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2.106 SECTION 2 TABLE 2.24 Integrals (Continued) Rational functions (continued) dx 1 b cx 1 2 23. tan C [ac b 0] a 2bx cx2 2 2 pac b pac b 2 1 pb ac b cx ln C 2 b2 ac b2 p p ac b cx [b2 1 b cx ac 0] 1 tanh C b2 ac b2 p p ac dx 1 2 24. C, when b ac a 2bx cx2 b cx (m nx) dx n mc nb dx 25. ln (a 2bx cx 2 ) 2 a 2bx cx 2c c a 2bx cx2 f(x) dx 26. In , if f(x) is a polynomial of higher than the first degree, divide a 2bx cx2 by the denomina<strong>to</strong>r before integrating. dx 1 b cx 27. (a 2bx cx 2) p 2(ac b 2)(p 1) (a 2bx cx 2) p1 (2p 3)c dx 2 2(ac b )(p 1) (a 2bx cx 2) p1 (m nx) dx n 1 28. (a 2bx cx 2) p 2c(p 1) (a 2bx cx 2) p1 mc nb dx c (a 2bx cx 2) p x m1(a bx) n1 (m 1)a m1 n m2 n 29. x (a bx) dx x (a bx) dx (m n)b (m n)b x m(a bx) n na x m1(a bx) n1 dx m n m n Irrational functions 2 dx 2 30. a bx dx (a bx) 3 p p C 31. pa bx C 3b pa bx b (m nx) dx 2 32. (3mb 2an nbx) pa bx C pa bx 3b 2 dx 33. ; substitute y pa bx, and use 21 and 22 (m nx) pa bx n f(x, pa bx) n 34. dx; substitute pa bx y F(x, n pa bx) dx x x 1 1 35. sin C cos c 2 2 pa x a a dx 2 2 1 x 36. ln (x pa x ) C sinh c 2 2 pa x a dx 2 2 1 x 37. ln (x px a ) C cosh c 2 2 px a a
GENERAL INFORMATION, CONVERSION TABLES, AND MATHEMATICS 2.107 TABLE 2.24 Integrals (Continued) Irrational functions (continued) dx 1 2 38. ln (b cx pc pa 2bx cx ) C, when c 0 2 pa 2bx cx pc 1 1 b cx sinh C, when ac b2 0 pc pac b 2 1 b cx 1 2 cosh C, when b ac 0 c b2 p p ac 1 b cx sin1 C, when c 0 c b2 p p ac (m nx) dx n mc nb dx 2 39. pa 2bx cx 2 c c 2 pa 2bx cx pa 2bx cx m m1 m2 m1 x dx x X (m 1)a x dx (2m 1)b x dx 40. , pa 2bx cx 2 mc mc X mc X when X pa 2bx cx 2 x a 2 41. a2 x2 dx a2 x2 ln (x a2 x 2 p p p ) C 2 2 2 x a x a2 x2 sinh1 p c 2 2 a 2 x a x 42. a2 x2 dx a2 x2 sin1 p p C 2 2 a x a 2 43. x2 a2 dx x2 a2 ln (x x2 a 2 p p p ) C 2 2 2 x a x x2 a2 cosh1 p c 2 2 a b cx 44. a 2bx cx2 dx a 2bx cx2 p p 2c 2 ac b dx C 2c a 2bx cx2 p a x 45. ax dx C Transcendental functions ln a xe n ax n n(n 1) n! n ax 2 2 n n a ax a x a x 46. xe dx 1 ··· C 47. ln xdx x ln x x C 2 ln x ln x 1 48. dx C x x x n (ln x) 1 n1 49. dx (ln x) C x n 1 2 50. sin xdx⁄4 1 sin 2x 1⁄2x C ⁄2 1 sin x cos x 1⁄2x C 51. cos2 xdx 1⁄4 sin 2x 1⁄2x C 1⁄2 sin x cos x 1⁄2x C cos mx 52. sin mx dx C m sin mx 53. cos mx dx C m
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LANGE'S HANDBOOK OF CHEMISTRY John
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Grateful acknowledgment is hereby m
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PREFACE TO FIFTEENTH EDITION This n
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PREFACE TO FIFTEENTH EDITION ix inv
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xii PREFACE TO FOURTEENTH EDITION l
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PREFACE TO FIRST EDITION This book
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For the detailed contents of any se
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1.2 SECTION 1 is derived from the G
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1.4 SECTION 1 rather than methylide
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1.6 SECTION 1 Styrene Toluene Xylen
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1.8 SECTION 1 TABLE 1.2 Fused Polyc
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1.10 SECTION 1 1.1.1.6 Bridged Hydr
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1.12 SECTION 1 TABLE 1.4 Suffixes f
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1.14 SECTION 1 TABLE 1.5 Trivial Na
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1.16 SECTION 1 TABLE 1.6 Trivial Na
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1.18 SECTION 1 Selection of the pri
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1.20 SECTION 1 attached to one anot
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1.22 SECTION 1 When side chains of
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1.24 SECTION 1 heterocyclic structu
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1.26 SECTION 1 Bivalent radicals of
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1.28 SECTION 1 Complex linear polya
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1.30 SECTION 1 TABLE 1.11 Names of
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1.32 SECTION 1 hydroxyamino- to the
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1.34 SECTION 1 may be named (1) by
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1.36 SECTION 1 Examples are methyl
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1.38 SECTION 1 tuted acid, respecti
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1.40 SECTION 1 FIGURE 1.2 Newman pr
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1.42 SECTION 1 from the ring are kn
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1.44 SECTION 1 FIGURE 1.11 Two isom
