ANALYTICAL EDITION
March 15, 1942 r-
STEEL TABLE111. ANALYSISOF COPPER-NICKEL Thiosulfate Method (3)
Cu
Sample
S i
Proposed Method Manufacturers Cu Si Cu Xi
1 Bureau of Standards No. 106 2 Low chromium 3 Low chromium 4
c /u
/c
%
B
R
%
0.13
,, ,
0.14
.,
0:ZO
.. ..
0:26 1.07
1:73
5
1.12
..
6
1.16
..
7 18-8
,.
1:OS
..
..
..
0.20 0.13
1.10 1.0s 1.10 1.10 1.14 0.15
.
1:70
..
..
..
..
1.62 8.50
1.12
1.56
..
8.56
amounts of ferric ion complex and ammonium ions, whereas in the proposed method room temperature prevails and the order of the reaction must be: (1) reduction of all hexavalent to trivalent chromium, probably by the electrolytic production of ferrous ion (which would reduce dichromic acid), (2) complete reduction of ferric to ferrous ions in the immediate vicinity of the cathode, and (3) complete deposition of the copper. Stirring the liquid will prevent formation of the copper plate, or will redissolve it after it has formed. Using a potential source of 4 volts, the actual potential across the electrodes of an agitated solution is about 1.6 volts, while the copper deposits in an unagitated solution only when the voltage drop is greater than 2 volts. Copper is deposited from electrolytes that show between 0.6 and 0.95 gram of ferrous ion. The as-
237
sumption is that, in an unstirred solution a protective coating of hydrogen gas forms and serves as a cause for overvoltage to permit deposition of copper and as a blanket to prevent resolution by the electrolyte. When phosphoric acid is present, copper begins to deposit sooner than in its absence. Manganese dioxide does not appear a t the anode. I n order t o procure bright adherent plates, if the copper is below 0.010 gram the voltage source (impressed voltage) must not be greater than 4 volts. Ni-Resist steels (6 per cent copper) give bright copper plates, but the results are about 0.02 per cent higher, on the general run of samples, than those obtained by the thiosulfate method (3). Seither manganese nor nickel has been detected in the copper plates. Nickel is easily determined in the electrolyte after oxidation of ferrous ion by persulfate or permanganate. Excess persulfate is destroyed by boiling, and even excess permanganate is avoided by ordinary precautions or additon of a sulfite. The paper neither affirms nor disaffirms the work of Frediani and Hale, since there are no points of common interest.
Literature Cited (1) Frediani, H.A,, and Hale, C. H., IND.ENG.CHBJM., ANAL.ED., 12, 736 (1940). (2) Lundell, G . E. F., and Hoffman, J. I., "Outlines of Methods of Chemical Analysis", p. 47, New York, John Wiley & Sons, 1938. (3) Silverman, Louis, IND. ENG.CHEX.,ANAL.ED.,12, 344 (1940). (4) Silverman, Louis, and Gates, O., Ibid., 12, 518 (1940).
Determination of Alcohol by Volume in Distilled Liquors Sources of Error L. C. CARTWRIGHT, Foster Dee h e l l , Inc., Brooklyn, N. Y.
P
ERSISTENT recurrence of relatively small but significant discrepancies between the results obtained in different laboratories in the determination of alcohol by volume on duplicate samples of distilled liquors led to an investigation of the A. 0. A. C. official method for alcohol by volume (1, p. 172). This investigation disclosed a source of error inherent in the method, exclusive of any experimental errors. The A. 0. A. C. official method rovides that the specific gravity of a distilled liquor shall be getermined in air at 20/20° C. Alcohol by weight is determined by weighing 20 t o 25 grams of sample, diluting with 100 nil. of water, distilling nearly 100 ml., weighing the distillate, determining the specific gravity of distillate, at room temperature if desired, obtaining the corresponding percentage of alcohol by weight from the proper A. 0. A. C. tables, multiplying this figure by weight of distillate, and dividing by weight of Sam le taken. Alcohol by vol%me is determined by either of two methods. In Method I, sample and distillate are treated as described above, the percentage of alcohol by volume corresponding to the specific gravity of the distillate is obtained from the proper A. 0. A. C. table. the volumes of the samde and distillate are calculated from their'respective weights and specific gravities, and the percentage of alcohol by volume in the distillate is multiplied by the volume of the distillate and divided by the volume of the sample to obtain the percentage of alcohol by volume in the original sample. In Method 11, a 25-ml. sample is measured at room temperature and the distillate is made t o a volume of 100 ml. at the same temperature. The specific gravity of the distillate is determined at room temperature and the corresponding percentage of alcohol by volume is multiplied by 4 to obtain the percentage of alcohol by volume in the original sample.
