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Principles and practice of agricultural analysis. Volume 3 (of 3), Agricultural products cover

Principles and practice of agricultural analysis. Volume 3 (of 3), Agricultural products

Chapter 15: GRAVIMETRIC COPPER METHODS.
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About This Book

A practical laboratory manual that presents methods for sampling, drying, incinerating, and extracting organic agricultural materials and for analyzing their constituents. It surveys physical and chemical techniques used to determine carbohydrates—including density measurements, polarimetric and reducing-sugar assays—and addresses starch hydrolysis, oils and fats, and analyses of dairy and animal products. The text emphasizes sample preparation, apparatus design, procedural variations, sources of error, and calculation steps, supplying illustrated guidance and adaptable procedures to help analysts and students perform accurate compositional determinations.

(1) A copper solution containing 24.95 grams of crystallized copper sulfate, 140 grams of sodium and potassium tartrate, and twenty-five grams of sodium hydroxid in one liter:

(2) A solution of sodium thiosulfate containing 24.8 grams of the salt in one liter:

(3) A solution of potassium iodid containing 12.7 grams of iodin in one liter.

The reaction is represented by the formula

2CuCl₂ + 4KI = Cu₂I₂ + 4KCl + I₂.

The analytical process is carried out as follows: In a 100 cubic centimeter flask are boiled fifty cubic centimeters of the copper solution, ten cubic centimeters of about one-tenth per cent reducing sugar solution are added, the boiling continued for five minutes, the flask filled to the mark with boiling water and its contents filtered. Fifty cubic centimeters of the hot filtrate are cooled, slightly acidified, potassium iodid solution added in slight excess; and the iodin set free determined by titration with sodium thiosulfate. The quantity of iodin obtained corresponds to the unreduced copper remaining after treatment with the reducing sugar. The number of cubic centimeters of thiosulfate used subtracted from twenty-five will give the number of cubic centimeters of the copper solution which would be reduced by five cubic centimeters of the sugar solution used.

Example.—In the proportions given above it was found that eleven cubic centimeters of thiosulfate were required to saturate the iodin set free. Then 25 - 11 = 14 cubic centimeters of copper solution reduced by five cubic centimeters of the sugar solution. Since one cubic centimeter of the copper solution is reduced by 0.0036 gram of dextrose the total dextrose in the five cubic centimeters = 0.0036 × 5 = 0.0180 gram.

The above method does not seem to have any practical advantage over those based on noting the disappearance of the copper and is given only to illustrate the principle of the process. While the titration of the iodin by sodium thiosulfate is easily accomplished in the absence of organic matter, it becomes difficult, as shown by Ewell, when organic matters are present, as they always are in the oxidation of a sugar solution. Ewell has therefore proposed to determine the residual copper by a standard solution of potassium cyanid, but the method has not yet been developed.[104]

GRAVIMETRIC COPPER METHODS.

135. General Principles.—In the preceding pages the principles of the volumetric methods of sugar analysis by means of alkaline copper solution have been set forth. They depend either on the total decomposition of the copper solution employed by the reducing sugar, or else on the collection and titration of the cuprous oxid formed in the reaction. In the gravimetric methods the general principle of the process rests upon the collection of the cuprous oxid formed and its reduction to metallic copper, the weight of which serves as a starting point in the calculations of the weight of reducing sugar, which has been oxidized in the solution.

The factors which affect the weight of copper obtained are essentially those which influence the results in the volumetric method. The composition of the copper solution, the temperature at which the reduction is accomplished, the time of heating, the strength of the sugar solution and the details of the manipulation, all affect more or less the quantity of copper obtained. As in the volumetric method also, the kind of reducing sugar must be taken in consideration, dextrose, levulose, invert sugar, maltose and other sugars having each a definite factor for reduction in given conditions. It follows, therefore, that only those results are of value which are obtained under definite conditions, rigidly controlled.

136. Gravimetric Methods of the Department of Agriculture Laboratory.—The process used in this laboratory is based essentially on the methods of Maercker, Behrend, Morgen, Meissl, Hiller and Allihn.[105] Where dextrose alone is present, the table of factors proposed by Allihn is used and also the copper solution corresponding thereto.

For pure invert sugar, the tables and solutions of Meissl are used. For invert sugar in the presence of sucrose, the table and process proposed by Hiller are used.

Figure 43. Apparatus for the Electrolytic Deposition of Copper.

