The mathematical expressions (Chapters 6.6-6.13) were given in order to describe the model, at the same time serving as a basis for establishing suitable computer programs.
Without computer support, it is rather laborious to construct the upper and lower predic- tion limits. In general, however, these limits are only needed in a region between X = 0 and X = X2 (see Figure 1). For a graphical derivation of the LDC and LDM it is, therefore, per- missible to substitute the curves for these limits by straight lines, which are drawn, parallel to the calibration line, through the points YUP and Y ^ . (A mathematical check of the quality of the approximation can be made by calculating some values for Y+ and Y_ using equation I.)
This simplification permits the derivation of the LDC and LDM "by hand" on graph paper.
The graphical procedure is described here, using Example 1:
- Calculate the terms E through N, as well as X, Y, A, B, YUP and Y ^ as described in 9.1
— Draw the calibration line by connecting two points, e. g. X = 0, Y = 9.65 and X = 100, Y = 94.8, using the linear equation Y = 9.65 + 0.85 • X to obtain the Y values
- Draw two lines, parallel to the calibration line, through YUP and Y ^
- Derive LDC as illustrated in Figure 7, obtaining a value of approx. 50 on the X-axis
— Derive Xj as shown in Figure 8, obtaining a value of approx. 75 on the X-axis
— For deriving Xm, draw a straight line through two points, e.g. X', Y* and X", Y**, so that it intersects the upper parallel as illustrated in Figure 9. Y* and Y** are obtained from the equation of the calibration line by multiplying the resulting Y values (Y' and Y") by 1 + 0.2 • t (for explanation, see 4.4); in this case, t = 2.45 (see Table 2).
22 Limits of Detection and Determination
Example: X' = 20, Y' = 26.7, Y* = 39.8 X" = 60, Y" = 60.8, Y** = 90.5
The point of intersection corresponds to Yc v and yields Xm being approx. 62.
The outcome of the graphical derivation is in good agreement with the results obtained from calculation (9.1). The approximation achieved by such a procedure will be sufficient for residue analyses in most cases.
LDC
Fig. 7. Graphical derivation of LDC.
UX X
Fig. 8. Graphical derivation of
Fig. 9. Graphical derivation of Xu
Limits of Detection and Determination 23
Appendix
Table 2. Critical values of the t distribution at a 95% level of statistical significance in relation to the degree of freedom f = n — 2.
two-sided 1
2 3 4 5 6 7 8 9
12.71 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262
f 10 11 12 13 14 15 20 30 40
t two-sided
2.228 2.201 2.179 2.160 2.145 2.131 2.086 2.042 2.021
Mass-Spectrometric El Data for Confirmation of Results
GC/MS is an excellent tool for the confirmation of results in pesticide residue analysis. For this reason, the six most abundant fragments and their relative intensities for approx. 150 pesticides and derivatives are listed in the following Table.
The data relate to electron impact ionization at 70 eV and can be helpful for identifying suitable fragments when multiple ion detection (MID) is used. The data given for the relative intensities, however, may vary to some extent according to the type of the mass-spectrometer or the mass-selective detector used. Therefore, any confirmation of identity is best based on comparison of mass spectra which were obtained under identical instrumental conditions.
Table. Main fragments and their relative intensities for pesticides and some derivatives.