The percentage of alcohol by volume in any mixture of ethyl alcohol and water varies with the temperature; therefore the temperature a t which a given mixture will have a stated percentage of alcohol by volume must be specified. The generally accepted standard of temperature for alcoholic concentration by volume is 60" F. or 15.56' C., and the A. 0. A. C. tables give percentages of alcohol by volume at this temperature. However, the ratio of the volumes of definite weights of any two aqueous solutions of ethyl alcohol of different alcoholic concentrations varies with temperature, and herein lies the inherent source of error in the A. 0. A. C. official method for alcohol by volume. I n both Methods I and I1 the volumes of the sample and of the distillate may be determined a t temperatures other than 15.56" C. Yet the true percentage by volume at 60' F. of ethyl alcohol in the distillate is multiplied by the inverse ratio of these volumes to obtain the percentage by volume at 60" F. of ethyl alcohol in the sample. The result is in error by an amount depending . upon the alcoholic concentrations of the sample and the distillate and the temperature at which the volumes of the sample and the distillate are determined. The calculated data presented in Tables I1 and 111 show that this inherent error is very substantial under conditions often prevailing in the determination of alcohol by volume by the A. 0. A. C. official method. I n order to show the magnitude of the inherent error over a wide range of conditions cdculations were made for a series of
INDUSTRIAL AND ENGINEERING CHEMISTRY
238
TARLEI. APPARENTSPECIFICGRAVITIESCORRESPOXDING TO PERCEXTAGES OF ETHYL ALCOHOL
10.000 L'0,ooo 30.000 40.000 50.000 60,000 i o . 000 80.000
12.392 24.472 36.181 47.326 57.830 67.689 76,909 85,458
0.98384 0.97136 0.95740 0,93925 0.91810 0.89550 0.81208 0,84787
0.98359 0,97032 0.95546 0.93677 0.91535 0.89258 0.86904 0.84476
0 98330 0,96920 0.95340 0.93413 0.91240 0.88948 0.86578 0.84138
0,98298 0.96810 0,95147 0.93165 0.90963 0.88648 0.86265 0.83817
0.98267 0,96704 0.9496% 0.92929 0,90696 0.88363 0.85965 0.83506
alcoholic concentrations of original sample ranging from 10 to 80 per cent by weight. The A. 0. A. C. tables used were Kos. 19 and 21 (1, XLIII). The \ :dues in the first column of Table I of the present paper, representing percentages of ethyl alcohol by weight in original samples, xere chosen arbitrarily as a basis of, calculation. The corresponding percentages by volume at 60 F. in the second column of Table I were obtained by interpolation from (1, Table 21, XLIII), and the corresponding apparent specific gravities in the remaining columns of Table I were obtained by interpolation from ( I , Table 19, XLIII). The values in the second column of Table I1 for weight of sample distilled were chosen arbitrarily. However, those for each alcoholic concentration of original sample include the values of 20 and 25 grams, the limits of sample weight given in the A. 0. A. C. official method, and extend upward to yield alcoholic concentrations of distillate ranging up to 25 per cent by weight and down\yard in the case of higher original alcoholic concentrations. The values in the third column of Table 11represent the calculated alcoholic concentration by weight in 100 grams of distillate
20
30
40
50
60
70
80
and were obtained by multiplying the values in the second column by the values in the first column and dividing by 100. The corresponding percentages by volume at 60" F. in the fourth column were obtained by interpolation from (1,Table 21, XLIII). The corresponding apparent specific gravities in columns 5 t o 9, inclusive, were obtained by interpolation from (1, Table 19, XLIII). The values in columns 10 to 14, inclusive, were calculated, as directed (1,XT'I, 4) by calculating the volumes of sample and distillate at each temperature from the corresponding apparent specific gravities, multiplying the values in column 4 by the volume of distillate at each temperature, and dividing by the volume of sample at the same temperature. The amounts by which these calculated values differ from the true percentages by volume at 60" F. are given in columns 6 to 10, inclusive, of Table 111. All the values in column 6 of Table I11 should, of course, be zero. The amounts by which these values differ from zero merely indicate the limits of accuracy of interpolations and logarithmic calculations involved. The largest of these differences is only 0.018 per cent by volume at 60" F., or 0.036 proof, and most of them are much smaller. Errors of such magnitude would not ordinarily be of any significance. However, as soon as the working temperature is raised to 20" or 25" C. or higher, with original alcoholic concentrations of 20 per cent by weight or higher and sample weights of 20 to 25 grams, the inherent error begins to be significant. For example, with 20 per cent alcohol by weight in the original sample, a 20-gram sample and 25' C. working temperature, the error is 0.055 per cent by volume, or 0.11 proof; with 40 per cent alcohol by weight in the original, a 20-gram sample and 25' C. temperature, the error is 0.248 per cent by volume, or 0.496 proof; and with 80 per cent alcohol by weight in the original, a 15-gram sample and 35" C. temperature, the error reaches a value of 1.16 per cent by volume, or 2.32 proof. The most obvious, and, whenever feasible, the easiest way to avoid this error is t o work at a temperature of 15.56" C. However, when the dew point is above 15.56" C., it is difficult to determine specific gravities accurately by pycnometer at that temperature.