The reduction of the copper solution and the electrolytic deposition of the copper are accomplished as follows:

The copper and alkali solutions are kept in separate bottles. After mixing the equivalent volume of the two solutions in a beaker, heat is applied and the mixture boiled. To the boiling liquid the proper volume of the cold sugar solution is added. This must always be less than the amount required for complete reduction. The solution is again brought into ebullition and kept boiling exactly two minutes. A two-minute sand glass is conveniently used to determine the time of boiling. At the end of this time an equal volume of freshly boiled cold water is added, and the supernatant liquor at once passed through a gooch under pressure. The residual cuprous oxid is covered with boiling water and washed by decantation until the wash water is no longer alkaline. It is more convenient to wash in such a way that, at the end, the greater part of the cuprous oxid is in the gooch. The felt and cuprous oxid are then returned to the beaker in which the reduction is made. The gooch is moistened with nitric acid to dissolve any adhering oxid and then is washed into the beaker. Enough nitric acid is added to bring all the oxid into solution, an excess being avoided, and a small amount of water added. The mixture is again passed under pressure through a gooch having a thin felt, to remove the asbestos and the filtrate collected in a flask of about 150 cubic centimeters capacity. The washing is continued until the gooch is free of copper, when the volume of the filtrate should be about 100 cubic centimeters. The liquid is transferred to a platinum dish holding about 175 cubic centimeters and the flask washed with about twenty-five cubic centimeters of water. From three to five cubic centimeters of strong sulfuric acid are added and the copper deposited by an electric current.

137. Precipitating the Copper.—When no more nitric acid is used than indicated in the previous paragraph, it will not be necessary to remove it by evaporation. The platinum dishes containing the solutions of the cuprous oxid are arranged as shown in the figure for the precipitation of the copper by the electric current. Each of the supporting stands has its base covered with sheet-copper, on which the platinum dishes rest. The uprights are made of heavy glass rods and carry the supports for the platinum cylinders which dip into the copper solutions. The current used is from the city service and is brought in through the lamp shown at the right of the figure. This current has a voltage of about 120. After passing the lamp it is conducted through the regulator shown at the right, a glass tube closed below by a stopper carrying a piece of platinum foil, and above by one holding a glass tube, in the lower end of which is sealed a piece of sheet platinum connected, through the glass tube, with the lamp. The regulating tube contains dilute sulfuric acid. The strength of current desired is secured by adjusting the movable pole. A battery of this kind easily secures the precipitation of sixteen samples at once, but only twelve are shown in the figure. The practice here is to start the operation at the time of leaving the laboratory in the afternoon. The next morning the deposition of the copper will be found complete. The wiring of the apparatus is shown in the figure. The wire from the regulator is connected with the base of the first stand, and thence passes through the horizontal support to the base of the second, and so on. The return to the lamp is accomplished by means of the upper wire. This plan of arranging the apparatus has been used for two years, and with perfect satisfaction.

Where a street current is not available, the following directions may be followed: Use four gravity cells, such as are employed in telegraphic work, for generating the current. This will be strong enough for one sample and by working longer for two. Connect the platinum dish with the zinc pole of the battery. The current is allowed to pass until all the copper is deposited. Where a larger number of samples is to be treated at once, the size of the battery must be correspondingly increased.

138. Method Used at the Halle Station.—The method used at the Halle station is the same as that originally described by Maercker for dextrose.[106] The copper solution employed is the same as in the allihn method, viz., 34.64 grams of copper sulfate in 500 cubic centimeters, and 173 grams of rochelle salt and 125 grams of potassium hydroxid in the same quantity of water. In a porcelain dish are placed thirty cubic centimeters of copper solution and an equal quantity of the alkali, sixty cubic centimeters of water added and the mixture boiled. To the solution, in lively ebullition, are added twenty-five cubic centimeters of the dextrose solution to be examined which must not contain more than one per cent of sugar. The mixture is again boiled and the separated cuprous oxid immediately poured into the filter and washed with hot water, until the disappearance of an alkaline reaction. For filtering, a glass tube is employed, provided with a platinum disk, and resembling in every respect similar tubes used for the extraction of substances with ether and alcohol. The arrangement of the filtering apparatus is shown in Fig. 44. In the Halle method it is recommended that the tubes be prepared by introducing a platinum cone in place of the platinum disk and filling it with asbestos felt, pressing the felt tightly against the sides of the glass tube and making the asbestos fully one centimeter in thickness. This is a much less convenient method of working than the one described above. After filtration and washing, the cuprous oxid is washed with ether and alcohol and dried for an hour at 110°, and finally reduced to metallic copper in a stream of pure dry hydrogen, heat being applied by means of a small flame. The apparatus for the reduction of the cuprous oxid is shown in Fig. 45. The metallic copper, after cooling and weighing, is dissolved in nitric acid, the tube washed with water, ether and alcohol, and again dried, when it is ready for use a second time. The percentage of dextrose is calculated from the milligrams of copper found by Allihn’s table.