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1.46 SECTION 1 Chiral Center. The c
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1.48 SECTION 1 FIGURE 1.15 Isomers
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1.50 SECTION 1 entries to bring tog
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1.52 SECTION 1 TABLE 1.13 Names and
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1.60 SECTION 1 TABLE 1.14 Empirical
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2.2 SECTION 2 2.3.6 Student’s Dis
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2.4 SECTION 2 TABLE 2.1 Fundamental
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2.6 SECTION 2 TABLE 2.1 Fundamental
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2.8 SECTION 2 TABLE 2.2 Physical an
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2.10 SECTION 2 TABLE 2.2 Physical a
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2.24 SECTION 2 TABLE 2.3 Mathematic
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2.26 SECTION 2 TABLE 2.6 Abbreviati
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2.36 SECTION 2 TABLE 2.7 Conversion
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2.54 SECTION 2 TABLE 2.8 Temperatur
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Page 170 and 171: 2.82 SECTION 2 TABLE 2.13 Viscosity
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Page 174 and 175: 2.86 SECTION 2 TABLE 2.15 Hydromete
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Page 178 and 179: 2.90 SECTION 2 TABLE 2.18 Pressure
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Page 186 and 187: 2.98 SECTION 2 TABLE 2.21 Transmitt
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Page 212 and 213: 2.124 SECTION 2 The distribution of
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Page 220 and 221: TABLE 2.29 F Distribution (Continue
Page 222 and 223: 2.134 SECTION 2 mathematical treatm
Page 224 and 225: 2.136 SECTION 2 The confidence limi
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Page 228 and 229: 3.2 SECTION 3 The alphabetical orde
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Page 232 and 233: 3.6 SECTION 3 PO phosphoryl SeO sel
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Page 238 and 239: 3.12 SECTION 3 3.2 PHYSICAL PROPERT
Page 240 and 241: TABLE 3.2 Physical Constants of Ino
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TABLE 3.2 Physical Constants of Ino
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3.62 SECTION 3 TABLE 3.3 Synonyms a
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SECTION 4 PROPERTIES OF ATOMS, RADI
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4.3 Fermium Fm 100 [Rn] 5f 12 7s 2
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Silver (argentum) Ag 47 [Kr] 4d 10
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PROPERTIES OF ATOMS,RADICALS,AND BO
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PROPERTIES OF ATOMS, RADICALS, AND
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SECTION 5 PHYSICAL PROPERTIES 5.1 S
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PHYSICAL PROPERTIES 5.3 5.1 SOLUBIL
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TABLE 5.1 Solubility of Gases in Wa
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TABLE 5.1 Solubility of Gases in Wa
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TABLE 5.2 Solubilities of Inorganic
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formateBa(CHO 2 ) 2 26.2 28.0 29.9
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(III) sulfateCe 2 (SO 4 ) 3 ·9H 2
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iodidePbI 2 0.044 0.056 0.069 0.090
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Nickel sulfateNiSO 4 ·6H 2 O (pale
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Praseodymium bromatePr(BrO 3 ) 3 55
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formate NaCHO 2 43.9 62.5 81.2 102
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Uranyl nitrate UO 2 (NO 3 ) 2 98 10
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PHYSICAL PROPERTIES 5.25 TABLE 5.3
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PHYSICAL PROPERTIES 5.57 5.3 BOILIN
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TABLE 5.12 Ternary Azeotropic Mixtu
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TABLE 5.12 Ternary Azeotropic Mixtu
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PHYSICAL PROPERTIES 5.83 5.4 FREEZI
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PHYSICAL PROPERTIES 5.87 5.5 DENSIT
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PHYSICAL PROPERTIES 5.89 dt Dt P
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PHYSICAL PROPERTIES 5.135 5.6.1 Ref
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PHYSICAL PROPERTIES 5.137 where the
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PHYSICAL PROPERTIES 5.139 5.7 COMBU