CALCULATED D.4TA ON DISTILLATE FROM SAIIPLES OF ORIGISAL AQUEOUS SOLUTIONS CONT.4INING ETHYL ALCOHOL Percentage b y Volume a t 60' F. of E t h y l Alcohol Distillate Bulked with Water t o 100 Grams----in Original, Calculated from Apparent Specific Percentage of n-t of Gravlties of Original and Distillate ..ipparpnt Specific Gravities----E t h y l .ilcohol Sample 15 5 6 , 25 35 35 BY BY volume U O 2 0 0~ 20 c. ,22 5j O C . 30 Lj.56 %OC. %OC. Taken, 30 3 j e. wt. a t 60' F. 15.56 Grams 12.385 12.382 12 378 12.374 0.99623 12,388 0.99625 0.99629 0.99627 0,99620 2.0 2.509 20 12.392 12.388 12.384 12.381 0.99531 12,395 0.99534 0.99536 0.99538 0.99539 2.5 3.135 25 12.394 12.391 12.388 12.385 12.382 0.99098 0,99090 0.99112 0.99106 0,99118 5.0 6.243 50 1 2 , 3 9 1 12.390 12.388 12.386 12.385 0.98675 0.98693 0.98710 0.98726 0.98739 7.5 9.327 75 12.392 12.392 12.392 12.392 12.392 0.98267 0.98298 0.98330 0.98359 0.98384 10.0 12.392 100 12.393 12.396 12.398 12.400 12.402 0,97871 0.97919 0.97966 0,98012 0.98056 12.5 15.440 125 24.444 24.417 24,470 24.391 24.366 0.99261 0,99277 0,99273 0,99267 0.99281 4.0 5.002 20 24.448 24.421 24.473 24.396 24.371 0,99098 0,99090 0.99106 0.99112 0,99118 5.0 6.243 25 24,447 24,423 24,470 24,400 24,379 0.98593 0.98615 0.98634 0.98651 0.98666 8.0 9.942 40 24.421 24.406 24,472 2 4 , 4 5 6 24.439 0,98081 0,98037 0,97994 0.97950 0,98120 12.0 14.832 60 24.453 24.463 24.444 N .436 24.472 0.97335 0,97480 0.97408 0.97556 0,97624 16.0 19.676 80 24.472 24.472 24.472 24.472 24,472 0,96704 0.96810 0.96920 0.97032 0.97136 20.0 24.472 100 36.177 36.107 36.033 35.963 35.899 0.98934 0.98922 0.98945 0.98954 0.98962 6.0 7.479 20 36,076 36.175 36.106 35.967 35.904 0.98963 0.98675 0.98710 0.98726 0.98739 7.5 9.327 25 36.043 36.178 36.112 35.978 3.5.919 0.98455 0.98429 0.98479 0.98503 0.98523 9.0 11.169 30 36.122 36.002 35.949 36.062 36.180 0.97994 0.97960 0.98081 0.98037 0.98120 12.0 14.832 40 36.138 36.054 36.018 36.095 36.179 0.97114 0.97024 0.97204 0.97297 0.97384 18.0 22,080 60 36.162 36.122 36.105 36.182 36.142 0.96181 0.96041 0.96325 0.96477 0.96620 24.0 29.212 80 47.203 47.078 46.963 46.854 47.321 0.98615 0.98593 0.98634 0.98651 0.98666 8.0 9.942 20 47.209 46.980 47.322 47.089 46.876 0.98298 0.98267 0.98330 0.98359 0.98384 10.0 12.392 25 47.109 47,326 47.220 47.004 46.906 0.97994 0.97950 0.98081 0.98037 0.98120 12.0 14.832 30 47.137 47.048 47,326 47.235 46.964 0.97408 0.97335 0.97480 0.97556 0.97624 16.0 19.676 40 47.251 47,172 47.101 47,326 47.033 0.96810 0.96704 0.97032 0.96920 0.97136 20.0 24.472 50 47.273 47.215 47.161 47.328 47.110 0.96181 0.96041 0.96325 0.96477 0.96620 24.0 29.212 60 57.650 57.475 57.310 57.151 57.811 0.98693 0.98675 0.98710 0.98726 0.98739 7.5 9.327 15 57.661 57.493 57.336 57.187 57.819 0.98298 0.98267 0.98330 0.98359 0.98384 1 0 . 