Figure 44. Apparatus for Filtering Copper Suboxid.

Figure 45. Apparatus for Reducing Copper Suboxid.

139. Tables for Use in the Gravimetric Determination of Reducing Sugars.—The value of a table for computing the percentage of a reducing sugar present in a solution, is based on the accuracy with which the directions for the determination are followed. The solution must be of the proper strength and made in the way directed. The degree of dilution prescribed must be scrupulously preserved and the methods of boiling during reduction and washing the reduced copper, followed. The quantity of copper obtained by the use of different alkaline copper solutions and of sugar solutions of a strength different from that allowed by the fixed limits, is not a safe factor for computation. It must be understood, therefore, that in the use of the tables the directions which are given are to be followed in every particular.

140. Allihn’s Gravimetric Method for the Determination of Dextrose.Reagents:

I.   34.639 grams of CuSO₄.5H₂O, dissolved in water and diluted
to half a liter:
II. 173 grams of rochelle salts dissolved in water and diluted
  125 grams of KOH, to half a liter.

Manipulation: Place thirty cubic centimeters of the copper solution (I), thirty cubic centimeters of the alkaline tartrate solution (II), and sixty cubic centimeters of water in a beaker and heat to boiling. Add twenty-five cubic centimeters of the solution of the material to be examined, which must be so prepared as not to contain more than one per cent of dextrose, and boil for two minutes. Filter immediately after adding an equal volume of recently boiled cold water and obtain the weight of copper by one of the gravimetric methods given. The corresponding weight of dextrose is found by the following table:

Allihn’s Table for the
Determination of Dextrose.

  • (A) = Milligrams of copper.
  • (B) = Milligrams of dextrose.
  (A)     (B)     (A)     (B)     (A)     (B)     (A)     (B)     (A)     (B)  
10  6.1 46 23.9  82 41.8 118 60.1 154 78.6
11  6.6 47 24.4  83 42.3 119 60.6 155 79.1
12  7.1 48 24.9  84 42.8 120 61.1 156 79.6
13  7.6 49 25.4  85 43.4 121 61.6 157 80.1
14  8.1 50 25.9  86 43.9 122 62.1 158 80.7
15  8.6 51 26.4  87 44.4 123 62.6 159 81.2
16  9.0 52 26.9  88 44.9 124 63.1 160 81.7
17  9.5 53 27.4  89 45.4 125 63.7 161 82.2
18 10.0 54 27.9  90 45.9 126 64.2 162 82.7
19 10.5 55 28.4  91 46.4 127 64.7 163 83.3
20 11.0 56 28.8  92 46.9 128 65.2 164 83.8
21 11.5 57 29.3  93 47.4 129 65.7 165 84.3
22 12.0 58 29.8  94 47.9 130 66.2 166 84.8
23 12.5 59 30.3  95 48.4 131 66.7 167 85.3
24 13.0 60 30.8  96 48.9 132 67.2 168 85.9
25 13.5 61 31.3  97 49.4 133 67.7 169 86.4
26 14.0 62 31.8  98 49.9 134 68.2 170 86.9
27 14.5 63 32.3  99 50.4 135 68.8 171 87.4
28 15.0 64 32.8 100 50.9 136 69.3 172 87.9
29 15.5 65 33.3 101 51.4 137 69.8 173 88.5
30 16.0 66 33.8 102 51.9 138 70.3 174 89.0
31 16.5 67 34.3 103 52.4 139 70.8 175 89.5
32 17.0 68 34.8 104 52.9 140 71.3 176 90.0
33 17.5 69 35.3 105 53.5 141 71.8 177 90.5
34 18.0 70 35.8 106 54.0 142 72.3 178 91.1
35 18.5 71 36.3 107 54.5 143 72.9 179 91.6
36 18.9 72 36.8 108 55.0 144 73.4 180 92.1
37 19.4 73 37.3 109 55.5 145 73.9 181 92.6
38 19.9 74 37.8 110 56.0 146 74.4 182 93.1
39 20.4 75 38.3 111 56.5 147 74.9 183 93.7
40 20.9 76 38.8 112 57.0 148 75.5 184 94.2
41 21.4 77 39.3 113 57.5 149 76.0 185 94.7
42 21.9 78 39.8 114 58.0 150 76.5 186 95.2
43 22.4 79 40.3 115 58.6 151 77.0 187 95.7
44 22.9 80 40.8 116 59.1 152 77.5 188 96.3
45 23.4 81 41.3 117 59.6 153 78.1 189 96.8
 