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Temperature, C Substance 40 20 0 20
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PHYSICAL PROPERTIES 5.171 This equa
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SECTION 6 THERMODYNAMIC PROPERTIES
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THERMODYNAMICPROPERTIES 6.3 6.1.1.2
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THERMODYNAMICPROPERTIES 6.5 A gener
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THERMODYNAMICPROPERTIES 6.7 TABLE 6
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THERMODYNAMICPROPERTIES 6.9 TABLE 6
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THERMODYNAMICPROPERTIES 6.11 TABLE
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THERMODYNAMIC PROPERTIES 6.21 TABLE
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THERMODYNAMIC PROPERTIES 6.101 TABL
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THERMODYNAMIC PROPERTIES 6.143 The
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SECTION 7 SPECTROSCOPY 7.1 X-RAY ME
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SPECTROSCOPY 7.3 TABLE 7.1 Waveleng
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SPECTROSCOPY 7.9 TABLE 7.3 Critical
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SPECTROSCOPY 7.11 TABLE 7.4 X-Ray E
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SPECTROSCOPY 7.13 Emission line K 1
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SPECTROSCOPY 7.15 TABLE 7.7 Analyzi
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SPECTROSCOPY 7.17 TABLE 7.8 Mass Ab
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SPECTROSCOPY 7.19 TABLE 7.9 Electro
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SPECTROSCOPY 7.21 TABLE 7.11 Absorp
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SPECTROSCOPY 7.23 TABLE 7.13 Solven
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SPECTROSCOPY 7.25 7.3 FLUORESCENCE
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SPECTROSCOPY 7.27 TABLE 7.16 Fluore
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SPECTROSCOPY 7.29 TABLE 7.18 Detect
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SPECTROSCOPY 7.35 TABLE 7.19 Sensit
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SPECTROSCOPY 7.37 TABLE 7.19 Sensit
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SPECTROSCOPY 7.39 In terms of m ,
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SPECTROSCOPY 7.41 The ionization co
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SPECTROSCOPY 7.67 TABLE 7.28 Infrar
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7.69
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SPECTROSCOPY 7.71 7.6 RAMAN SPECTRO
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SPECTROSCOPY 7.73 TABLE 7.30 Raman
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SPECTROSCOPY 7.89 7.7 NUCLEAR MAGNE
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SPECTROSCOPY 7.91 TABLE 7.41 Nuclea
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SPECTROSCOPY 7.93 TABLE 7.42 Proton
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SPECTROSCOPY 7.95 TABLE 7.44 Estima
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SPECTROSCOPY 7.97 TABLE 7.46 Proton
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SPECTROSCOPY 7.99 TABLE 7.48 Solven
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SPECTROSCOPY 7.101 TABLE 7.49 Carbo
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SPECTROSCOPY 7.103 TABLE 7.51 Effec
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SPECTROSCOPY 7.107 TABLE 7.56 One-B
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SPECTROSCOPY 7.113 TABLE 7.63 Nitro
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SPECTROSCOPY 7.115 TABLE 7.64 Nitro
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SPECTROSCOPY 7.117 TABLE 7.69 Fluor
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SPECTROSCOPY 7.119 TABLE 7.72 Silic
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SPECTROSCOPY 7.121 TABLE 7.73 Phosp
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SPECTROSCOPY 7.123 TABLE 7.74 Phosp
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SPECTROSCOPY 7.125 when z 3 and y
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SPECTROSCOPY 7.127 Masses 19 and 31
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SPECTROSCOPY 7.129 TABLE 7.76 Conde
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SECTION 8 ELECTROLYTES, ELECTROMOTI
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ELECTROLYTES, EMF, AND CHEMICAL EQU
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TABLE 8.7 Proton Transfer Reactions
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TABLE 8.7 Proton Transfer Reactions
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TABLE 8.9 Selected Equilibrium Cons
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8.75 3-tert-Butylbenzoic acid (0) 4