0 12.392 20 57.678 57.521 57.374 57.233 57.827 0.97919 0.97871 0.97966 0.98012 0.98056 12.5 15.440 25 57.688 57.542 57.406 57.274 57.826 0.97551 0.97488 0.97683 0.97617 0.97744 15.0 18.469 30 57.713 57.596 57.485 57.379 57.826 0.96810 0.96704 0.96920 0.97032 0.97136 20.0 24.472 40 57,744 57.657 57.572 57.492 67.828 0.96018 0.95871 0.96172 0.96334 0.96485 25.0 30.386 50 67.471 67.251 67.043 66.845 67,679 0.98455 0.98429 0.98479 0.98503 0,98523 9.0 11.169 15 67,283 67.086 66.902 67.683 67.489 0.97994 0.97950 0,98081 0.98037 0.98120 12.0 14.832 20 67.314 67.134 66.961 67.684 67.505 0.97551 0.97488 0.97617 0.97683 0.97744 15.0 18.469 25 67.347 67.520 67.185 67.030 67.681 0.97114 0.97024 0.96297 0.97204 0,97384 18.0 22.080 30 67.388 67.541 67.247 67.107 67.682 0.96655 0.96543 0.96774 0.96895 0.97010 21.0 25.662 35 67.311 67.192 67.435 67.566 67.688 0.96181 0.96041 0.96325 0.96477 0.96620 24.0 29.212 40 76.143 75.909 76.648 76.390 76.891 0.98076 0,98155 0.98116 0.98190 0.98224 11.2 1 3 857 16 76.198 75.976 76.670 76.429 76.897 0.97698 0.97641 0.97755 0.97813 0.97866 14.0 17.259 20 76.251 76.047 76,689 76,465 76.896 0.97213 0.97290 0,97453 0.97370 0,97529 1 6 . 8 20.639 24 76.314 76.128 76.710 76.507 76.898 0.96871 0.96769 0.96977 0,97085 0.97186 1 9 . 6 23.995 28 76.214 7 6 , 5 5 3 76.378 76.731 76.899 0.96437 0.96310 0.96566 0.96704 0.96831 22.4 27.323 32 76.299 76,600 76.446 76.756 76.902 0.95984 0.95836 0.96140 0.96305 0.96458 25.2 30.021 36 84.300 84.862 84.575 85.163 85,443 0.97994 0.97950 0.98037 0.98081 0.98120 12.0 14.832 15 84.354 84.888 84.617 85.175 85.440 0.97640 0.97580 0.97761 0.97700 0.97817 14.4 17.743 18 84.424 84.928 84.672 85,194 85.441 0.97290 0.97213 0.97370 0.97453 0.97529 16.8 20.639 21 84.733 84.502 84.964 85.213 85.442 0.96932 0.96833 0.97139 0.97034 0.97236 19.2 23.517 24 84.578 85.002 84.791 85.233 85.441 0.96562 0.96444 0.96686 0.96814 0.96934 21.6 26.374 27 85.859 84.666 85.260 85.054 85.448 0.96041 0.96325 0.96181 0.96477 0.96620 24.0 29.212 30
TABLE 11. Ethyl Alc,l>h,,l In Original, 70b y W t . 10
Vol. 14, No. 3
-
-------
c.
c.
got.
ET.