P , Molar Main fragments m/z (intensities)
mass*) 1 2 3 4 5
Acephate Alachlor Aldicarb Aldrin Allethrin Atrazine Azinphos-methyl Barban
Benazolin methyl ester Bendiocarb
Bromacil
Bromacil N-methyl derivative Bromophos
Bromophos-ethyl Bromoxynil methyl ether Captafol
Captan Carbaryl Carbendazim Carbetamide Carbofuran Chlorbromuron Chlorbufam cis-Chlordane trans-Chlordane Chlorfenprop-methyl Chlorfenvinphos Chloridazon Chloroneb
183 269 190 362 302 215 317 257 257 223 260 274 364 392 289 347 299 201 191 236 221 292 223 406 406 232 358 221 206
43 45 41 66 123 43 77 51 170 151 205 219 331 97 291 79 79 144 159 119 164 61 53 373 373 125 81 77 191
(100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100)
44 188 86 91 79 58 160 153 134 126 207 221 125 65 88 80 80 115 191 72 149 46 127 375 375 165 267 221 193
(88) (23) (89) (50) (40) (84) (77) (76) (75) (58) (75) (68) (91) (35) (77) (42) (61) (82) (57) (54) (70) (24) (20) (84) (93) (64) (73) (60) (61)
136 160 58 79 43 44 132 87 198 166 42 41 329 303 276 77 77 116 103 91 41 62 51 377 377 75 109 88 206
(80) (18) (85) (47) (32) (75) (67) (66) (74) (48) (25) (45) (80) (32) (67) (28) (56) (48) (38) (44) (27) (11) (13) (46) (53) (46) (55) (37) (60)
94 77 85 263 81 200 44 222 257 51 70 188 79 125 289 78 44 57 104 45 58 63 164 371 371 196 269 220 53
(58) (7) (61) (42) (31) (69) (30) (44) (73) (19) (16) (41) (57) (28) (55) (19) (44) (31) (37) (38) (25) (10) (13) (39) (47) (43) (47) (35) (57)
47 146 87 65 91 68 105 52 172 58 206 190 109 359 293 151 78 58 52 64 131 60 223 44 272 51 323 51 208
(56) (6) (50) (35) (29) (43) (29) (43) (40) (18) (16) (40) (53) (27) (53) (17) (37) (20) (32) (37) (25) (9) (13) (36) (36) (43) (26) (26) (39)
95 224 44 101 136 215 104 63 200 43 162 56 93 109 248 51 149 63 51 74 122 124 70 109 237 101 91 105 141
(32) (6) (50) (34) (27) (40) (27) (43) (31) (17) (12) (37) (45) (27) (50) (13) (34) (20) (29) (29) (25) (8) (10) (36) (30) (37) (23) (24) (35)
26 List of Mass-Spectrometric Data
Table, (contd.)
Compound Chlorotoluron
3-Chloro-4-methylaniline (GLC degradation product of chlorotoluron)
Chloroxuron Chlorpropham Chlorpyrifos Chlorthal-dimethyl Chlorthiamid Cinerin I Cinerin II Cyanazine Cypermethrin 2,4-DB methyl ester Dalapon
Dazomet Demeton-S-methyl Desmetryn Dialifos Di-allate Diazinon
Dicamba methyl ester Dichlobenil
Dichlofenthion Dichlofluanid 2,4-D isooctyl ester 2,4-D methyl ester Dichlorprop isooctyl ester Dichlorprop methyl ester Dichlorvos
Dicofol o,p'-DDT p,p'-DDT Dieldrin
Dimethirimol methyl ether Dimethoate
DNOC methyl ether Dinoterb methyl ether Dioxacarb