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4-Hydroxyproline (1) 1.900 1C 1.850
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N-Propionylglycine (1) 3.728 3.723
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TABLE 8.14 National Bureau of Stand
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1 part 0.1% neutral red in alc. * V
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3,3-Dimethoxybenzidine dihydrochlor
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TABLE 8.35 Equivalent Conductivitie
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KCl 127.3 124.4 122.4 115.8 112.0 1
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NaIO 3 75.2 72.6 70.9 64.4 60.5 1
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9.2 SECTION 9 9.1 LINEAR FREE ENERG
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9.4 SECTION 9 TABLE 9.1 Hammett and
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9.6 SECTION 9 TABLE 9.1 Hammett and
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9.8 SECTION 9 TABLE 9.3 pK a and Rh
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10.2 SECTION 10 10.4.6 Polyacrylate
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10.4 SECTION 10 10.2 ADDITIVES TO P
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10.6 SECTION 10 injection molding.
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10.8 SECTION 10 10.3 FORMULAS AND K
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10.10 SECTION 10 Key properties of
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10.12 SECTION 10 10.3.8 Fluorocarbo
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10.14 SECTION 10 10.3.11 Phenolics
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10.16 SECTION 10 The resin has the
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10.18 SECTION 10 10.3.19 Polyuretha
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10.20 SECTION 10 10.3.22 Sulfones B
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TABLE 10.2 Properties of Commercial
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10.58 SECTION 10 10.4 FORMULAS AND
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10.60 SECTION 10 10.4.8 Polychlorop
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10.62 SECTION 10 Styrene-butadiene
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10.5 CHEMICAL RESISTANCE TABLE 10.4
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10.6 GAS PERMEABILITY TABLE 10.5 Ga
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TABLE 10.5 Gas Permeability Constan
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TABLE 10.7 Constants ofFats and Oil
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TABLE 10.8 Constants ofWaxes Wax Me
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SECTION 11 PRACTICAL LABORATORY INF
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11.4 SECTION 11 TABLE 11.2 Molecula
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11.6 SECTION 11 A saturated aqueous
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11.8 SECTION 11 TABLE 11.6 Relative
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11.10 SECTION 11 11.3 BOILING POINT
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11.12 SECTION 11 TABLE 11.8 Organic
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11.14 SECTION 11 TABLE 11.9 Molecul
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11.4 SEPARATION METHODS TABLE 11.11
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11.18 SECTION 11 TABLE 11.12 Solven
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11.20 SECTION 11 TABLE 11.12 Solven
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TABLE 11.13 McReynolds’ Constants
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TABLE 11.13 McReynolds’ Constants
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11.26 SECTION 11 11.4.1 McReynolds
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11.28 SECTION 11 11.4.2.2 Partition
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11.30 SECTION 11 FIGURE 11.2 Band a
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11.32 SECTION 11 11.4.3 Ion-Exchang
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11.34 SECTION 11 TABLE 11.16 Guide
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11.36 SECTION 11 TABLE 11.16 Guide
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11.38 SECTION 11 TABLE 11.18 Relati
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11.40 SECTION 11 distribution coeff
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11.42 SECTION 11 TABLE 11.19 Gravim
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11.68 SECTION 11 TABLE 11.20 Elemen
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11.70 SECTION 11 TABLE 11.22 Common
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11.72 SECTION 11 TABLE 11.25 Tolera