  (A)     (B)     (A)     (B)     (A)     (B)     (A)     (B)     (A)     (B)  
190  97.3 233 120.1 276 143.3 319 167.0 362 191.1
191  97.8 234 120.7 277 143.9 320 167.5 363 191.7
192  98.4 235 121.2 278 144.4 321 168.1 364 192.3
193  98.9 236 121.7 279 145.0 322 168.6 365 192.9
194  99.4 237 122.3 280 145.5 323 169.2 366 193.4
195 100.0 238 122.8 281 146.1 324 169.7 367 194.0
196 100.5 239 123.4 282 146.6 325 170.3 368 194.6
197 101.0 240 123.9 283 147.2 326 170.9 369 195.1
198 101.5 241 124.4 284 147.7 327 171.4 370 195.7
199 102.0 242 125.0 285 148.3 328 172.0 371 196.3
200 102.6 243 125.5 286 148.8 329 172.5 372 196.8
201 103.1 244 126.0 287 149.5 330 173.1 373 197.4
202 103.7 245 126.6 288 149.4 331 173.7 374 198.0
203 104.2 246 127.1 289 150.9 332 174.2 375 198.6
204 104.7 247 127.6 290 151.0 333 174.8 376 199.1
205 105.3 248 128.1 291 151.6 334 175.3 377 199.7
206 105.8 249 128.7 292 152.1 335 175.9 378 200.3
207 106.3 250 129.2 293 152.7 336 176.5 379 200.8
208 106.8 251 129.7 294 153.2 337 177.0 380 201.4
209 107.4 252 130.3 295 153.8 338 177.6 381 202.0
210 107.9 253 130.8 296 154.3 339 178.1 382 202.5
211 108.4 254 131.4 297 154.9 340 178.7 383 203.1
212 109.0 255 131.9 298 155.4 341 179.3 384 203.7
213 109.5 256 132.4 299 156.0 342 179.8 385 204.3
214 110.0 257 133.0 300 156.5 343 180.4 386 204.8
215 110.6 258 133.5 301 157.1 344 180.9 387 205.4
216 111.1 259 134.1 302 157.6 345 181.5 388 206.0
217 111.6 260 134.6 303 158.2 346 182.1 389 206.5
218 112.1 261 135.1 304 158.7 347 182.6 390 207.1
219 112.7 262 135.7 305 159.3 348 183.2 391 207.7
220 113.2 263 136.2 306 159.8 349 183.7 392 208.3
221 113.7 264 136.8 307 160.4 350 184.3 393 208.8
222 114.3 265 137.3 308 160.9 351 184.9 394 209.4
223 114.8 266 137.8 309 161.5 352 185.4 395 210.0
224 115.3 267 138.4 310 162.0 353 186.0 396 210.6
225 115.9 268 138.9 311 162.6 354 186.6 397 211.2
226 116.4 269 139.5 312 163.1 355 187.2 398 211.7
227 116.9 270 140.0 313 163.7 356 187.7 399 212.3
228 117.4 271 140.6 314 164.2 357 188.3 400 212.9
229 118.0 272 141.1 315 164.8 358 188.9 401 213.5
230 118.5 273 141.7 316 165.3 359 189.4 402 214.1
231 119.0 274 142.2 317 165.9 360 190.0 403 214.6
232 119.6 275 142.8 318 166.4 361 190.6 404 215.2
 