Diphenamid Disulfoton Diuron Dodine Endosulfan Endrin Ethiofencarb Ethirimol
Ethirimol methyl ether
Molar mass*) 212
141 290 213 349 330 205 316 360 240 415 262 142 162 230 213 393 269 304 234 171 314 332 332 234 346 248 220 368 352 352 378 223 229 212 254 223 239 274 232 227 404 378 225 209 223
72
141 72 43 97 301 170 123 107 44 163 101 43 162 88 213 208 43 137 203 171 97 123 43 199 43 162 109 139 235 235 79 180 87 182 239 121 72 88 72 43 195 67 107 166 180 1 (100)
(100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) (100)
Main fragments m/z 2 3 44 (29)
140 (37) 245 (37) 127 (49) 195 (59) 299 (81) 60 (61) 43 (35) 93 (57) 43 (60) 181 (79) 59 (95) 61 (81) 42 (87) 60 (50) 57 (67) 210 (31) 86 (62) 179 (74) 205 (60) 173 (62) 279 (92) 92 (33) 57 (98) 45 (97) 57 (83) 164 (80) 185 (18) 111 (39) 237 (59) 237 (58) 82 (32) 223 (23) 93 (76) 165 (74) 209 (41) 122 (62) 167 (86) 89 (43) 44 (34) 73 (80) 36 (95) 81 (67) 69 (48) 209 (17) 223 (23)
167 (28)
106 (68) 44 (31) 41 (35) 199 (53) 303 (47) 171 (50) 93 (33) 121 (53) 68 (60) 165 (68) 41 (39) 62 (67) 89 (79) 109 (24) 58 (66) 76 (20) 41 (38) 152 (65) 234 (27) 100 (31) 223 (90) 224 (29) 41 (76) 175 (94) 41 (61) 59 (62) 79 (17) 141 (33) 165 (33) 165 (37) 81 (30) 181 (10) 125 (56) 89 (69) 43 (36) 166 (46) 165 (42) 61 (40) 73 (25) 59 (52) 237 (91) 263 (59) 77 (29) 167 (14) 85 (14)
(intensities) 4 5 132 (25)
142 (36) 75 (21) 45 (20) 65 (27) 332 (29) 172 (49) 121 (27) 91 (50) 212 (48) 91 (41) 162 (36) 97 (59) 44 (73) 142 (17) 198 (58) 173 (17) 44 (25) 93 (47) 188 (26) 136 (24) 109 (67) 167 (27) 55 (54) 145 (70) 71 (48) 189 (56) 187 (6) 75 (18) 236 (16) 236 (16) 263 (17) 224 (3) 58 (40) 90 (57) 91 (35) 165 (42) 239 (21) 60 (39) 42 (20) 55 (47) 41 (89) 36 (58) 41 (26) 96 (12) 181 (12)
45 (20)
143 (28) 45 (19) 44 (18) 47 (23) 142 (26) 205 (35) 81 (27) 149 (35) 41 (47) 77 (33) 69 (28) 45 (59) 76 (59) 79 (14) 82 (44) 209 (12) 42 (24) 153 (42) 97 (21) 75 (24) 162 (53) 63 (23) 71 (41) 111 (69) 55 (47) 63 (39) 145 (6) 83 (17) 199 (12) 75 (12) 77 (17) 42 (2) 47 (39) 212 (48) 77 (33) 73 (35) 152 (17) 97 (36) 232 (19) 72 (46) 24 (79) 79 (47) 81 (21) 194 (4) 55 (10)
6 77(11)
77 (25) 63 (16) 129 (16) 314 (21) 221 (24) 173 (29) 150 (27) 105 (33) 42 (34) 51 (29) 63 (25) 44 (47) 43 (53) 47 (11) 171 (39) 357 (10) 70 (19) 199 (39) 201 (20) 50 (19) 251 (46) 77 (22) 69 (27) 109 (68) 162 (41) 191 (35) 47 (5) 251 (16) 75 (12) 239 (11) 108 (14) 109 (2) 63 (33) 51 (47) 254 (33) 45 (31) 168 (14) 65 (23) 187 (13) 100 (46) 75 (78) 82 (41) 45 (17) 55 (2) 96 (9)
List of Mass-Spectrometric Data 27
Table, (contd.)
