SIMPLIFIED CALCULATIONS IN COLORIMETRY ROBERT P. MCCRACKAN, EMANUEL PASSAMANECK, AND KATEE. HARMAN, MEDICAL COLLEGE oa VIRGINIA, RICHMOND, VA. In colorimetric analyses, a reading on the known ( K ) and a reading on the unknown ( U ) have to be taken, whether the colorimeter be of the single plunger, the two plunger, or the dilution type. These readings become the terms of fractions used in obtaining factors that form a part of calculation formulas, K / U being nsed for plunger type calorimeters, and U / K for those of the dilution type. These ratios are constant throughout a comparison in a colorimeter, and since they are used as factors they may be represented by F in the expressions: K / U = F,and U / K
=
P
If any fixed value be assigned to K, then U will assume a corresponding value, and vice versa. As the analyst can choose which term he will make constant, and can choose any value within wide limits, it is evidently advantageous to choose a whole number, and one expressible by one significant figure, for the divisor, such as 8, 10, 20, or 30. By so doing he can make all division short. He should, therefore, set the unknown in applying a plunger type colorimeter, and get a reading for the known, and in applying the dilution type colorimeter, vice versa. In using 15 as a divisor, as one would be compelled to do in using a 15 mm. Bock-Benedict cell for the unknown, he could divide successively by 3 and 5, the factors of 15, and avoid long division, and a similar procedure could be followed with any other factorable number. Most writers on colorimetry assume the use of the plunger type colorimeter for exact work, and they usually direct that the known be given a value, and that a reading for the unknown be made after the fields are matched. The number 20 is most often nsed for the known, and the readings for the unknown, made to one decimal place usually, give values that make long division necessary, and the factors obtained by the division usually have to be rounded off to prevent the use of figures to more than the third decimal place. The Klett Mfg. Co. has copyrighted tables prepared by 'Benedict showing values rounded off to three decimal places for values of K / U when K is 15, and U is 6.0 to 29.9, and when K is 20, and U is 8.0 to 32.9. Mathewsl includes tables from Hnlton-Frankel in his latest text, showing creatinine and sugar percentages in blood for readings for the unknowns when the known is set a t 20, and Palisi and Lawton2 give tables for calculating creatinine, non-protein nitrogen, urea nitrogen, sugar, and wic acid for readings for the unknowns when the known is set a t 20. All such tables could more easily be prepared for readings on the knowns
when the unknowns are set, and the ease with which calculations could be verified would make work less empirical. We present a table showing all values for K / U and U i R when the divisor is made 20 and the dividend varies from 10.0 to 45.9. None of these factors are rounded off, yet only 50% of them require as many as three decimal places. They are absolutely exact, and all are obtained by short division making i t possible for students and analysts to verify calculations with little loss of time and energy, a thing that the best pedagogy would seem to demand. Where most accurate work is done with calorimeters reading to the second decimal place, the wisdom of having a divisor with one significant figure is still more apparent. With such instruments and the unknown set on 20, factors absolutely accurate to the fourth decimal place, from an arithmetical point of view, can be obtained, and only 50% of them need four decimals to express them. A table giving these factors would be just ten times as long as our three place table based on readings made to one place. COLORIMETER TABLE All values for XI20 are shown when X varies from 10.0 to 45.9. In bath the calculation formulas, KnownfUnknown = F,and UnknownfKnown = F, the dividend is represented by X, and the divisor by 20.