  (A)     (B)     (A)     (B)     (A)     (B)     (A)     (B)     (A)     (B)  
405 215.8 417 222.8 429 229.8 441 236.9 453 244.0
406 216.4 418 223.3 430 230.4 442 237.5 454 244.6
407 217.0 419 223.9 431 231.0 443 238.1 455 245.2
408 217.5 420 224.5 432 231.6 444 238.7 456 245.7
409 218.1 421 225.1 433 232.2 445 239.3 457 246.3
410 218.7 422 225.7 434 232.8 446 239.8 458 246.9
411 219.3 423 226.3 435 233.4 447 240.4 459 247.5
412 219.9 424 226.9 436 233.9 448 241.0 460 248.1
413 220.4 425 227.5 437 234.5 449 241.6 461 248.7
414 221.0 426 228.0 438 235.1 450 242.2 462 249.3
415 221.6 427 228.6 439 235.7 451 242.8 463 249.9
416 222.2 428 229.2 440 236.3 452 243.4    

141. Meissl’s Table for Invert Sugar.—Invert sugar is usually the product of the hydrolysis of sucrose. The following table is to be used when the hydrolysis is complete, i. e., when no sucrose is left in the solution. The solution of copper sulfate and of the alkaline tartrate are made up as follows: 34.64 grams of copper sulfate in half a liter, and 173 grams of rochelle salt and 51.6 grams sodium hydroxid in the same volume. The quantity of sugar solution used must not contain more than 245 nor less than ninety milligrams of invert sugar.

In the determination twenty-five cubic centimeters of the copper solution and an equal volume of the alkaline tartrate are mixed and boiled, the proper amount of sugar solution added to secure a quantity of invertose within the limits named, the volume completed to 100 cubic centimeters with boiling water, and the mixture kept in lively ebullition for two minutes. An equal volume of recently boiled cold water is added and the cuprous oxid at once separated by filtration on asbestos under pressure, and washed free of alkali with boiling water. The metallic copper is secured by one of the methods already described.

Table for Invert Sugar by Meissl and Wien.[107]

  • (A) = Milligrams of copper.
  • (B) = Milligrams of invert sugar.
  (A)     (B)      (A)     (B)      (A)     (B)      (A)     (B)   
 90 46.9 133 69.7 176  93.0 219 117.0
 91 47.4 134 70.3 177  93.5 220 117.5
 92 47.9 135 70.8 178  94.1 221 118.1
 93 48.4 136 71.3 179  94.6 222 118.7
 94 48.9 137 71.9 180  95.2 223 119.2
 95 49.5 138 72.4 181  95.7 224 119.8
 96 50.0 139 72.9 182  96.2 225 120.4
 97 50.5 140 73.5 183  96.8 226 120.9
 98 51.1 141 74.0 184  97.3 227 121.5
 99 51.6 142 74.5 185  97.8 228 122.1
100 52.1 143 75.1 186  98.4 229 122.6
101 52.7 144 75.6 187  99.0 230 123.2
102 53.2 145 76.1 188  99.5 231 123.8
103 53.7 146 76.7 189 100.1 232 124.3
104 54.3 147 77.2 190 100.6 233 124.9
105 54.8 148 77.8 191 101.2 234 125.5
106 55.3 149 78.3 192 101.7 235 126.0
107 55.9 150 78.9 193 102.3 236 126.6
108 56.4 151 79.4 194 102.9 237 127.2
109 56.9 152 80.0 195 103.4 238 127.8
110 57.5 153 80.5 196 104.0 239 128.3
111 58.0 154 81.0 197 104.6 240 128.9
112 58.5 155 81.6 198 105.1 241 129.5
113 59.1 156 82.1 199 105.7 242 130.0
114 59.6 157 82.7 200 106.3 243 130.6
115 60.1 158 83.2 201 106.8 244 131.2
116 60.7 159 83.8 202 107.4 245 131.8
117 61.2 160 84.3 203 107.9 246 132.3
118 61.7 161 84.8 204 108.5 247 132.9
119 62.3 162 85.4 205 109.1 248 133.5
120 62.8 163 85.9 206 109.6 249 134.1
121 63.3 164 86.5 207 110.2 250 134.6
122 63.9 165 87.0 208 110.8 251 135.2
123 64.4 166 87.6 209 111.3 252 135.8
124 64.9 167 88.1 210 111.9 253 136.3
125 65.5 168 88.6 211 112.5 254 136.9
126 66.0 169 89.2 212 113.0 255 137.5
127 66.5 170 89.7 213 113.6 256 138.1
128 67.1 171 90.3 214 114.2 257 138.6
129 67.6 172 90.8 215 114.7 258 139.2
130 68.1 173 91.4 216 115.3 259 139.8
131 68.7 174 91.9 217 115.8 260 140.4
132 69.2 175 92.4 218 116.4 261 140.9
 