Compound Molar
mass *)
Main fragments m/z (intensities) 2 3 4 5 Etnmfos
Fenarimol Fenitrothion
Fenoprop isooctyl ester Fenoprop methyl ester Fenuron
Flamprop-isopropyl Flamprop-methyl Formothion Heptachlor Iodofenphos Ioxynil isooctyl ether Ioxynil methyl ether Isoproturon Jasmolin I Jasmolin II Lenacil
Lenacil N-methyl derivative Lindane
Linuron
MCPB isooctyl ester MCPB methyl ester Malathion
Mecoprop isooctyl ester Mecoprop methyl ester Metamitron
Methabenzthiazuron Methazole
Methidathion Methiocarb Methomyl Metobromuron Metoxuron Metribuzin Mevinphos Monocrotophos Monolinuron Napropamide Nicotine Nitrofen Nuarimol Omethoate Oxadiazon Parathion Parathion-methyl Pendimethalin Permethrin Phenmedipham
292 330 277 380 282 164 363 335 257 370 412 483 385 206 330 374 234 248 288 248 340 242 330 326 228 202 221 260 302 225 162 258 228 214 224 223 214 271 162 283 314 213 344 291 263 281 390 300
125 (100) 139 (100) 125 (100) 57 (100) 196 (100) 72 (100) 105 (100) 105 (100) 93 (100) 100 (100) 125 (100) 127 (100) 385 (100) 146 (100) 123 (100) 107 (100) 153 (100) 167 (100) 181 (100) 61 (100) 87 (100) 101 (100) 125 (100) 43 (100) 169 (100) 104 (100) 164 (100) 44 (100) 85 (100) 168 (100) 44 (100) 61 (100) 72 (100) 198 (100) 127 (100) 127 (100) 61 (100) 72 (100) 84 (100) 283 (100) 107 (100) 110 (100) 43 (100) 97 (100) 109 (100) 252 (100) 183 (100) 133 (100)
292 107 109 43 198 164 77 77 125 272 377 57 243 72 43 91 154 166 183 187 57 59 93 57 143 202 136 161 145 153 58 46 44 41 192 67 126 100 133 285 235 156 175 109 125 43 163 104
(91) (95) (92) (94) (89) (27) (44) (46) (89) (81) (78) (96) (56) (54) (52) (69) (20) (45) (97) (43) (81) (70) (96) (94) (79) (66) (73) (44) (90) (84) (81) (43) (27) (78) (30) (25) (63) (81) (21) (67) (91) (83) (92) (90) (80) (53) (100) (52)
181 111 79 41 59 119 276 276 126 274 47 41 370 44 55 135 110 168 109 189 43 77 127 169 59 42 135 124 93 45 105 60 183 57 109 97 153 128 42 202 203 79 57 291 263 57 165 132
(90) (40) (62) (85) (82) (24) (21) (20) (68) (42) (64) (34) (41) (35) (34) (69) (15) (12) (89) (29) (62) (40) (75) (77) (58) (42) (69) (36) (32) (40) (69) (15) (23) (54) (27) (23) (42) (62) (18) (55) (85) (39) (84) (57) (56) (43) (25) (34)
47 219 47 196 55 91 106 106 42 237 79 43 127 128 93 93 109 165 219 124 71 107 173 41 141 174 163 187 125 109 45 91 228 43 67 109 214 44 162 50 139 109 177 139 79 41 44 91
(84) (39) (57) (63) (36) (22) (18) (14) (49) (33) (59) (33) (13) (29) (25) (67) (15) (12) (86) (28) (45) (25) (55) (70) (57) (35) (42) (31) (22) (37) (59) (13) (22) (39) (20) (14) (34) (55) (17) (55) (60) (32) (60) (47) (26) (41) (15) (34)
153 141 63 71 87 42 278 230 47 102 93 55 386 45 91 55 152 124 111 46 41 41 158 142 228 77 69 159 47 91 42 258 45 47 43 58 46 115 161 139 123 58 42 125 63 281 184 165
(84) (33) (44) (60) (34) (14) (7) (12) (48) (33) (54) (26) (10) (28) (24) (66) (13) (9) (75) (28) (42) (22) (37) (69) (54) (24) (30) (24) (21) (31) (55) (13) (21) (38) (8) (14) (29) (41) (15) (37) (46) (30) (35) (41) (18) (37) (15) (3D
56 251 93 198 223 44 51 44 87 109 37 88 161 81 121 136 123 217 44 69 142 99 55 107 103 58 163 58 58 47 170 73 74 193 192 125 127 105 63 95 47 258 137 93 253 91 44
(73) (31) (40) (59) (31) (11) (5) (11) (40) (49) (16) (9) (25) (23) (58) (10) (6) (68) (23) (29) (20) (35) (52) (50) (19) (25) (23) (20) (21) (52) (12) (15) (36) (7) (13) (25) (36) (9) (37) (35) (21) (22) (39) (18) (34) (13) (27)
