 285 2.69 260 254 246 242 240 225 230 13| 4.67 381 341 818 303 292 277 2.60 251 246 238 234 232 2.26 2,21 14[| 4.60 3,74 334 3,11 296 285 270 253 244 239 231 227 224 219 213 15| 4.54 368 329 3.06 290 2.79 264 248 239 2383 225 221 218 212 2.07 16 | 4.49 3.63 38.24 3,01 285 274 259 242 238 228 220 216 213 207 2.01 17| 445 3,59 320 296 281 2.70 255 238 229 223 215 211 208 202 1.96 18/ 441 3855 316 293 277 2.66 251 234 225 2.19 211 207 204 198 1.92 19] 438 3.52 313 290 274 2.63 248 231 221 215 207 202 200 194 1.88 20| 435 349 310 287 2.71 260 245 228 218 2.12 204 199 196 1.00 1.84 22| 430 344 305 282 266 255 240 223 213 207 198 1.93 191 184 178 24 | 426 3.40 301 278 262 251 2.86 218 209 2.03 194 189 186 180 1.73 26| 423 3.37 298 274 259 247 232 215 205 199 190 185 182 1.76 1.69 28| 4,20 3,34 295 2.71 2.56 245 2.29 212 2.02 196 1.87 181 1.78 172 165 30| 4.17 282 292 269 253 2.42 227 209 199 193 184 179 176 1.69 162 40| 4.08 3.23 284 2.61 245 234 218 200 190 184 174 169 168 1.59 151 50| 403 318 279 256 240 229 213 195 185 178 169 1.63 160 152 1.44 60| 400 315 2.76 253 287 2.25 210 192 1.81 175 165 159 156 148 1.39 70| 598 313 274 250 2.35 223 207 189 179 1.72 162 1.58 152 145 135 80| 3.98 3.11 272 248 233 221 205 188 177 1.70 160 154 151 142 1.32 100 | 3.94 3,09 270 246 230 2.19 203 185 1.75 168 1.57 151 148 139 1.28 150 | 3.91 3.06 267 243 227 216 2.00 1.82 171 164 154 147 144 134 1.22 200 | 3.89 3.04 265 241 226 214 198 180 169 162 152 145 142 132 1.19 400| 3.86 3.02 2.62 239 2.23 2.12 196 1.78 167 160 149 142 138 128 1.18 » 384 299 260 2387 221 2.09 194 1.75 164 157 146 140 132 124 1.00 Source: G. W. Snedecor and W. G. Cochran, Statistical Methods (6th edition, 1967), lowa State University Press, Ames, Iowa, by permission of the authors and publisher. 260