  (A)     (B)     (A)     (B)     (A)     (B)     (A)     (B)  
262 141.5 305 166.8 348 192.6 391 219.3
263 142.1 306 167.3 349 193.2 392 219.9
264 142.7 307 167.9 350 193.8 393 220.5
265 143.2 308 168.5 351 194.4 394 221.2
266 143.8 309 169.1 352 195.0 395 221.8
267 144.4 310 169.7 353 195.6 396 222.4
268 144.9 311 170.3 354 196.2 397 223.1
269 145.5 312 170.9 355 196.8 398 223.7
270 146.1 313 171.5 356 197.4 399 224.3
271 146.7 314 172.1 357 198.0 400 224.9
272 147.2 315 172.7 358 198.6 401 225.7
273 147.8 316 173.3 359 199.2 402 226.4
274 148.4 317 173.9 360 199.8 403 227.1
275 149.0 318 174.5 361 200.4 404 227.8
276 149.5 319 175.1 362 201.1 405 228.6
277 150.1 320 175.6 363 201.7 406 229.3
278 150.7 321 176.2 364 202.3 407 230.0
279 151.3 322 176.8 365 203.0 408 230.7
280 151.9 323 177.4 366 203.6 409 231.4
281 152.5 324 178.0 367 204.2 410 232.1
282 153.1 325 178.6 368 204.8 411 232.8
283 153.7 326 179.2 369 205.5 412 233.5
284 154.3 327 178.8 370 206.1 413 234.3
285 154.9 328 180.4 371 206.7 414 235.0
286 155.5 329 181.0 372 207.3 415 235.7
287 156.1 330 181.6 373 208.0 416 236.4
288 156.7 331 182.2 374 208.6 417 237.1
289 157.2 332 182.8 375 209.2 418 237.8
290 157.8 333 183.5 376 209.9 419 238.5
291 158.4 334 184.1 377 210.5 420 239.2
292 159.0 335 184.7 378 211.1 421 239.9
293 159.6 336 185.4 379 211.7 422 240.6
294 160.2 337 186.0 380 212.4 423 241.3
295 160.8 338 186.6 381 213.0 424 242.0
296 161.4 339 187.2 382 213.6 425 242.7
297 162.0 340 187.8 383 214.3 426 243.4
298 162.6 341 188.4 384 214.9 427 244.1
299 163.2 342 189.0 385 215.5 428 244.9
300 163.8 343 189.6 386 216.1 429 245.6
301 164.4 344 190.2 387 216.8 430 246.3
302 165.0 345 190.8 388 217.4    
303 165.6 346 191.4 389 218.0    
304 166.2 347 192.0 390 218.7    

142. Table for the Determination of Invert Sugar (Reducing Sugars) in the Presence of Sucrose.—The method adopted by the Association of Official Agricultural Chemists is essentially that proposed by Meissl and Hiller.[108] Prepare a solution of the material to be examined in such a manner that it contains twenty grams of the mixed sugars in one hundred cubic centimeters, after clarification and the removal of the excess of lead. Prepare a series of solutions in large test tubes by adding one, two, three, four, five etc. cubic centimeters of this solution to each tube successively. Add five cubic centimeters of the mixed copper reagent to each, heat to boiling, boil two minutes and filter. Note the volume of sugar solution which gives the filtrate lightest in tint, but still distinctly blue. Place twenty times this volume of the sugar solution in a 100 cubic centimeter flask, dilute to the mark, and mix well. Use fifty cubic centimeters of the solution for the determination, which is conducted as already described, until the weight of copper is obtained. For the calculation of the results use the following formulas and table of factors of Meissl and Hiller:[109]

Let Cu = the weight of the copper obtained;
P = the polarization of the sample;
W = the weight of the sample in the fifty cubic
  centimeters of the solution used for determination;
F = the factor obtained from the table for conversion
  of copper to invert sugar;
 Cu  = approximate absolute weight of invert sugar = Z;
2
100    
Z  × ——  =   approximate per cent of invert sugar = y;
W     
 100P  = R, relative number for sucrose;
P + y
100 - R = I, relative number for invert sugar;
 Cu  = per cent of invert sugar.
W

Z indicates the vertical column, and the ratio of R to I, the horizontal column of the table, which are to be used for the purpose of finding the factor (F) for calculating copper to invert sugar.