X is the dividend in Kf U, and in UIK
x
x/20
10.0 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 11.0 11.1 11.2 11.3 11.4 11.5
0.500 0.505 0.510 0.515 0.520 0.525 0.530 0.535 0.540 0.545 0.550 0.555 0.560 0.565 0.570 0.575
X
12.4 12.5 12.6 12.7 12.8 12.9 13.0 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9
X/20
0.620 0.625 0.630 0.635 0.640 0.645 0.650 0.655 0.660 0.665 0.670 0.675 0.680 0.685 0.690 0.695
X
14.8 14.9 15.0 15.1 15.2 15.3' 15.4 15.5 15.6 15.7 15.8 15.9 16.0 16.1 16.2 16.3
x/zo
X
x/20
X
x/20
X
x/20
0.740 0.745 0.750 0.755 0.760 0.765 0.770 0.775 0.780 0.785 0.790 0.795 0.800 0.805 0.810 0.815
17.2 17.3 17.4 17.5 17.6 17.7 17.8 17.9 18.0 18.1 18.2 18.3 18.4 18.5 18.6 18.7
0.860 0.865 0.870 0.875 0.880 0.885 0.890 0.895 0.900 0.905 0.910 0.915 0.920 0.925 0.930 0.935
19.6 19.7 19.8 19.9 20.0 20.1 20.2 20.3 20.4 20.5 20.6 20.7 20.8 20.9 21.0 21.1
0.980 0.985 0.990 0.995 1.000 1.005 1.010 1.015 1.020 1.025 1.030 1.035 1.040 1.045 1.050 1.055
22.0 22.1 22.2 22.3 22.4 22.5 22.6 22.7 22.8 22.9 23.0 23.1 23.2 23.3 23.4 23.5
1.100 1.105 1.110 1.115 1.120 1.125 1.130 1.135 1.140 1.145 1,150 1.155 1.160 1.165 1.170 1.175
x
x/20
24.4 24.5 24.6 24.7 24.8 24.9 25.0 25.1 25.2 25.3 25.4 25.5 25.6 25.7 25.8 25.9 26.0 26.1 26.2 26.3 26.4 26.5 26.6 26.7 26.8 26.9 27.0 27.1 27.2 27.3 27.4 27.5 27.6 27.7 27.8 27.9
1.220 1.225 1.230 1.235 1.240 1.245 1.250 1.255 1.260 1.265 1.270 1.275 1.280 1.285 1.290 1.295 1.300 1.305 1,310 1.315 1.320 1.325 1.330 1.335 1.340 1.345 1.350 1.355 1.360 1.365 1.370 1.375 1.380 1.385 1.390 1.395
X 28.0 28.1 28.2 28.3 28.4 28.5 28.6 28.7 28.8 28.9 29.0 29.1 29.2 29.3 29.4 29.5 29.6 29.7 29.8 29.9 30.0 30.1 30.2 30.3 30.4 30.5 30.6 30.7 30.8 30.9 31.0 31.1 31.2 31.3 31.4 31.5
COLORIMHTER TABLE (Cmc22CdCd) X x/20 X x/20 X 1.400 31.6 1.580 35.2 1.760 38.8 1.405 31.7 1.585 35.3 1.765 38.9 1.410 31.8 1.590 35.4 1.770 39.0 1.415 31.9 1.595 35.5 1.775 39.1 1.420 32.0 1.600 35.6 1.780 39.2 1.425 32.1 1.605 35.7 1.785 39.3 1.430 32.2 1.610 35.8 1.790 39.4 1.435 32.3 1.615 35.9 1.795 39.5 1.440 32.4 1.620 36.0 1.800 39.6 1.445 32.5 1.625 36.1 1.805 39.7 1.450 32.6 1.630 36.2 1.810 39.8 1.455 32.7 1.635 36.3 1.815 39.9 1.460 32.8 1.640 36.4 1.820 40.0 1.465 32.9 1.645 36.5 1.825 40.1 1.470 33.0 1.650 36.6 1.830 40.2 1.475 33.1 1.655 36.7 1.835 40.3 1.480 33.2 1.660 36.8 1.840 40.4 1.485 33.3 1.665 36.9 1.845 40.5 1.490 33.4 1.670 37.0 1.850 40.6 1.495 33.5 1.675 37.1 1.855 40.7 1.500 33.6 1.680 37.2 1.860 40.8 1.505 33.7 1.685 37.3 1.865 40.9 1.510 33.8 1.690 37.4 1.870 41.0 1.515 33.9 1.695 37.5 1.875 41.1 1.520 34.0 1.700 37.6 1.880 41.2 1.525 34.1 1.705 37.7 1.885 41.3 1.530 34.2 1.710 37.8 1.890 41.4 1.535 34.3 1.715 37.9 1.895 41.5 1.540 34.4 1.720 38.0 1.900 41.6 1.545 34.5 1.725 38.1 1.905 41.7 1.550 34.6 1.730 38.2 1.910 41.8 1.555 34.7 1.735 38.3 1.915 41.9 1.560 34.8 1.740 38.4 1.920 42.0 1.565 34.9 1.745 38.5 1.925 42.1 1.570 35.0 1.750 38.6 1.930 42.2 1.575 35.1 1.755 38.7 1.935 42.3 x/20
X/20
1.940 1.945 1.950 1.955 1.960 1.965 1.970 1.975 1.980 1.985 1.990 1.995 2.000 2.005 2.010 2.015 2.020 2.025 2.030 2.035 2.040 2.045 2.050 2.055 2.060 2.065 2.070 2.075 2.080 2.085 2.090 2.W5 2.100 2.105 2.110 2.115
X 42.4 42.5 42.6 42.7 42.8 42.9 43.0 43.1 43.2 43.3 43.4 43.5 43.6 43.7 43.8 43.9 44.0 44.1 44.2 44.3 44.4 44.5 44.6 44.7 44.8 44.9 45.0 45.1 45.2 45.3 45.4 45.5 45.6 45.7 45.8 45.9
x/20
2.120 2.125 2.130 2.135 2.140 2.145 2.150 2.155 2.160 2.165 2.170 2.175 2.180 2.185 2.190 2.195 2.200 2.205 2.210 2.215 2.220 2.225 2.230 2.235 2.240 2.245 2.250 2.255 2.260 2.265 2.270 2.275 2.280 2.285 2.290 2.295
BIBLIOGRAF~Y 'Mathem, Albert P . : "Physiological Chemistry," William Wood & Co., New
York, 1925, fourth ed., pp. 1073 and 1074. 'Falisi, J. Vincent, and Lawton, Vera A,: "Tables for Blood Chemistry Calculations," J. Leb. end Clin. Med., 9,566-71 (1924).
Folin, Otto: "A Laboratory Manual," D. Appleton & CO.,New ~ & k 1922. , Myers, Victor C.: "Practical Chemical Analysis of Blood," C. V. Mosby Medical Book and Pub. Co., St. Louis, 1924.