March 15, 1942
ANALYTICAL EDITION
239
With relatively low alcoholic concentration T.4BLE 111. TABLE O F CORRECTIONS of the original sample, it is feasible to use much (To be added t o percentages b y volume a t 60' F. of ethyl alcohol in original samples ah dcterlarger sample weights than 20 to 25 grams, thus mined b y distillation of various weights of samples t o give 100 grams of distillate and calcuminimizing the error. This method is limited lation from apparent specific gravities of originals and distillates a t various temperatures) Percentage of Percentage of in its application, however, by the danger of E t h y l Alcohol reaching a point where not all of the alcohol mill Weight " , h & ~ ~ & ~ ~ lCorrection t o Be Added to Percentage b y Vulume in Original a t GOo F. of E t h y l dlsohol in Original a s Deterof B~ BY be distilled over in 100 grams of distillate. volume mined a t volume Sample By at Taken, BY at 2 0 0 ~ . c, The author has not investigated the maximum wt. 60' F. 15.56 ' 20 wt. 60' F. Grams alcoholic concentration of distillate that will 0.004 0.007 0.010 0.014 0.018 2.0 2.509 10 12.392 20 0.000 0.004 0.008 0.011 25 2.5 3.136 -0,003 permit substantially complete recovery of al0.007 0.010 0.001 0.004 5.0 6.243 -0,002 50 cohol from the original sample, but it seems 0.006 0.007 0.001 0.002 0.004 7.5 9.327 75 100 10.0 12.392 0.000 0.000 0.000 0.000 0.000 probable that this should not exceed 20 per cent 125 12.5 15,440 -0,001 -0.004 - 0 . 0 0 6 -0,008 -0.010 4.0 5.002 0.002 0.028 0.055 0.081 0.106 by weight. 20 20 24.472 5.0 G.243 -0,001 0.024 0.051 0.076 0.101 25 The methods of calculation used in this paper 40 8.0 9.942 0.002 0.025 0.040 0.072 0.093 0 , 0 0 0 0.016 0.033 0.051 0.000 12.0 14.832 60 permit calculation of and correction for the 0.000 0.009 0.019 0.025 0.080 16.0 19.676 80 0.000 0.000 0.000 0.000 0.000 error due to different temperature coefficients 20.0 24.472 100 0.282 7.479 0,004 0,074 0.148 0.218 20 6.0 30 36.181 of expansion of sample and distillate for any 0.277 0.006 0,075 0.145 0.214 7.5 9.327 25 0.202 0,003 0.069 0.138 0.203 9.0 11.169 30 specific conditions of alcoholic concentrations 0.179 0.232 0,059 0.119 12.0 14.832 0.001 40 of sample and distillate and working tempera0.127 0.16:1 0.043 0,002 0.086 60 18.0 22.080 0.076 24.0 29.212 -0.001 0,019 0,039 0.059 80 ture, assuming only that the temperature coeffi0.368 0,472 0,123 0.248 20 8.0 0 , 0 0 5 9.942 40 47.326 cient of expansion of the original sample does 0.346 0.460 0,237 0.117 10.0 12.392 0.004 25 0.322 0.420 0.217 0.106 12.0 14.832 0.000 30 not differ significantly from that of a solution 0.278 0.362 0.189 0.000 0,091 16.0 19.676 40 0.298 0.075 0 . 2 2 5 0.154 20.0 24.472 0.000 50 of pure ethyl alcohol in water of the same alco0.053 0.165 0.216 0.111 24.0 29,212 -0.002 00 holic concentration by n eight. For distilled 0,520 0.67'3 0.355 0.013 0.180 15 7.5 9.327 50 57.830 0.043 0.011 0.494 0.169 0.337 20 10.0 12.392 liquors with relatively low solids content this 0.456, 0.597 0.152 0.309 12.5 15.440 0.003 25 0.556 0,424 0.142 0,288 0,004 30 15.0 18.469 will be substantially true, but the method 0.234 0.451 0.343 0.004 0.117 40 2 0 . 0 24.472 will not give accurate results on cordials or 0,173 0.258 0.33s 0,002 0.086 2 5 . 0 30.380 50 0.844 0.438 0.646 0.010 0.218 9.0 11.169 15 60 67.689 sweet wines, because of the effect of the dissolved 0,603 0.787 0,200 0.406 0.006, 12.0 14.832 20 sugar on the temperature coefficient of expan0.5L57 0.728 0.184 0.375 0.005 15.0 18.469 25 0.504 0.659 0.169 0,342 22.080 0.008 18.0 30 sion. I n such cases it is best to determine 0,301 0.442 0.582 0.148 21.0 25.662 0.007 35 24.0 28.212 0.001 0.123 0 . 2 5 4 0.375 0.497 ~. 40 specific gravities of sample and distillate a t 0,519 0.766, 0.261 1.000 11.2 13.857 0.01s 16 70 76.909 15.56' C., or to use the generally less accurate 0.012 0,480 0.711 0.933 0.239 14.0 17.259 20 0.220 0.444 0.658 0.862 0.013 20.639 10.8 24 method of measuring the volume of sample 0.402 0.595 0.781 0.011 0,199 19.6 23.995 28 0.356 0.531 0.693 and distillate directly a t 15.56" C. I n the lat0.178 0.010 22.4 27.323 32 0.153 n ,309 0,403 0.610 0.007 25.2 30.621 36 ter case, the specific gravity of the distillate 0 . 