Example:—The polarization of a sugar is 86.4, and 3.256 grams of it (W) are equivalent to 0.290 gram of copper. Then:

Cu   =   0.290   =  0.145 = Z
2 2
Z ×   100   = 0.145 ×   100   = 4.45 = y
W 3.256
100P   =   8640   =  95.1 = R
P + y 86.4 + 4.45

100 - R = 100 - 95.1 = 4.9 = I

R : I = 95.1 : 4.9

By consulting the table it will be seen that the vertical column headed I = 150 is nearest to Z, 145, the horizontal column headed 95: 5 is nearest to the ratio of R to I, 95.1: 4.9. Where these columns meet we find the factor 51.2, which enters into the final calculation:

CuF   =   .290 × 51.2   =  4.56 the true per cent of invert sugar.
W 3.256

Meissl and Hiller’s Factors for the Determination of
More Than One Per Cent of Invert Sugar.

Ratio of
sucrose
to invert
sugar =
Approximate absolute weight of invert sugar = Z.
I = 200 I = 175 I = 150 I = 125 I = 100 I = 75 I = 50
R : I. mg. mg. mg. mg. mg. mg. mg.
  0 : 100 56.4 55.4 54.5 53.8 53.2 53.0 53.0
10 : 90 56.3 55.3 54.4 53.8 53.2 52.9 52.9
20 : 80 56.2 55.2 54.3 53.7 53.2 52.7 52.7
30 : 70 56.1 55.1 54.2 53.7 53.2 52.6 52.6
40 : 60 55.9 55.0 54.1 53.6 53.1 52.5 52.4
50 : 50 55.7 54.9 54.0 53.5 53.1 52.3 52.2
60 : 40 55.6 54.7 53.8 53.2 52.8 52.1 51.9
70 : 30 55.5 54.5 53.5 52.9 52.5 51.9 51.6
80 : 20 55.4 54.3 53.3 52.7 52.2 51.7 51.3
90 : 10 54.6 53.6 53.1 52.6 52.1 51.6 51.2
91 : 9  54.1 53.6 52.6 52.1 51.6 51.2 50.7
92 : 8  53.6 53.1 52.1 51.6 51.2 50.7 50.3
93 : 7  53.6 53.1 52.1 51.2 50.7 50.3 49.8
94 : 6  53.1 52.6 51.6 50.7 50.3 49.8 48.9
95 : 5  52.6 52.1 51.2 50.3 49.4 48.9 48.5
96 : 4  52.1 51.2 50.7 49.8 48.9 47.7 46.9
97 : 3  50.7 50.3 49.8 48.9 47.7 46.2 45.1
98 : 2  49.9 48.9 48.5 47.3 45.8 43.3 40.0
99 : 1  47.7 47.3 46.5 45.1 43.3 41.2 38.1

143. Table for the Estimation of Milk Sugar.—The solutions to be used for this table are the same as those employed in the preceding table for the estimation of invert sugar. The milk sugar is supposed to be in a pure form in solution before beginning the analysis. The method to be employed for milk will be given in the part devoted to dairy products.

In the conduct of the work twenty-five cubic centimeters of the copper solution are mixed with an equal quantity of the alkaline tartrate mixture, and from twenty to one hundred cubic centimeters of the sugar solution added, according to its concentration. This solution should not contain less than seventy nor more than 306 milligrams of lactose. The volume is completed to 150 cubic centimeters with boiling water and kept in lively ebullition for six minutes. The rest of the operation is conducted in the manner already described. From the weight of copper obtained the quantity of milk sugar is determined by inspecting the table. It is recommended to use such a weight of milk sugar as will give about 200 milligrams of copper.

Table for Determining Milk Sugar.