28 List of Mass-Spectrometric Data Table, (contd.)
„ , Molar Main fragments m/z (intensities)
P mass*) 1 2 3 4 5
Phosalone Pirimicarb Pirimiphos-ethyl Pirimiphos-methyl Propachlor Propanil Propham Propoxur Pyrethrin I Pyrethrin II Quintozene Resmethrin Simazine Tecnazene Terbacil
Terbacil N-methyl derivative Tetrachlorvinphos
Tetrasul Thiabendazole Thiofanox Thiometon Thiophanate-methyl Thiram
Tri-allate Trichlorfon Tridemorph Trietazine Trifluralin Vamidothion Vinclozolin
367 238 333 305 211 217 179 209 328 372 293 338 201 259 216 230 364 322 201 218 246 342 240 303 256 297 229 335 287 285
182 (100) 72 (100) 168 (100) 290 (100) 120 (100) 161 (100) 43 (100) 110 (100) 123 (100) 91 (100) 142 (100) 123 (100) 201 (100) 203 (100) 160 (100) 56 (100) 109 (100) 252 (100) 201 (100) 57 (100) 88 (100) 44 (100) 88 (100) 43 (100) 109 (100) 128 (100) 200 (100) 43 (100) 87 (100) 54 (100)
121 166 318 276 77 163 93 152 43 133 237 171 44 201 161 174 329 254 174 42 60 73 42 86 79 43 43 264 58 53
(48) (85) (94) (93) (66) (70) (88) (47) (62) (70) (96) (67) (96) (69) (99) (79) (48) (67) (72) (75) (63) (97) (25) (73) (34) (26) (81) (33) (47) (93)
97 42 152 125 93 57 41 43 91 161 44 128 186 108 117 175 331 324 63 68 125 159 44 41 47 42 186 306 44 43
(36) (63) (88) (69) (36) (64) (42) (28) (58) (55) (75) (52) (72) (69) (69) (31) (42) (51) (12) (39) (56) (89) (20) (43) (26) (18) (52) (32) (40) (82)
184 44 304 305 43 217 120 58 81 117 214 143 68 215 42 57 79 108 202 61 61 191 208 42 44 44 229 57 61 124
(32) (44) (79) (53) (35) (16) (24) (27) (47) (48) (67) (49) (63) (60) (45) (24) (20) (49) (11) (38) (52) (80) (18) (31) (20) (13) (52) (7) (29) (65)
154 43 180 233 51 165 65 41 105 107 107 81 173 44 41 176 333 75 64 55 47 86 73 70 185 129 214 42 59 212
(24) (24) (73) (44) (30) (11) (24) (21) (45) (47) (62) (38) (57) (57) (41) (23) (14) (40) (11) (34) (49) (72) (15) (23) (17) (11) (50) (6) (26) (63)
111 238 42 42 41 219 137 111 55 160 212 91 96 213 162 41 93 322 65 47 93 150 45 44 80 55 42 290 60 187
(24) (23) (71) (41) (27) (9) (23) (20) (43) (43) (61) (28) (40) (51) (37) (20) (9) (40) (9) (33) (47) (71) (10) (21) (8) (5) (48) (5) (25) (61)
*) Molecular ions; chloro and bromo compounds with Cl = 35 and Br = 79.
Part 2