2 8 3 0.596, 0 , 8 8 3 1.138 0 015 12.0 14,832 15 80 85.458 0.570 0.841 1.104 0.018 0.283 14.4 17.743 18 may then be determined a t room temperature 0.786 1.034 0,533 0.017 0.264 21 16.8 20.639 and its percentage of alcohol by volume a t 0.856, 0.016 0,245 0.725 0,494 19.2 23.502 24 0. s8o 0.4*50 0 667 0.017 0,225 27 21.6 26.374 60 ' F. (1, Table 19, XLIII). 0 792 0,404 0 389 0.010 0.198 30 24.0 29.212 Instead of actually Calculating the error for each specific set of conditions, the value of the correction may be obtained by interpolation distillate will contribute an experimental error of 0.025 proof from Table 111. This table may be expanded, if desired, by to the determined result. While the above experimental similar calculations to include intermediate values of original errors are not very large, they may be significant when accualcoholic concentrations, sample weights, and working temrate results are desired, and they can be greatly minimized by peratures, thus reducing the error of interpolation. Howweighing the sample and distillate and calculating their ever, in its present form it will serve to yield substantially volumes from their specific gravities. accurate values for correcting determined results, permitting When volumes of sample and distillate are calculated from reduction of total error in the corrected results approximately n eights and specific gravities, the most probably significant to the magnitude of experimental error alone. experimental errors are likely to occur in the determination of The corrections in Table I11 are equally applicable whether the specific gravity of the distillate, since this value is used t o the volumes of sample and distillate are calculated from apobtain the alcoholic concentration of the distillate, and any parent specific gravities or are measured directly. error in this value is multiplied by 4 or 5 in calculating the If the volumes of sample and distillate are measured alcoholic concentration of the original. With an alcoholic directly, the experimental error of measurement is likely to concentration of 10 per cent by volume a t 60' F. in the disbe significant unless considerable care is taken. Il7ith an tillate, and a 25-ml. pycnometer, an error of 0.001 ml. in filling original alcoholic concentration of 40 per cent by weight, an the pycnometer, or an error of 0.001 gram in weighing it, or an error of 0.01 ml. in measuring the volume of a 25-m1. sample error of 0.15" C. in measuring the temperature of its contents, will contribute an experimental error of only 0.02 per cent by nil1 contribute an error of 0.00004 to the calculated specific volume to the determined result, but a not improbable error gravity, or an error of 0.032 to the percentage of alcohol by of 0.05 ml. in measuring the volume of a 25-m1. sample will volume in the distillate, or an error of 0.13 to 0.16 per cent by contribute an experimental error of 0.1 per cent by volume, volume, or 0.26 to 0.32 proof, to the determined result. This or 0.2 proof, to the determined result. An error of 0.05 ml. is a significant error when very accurate results are desired, in measuring the volume of the 100 ml. of distillate will conyet it requires very careful technique to keep the experitribute an experimental error of 0.024 per cent by volume, or mental error down even to this magnitude. 0.048 proof, to the determined result. An error of 1" C. in measuring the temperature of the 25-ml, sample described Literature Cited above will contribute an experimental error of 0.04 per cent by volume, or 0.08 proof, to the determined result, while an (1) .~ssoc. Official Agr. Chom., Official and Tentative 3Iethods of Analysis, 5th ed., 1940. error of 1" C. in measuring the temperature of the 100 ml. of $ 0
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