  • (A) = Milligrams of copper.
  • (B) = Milligrams of milk sugar.
  (A)       (B)     (A)       (B)     (A)     (B)      (A)     (B)   
100  71.6 120  86.4 140 101.3 160 116.4
101  72.4 121  87.2 141 102.0 161 117.1
102  73.1 122  87.9 142 102.8 162 117.9
103  73.8 123  88.7 143 103.5 163 118.6
104  74.6 124  89.4 144 104.3 164 119.4
105  75.3 125  90.1 145 105.1 165 120.2
106  76.1 126  90.9 146 105.8 166 120.9
107  76.8 127  91.6 147 106.6 167 121.7
108  77.6 128  92.4 148 107.3 168 122.4
109  78.3 129  93.1 149 108.1 169 123.2
110  79.0 130  93.8 150 108.8 170 123.9
111  79.8 131  94.6 151 109.6 171 124.7
112  80.5 132  95.3 152 110.3 172 125.5
113  81.3 133  96.1 153 111.1 173 126.2
114  82.0 134  96.9 154 111.9 174 127.0
115  82.7 135  97.6 155 112.6 175 127.8
116  83.5 136  98.3 156 113.4 176 128.5
117  84.2 137  99.1 157 114.1 177 129.3
118  85.0 138  99.8 158 114.9 178 130.1
119  85.7 139 100.5 159 115.6 179 130.8
 
  (A)     (B)     (A)     (B)     (A)     (B)     (A)     (B)  
180 131.6 223 164.2 266 197.2 309 231.4
181 132.4 224 164.9 267 198.0 310 232.2
182 133.1 225 165.7 268 198.8 311 232.9
183 133.9 226 166.4 269 199.5 312 233.7
184 134.7 227 167.2 270 200.3 313 234.5
185 135.4 228 167.9 271 201.1 314 235.3
186 136.2 229 168.6 272 201.9 315 236.1
187 137.0 230 169.4 273 202.7 316 236.8
188 137.7 231 170.1 274 203.5 317 237.6
189 138.5 232 170.9 275 204.3 318 238.4
190 139.3 233 171.6 276 205.1 319 239.2
191 140.0 234 172.4 277 205.9 320 240.0
192 140.8 235 173.1 278 206.7 321 240.7
193 141.6 236 173.9 279 207.5 322 241.5
194 142.3 237 174.6 280 208.3 323 242.3
195 143.1 238 175.4 281 209.1 324 243.1
196 143.9 239 176.2 282 209.9 325 243.9
197 144.6 240 176.9 283 210.7 326 244.6
198 145.4 241 177.7 284 211.5 327 245.4
199 146.2 242 178.5 285 212.3 328 246.2
200 146.9 243 179.3 286 213.1 329 247.0
201 147.7 244 180.1 287 213.9 330 247.7
202 148.5 245 180.8 288 214.7 331 248.5
203 149.2 246 181.6 289 215.5 332 249.2
204 150.0 247 182.4 290 216.3 333 250.0
205 150.7 248 183.2 291 217.1 334 250.8
206 151.5 249 184.0 292 217.9 335 251.6
207 152.2 250 184.8 293 218.7 336 252.5
208 153.0 251 185.5 294 219.5 337 253.3
209 153.7 252 186.3 295 220.3 338 254.1
210 154.5 253 187.1 296 221.1 339 254.9
211 155.2 254 187.9 297 221.9 340 255.7
212 156.0 255 188.7 298 222.7 341 256.5
213 156.7 256 189.4 299 223.5 342 257.4
214 157.5 257 190.2 300 224.4 343 258.2
215 158.2 258 191.0 301 225.2 344 259.0
216 159.0 259 191.8 302 225.9 345 259.8
217 159.7 260 192.5 303 226.7 346 260.6
218 160.4 261 193.3 304 227.5 347 261.4
219 161.2 262 194.1 305 228.3 348 262.3
220 161.9 263 194.9 306 229.1 349 263.1
221 162.7 264 195.7 307 229.8 350 263.9
222 163.4 265 196.4 308 230.6 351 264.7
 
  (A)     (B)     (A)     (B)     (A)     (B)     (A)     (B)  
352 265.5 365 276.2 377 286.5 389 296.8
353 266.3 366 277.1 378 287.4 390 297.7
354 267.2 367 277.9 379 288.2 391 298.5
355 268.0 368 278.8 380 289.1 392 299.4
356 268.8 369 279.6 381 289.9 393 300.3
357 269.6 370 280.5 382 290.8 394 301.1
358 270.4 371 281.4 383 291.7 395 302.0
359 271.2 372 282.2 384 292.5 396 302.8
360 272.1 373 283.1 385 293.4 397 303.7
361 272.9 374 283.9 386 294.2 398 304.6
362 273.7 375 284.8 387 295.1 399 305.4
363 274.5 376 285.7 388 296.0 400 306.3
364 275.3