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11.74 SECTION 11 TABLE 11.26 Heatin
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11.76 SECTION 11 TABLE 11.28 Titrim
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11.84 SECTION 11 appears becomes le
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11.86 SECTION 11 TABLE 11.29 Equati
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11.88 SECTION 11 TABLE 11.29 Equati
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11.90 SECTION 11 The more stable th
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11.92 SECTION 11 11.6.6.2.5 Buffer
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11.94 SECTION 11 TABLE 11.30 Standa
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TABLE 11.32 Properties and Applicat
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11.98 SECTION 11 TABLE 11.36 Maskin
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11.100 SECTION 11 TABLE 11.37 Anion
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11.102 SECTION 11 TABLE 11.39 Amino
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11.104 SECTION 11 TABLE 11.44 Facto
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11.106 SECTION 11 11.7 LABORATORY S
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11.108 SECTION 11 TABLE 11.48 Stand
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11.110 SECTION 11 Alizarin yellow G
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11.112 SECTION 11 Bromchlorophenol
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11.114 SECTION 11 p-Ethoxychrysoidi
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11.116 SECTION 11 Mercurous nitrate
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11.118 SECTION 11 Potassium carbona
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11.120 SECTION 11 until the ammoniu
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11.122 SECTION 11 TABLE 11.49 TLV C
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11.130 SECTION 11 TABLE 11.50 Chemi
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11.138 SECTION 11 of water which is
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TABLE 11.55 Thermoelectric Values i
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TABLE 11.56 Type B Thermocouples: P
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TABLE 11.58 Type J Thermocouples: I
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TABLE 11.60 Type N Thermocouples: N
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TABLE 11.62 Type S Thermocouples: P
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11.150 SECTION 11 11.11 CORRECTION
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Index Terms Links 2 Acid-base indic
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Index Terms Links 4 Alkynes, nomenc
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Index Terms Links 6 Aurintricarboxy
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Index Terms Links 8 Boron-11 chemic
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Index Terms Links 10 Cellulose acet
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Index Terms Links 12 Collective ino
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Index Terms Links 14 Degree Fahrenh
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Index Terms Links 16 Electrical res
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Index Terms Links 18 Equivalent wei
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Index Terms Links 20 Fluorocarbon p
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Index Terms Links 22 Halogenated hy
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Index Terms Links 24 Impact strengt
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Index Terms Links 26 Kα 1 lines, m
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Index Terms Links 28 Melmine phenol
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Index Terms Links 30 Neon-neon bond
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Index Terms Links 32 One-tailed tes
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Index Terms Links 34 Physical chemi
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Index Terms Links 36 Polyolefin the
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Index Terms Links 38 Pyridine: bina
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Index Terms Links 40 Rho values: fo
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Index Terms Links 42 Single-bond ra
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Index Terms Links 44 Stereoisomers
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Index Terms Links 46 Tension, aqueo
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Index Terms Links 48 Triethylenetet
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Index Terms Links 50 Water (Cont.)
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