386
VOL. 7, NO. 6
INDUSTRIAL AND ENGINEERING CHEMISTRY
Whole eggs, U. S. Extras Whole eggs, U. S. Standards Commercial yolks Dry yolks All yolks (combination of data on '(dry" and %ommercial" yolks) "
S = 497.0R - 658.29 S = 439.9R - 579.49 S = 503.1R - 663.15 S = 542.4R - 718.19 S
=
565.4R
- 750.76
After having derived these equations, the total solids content for each specimen included in the data was calculated by substitution of the observed values for R. The differences, d, between the observed and calculated values for the per cent total solids were then used to calculate the standard deviation, 8. D., by means of the formula X.D. = d y w h e r e n equals the number of cases, with the following results:
Whole eggs, U. S. Extras Whole eggs, U. S. Standards Commercial yolks Dry yolks All yolks
S. D. = '0.30
S.D.
= *0.31 S. D. = *0.59 S. D. = '0.45 S. D. = *0.55
The standard deviations for the yolks are seen to be higher than those for the whole eggs, despite the more distinct line between light and shadow in the refractometer observed in the case of the yolks. Thus the relationship between refractive index and total solids is more variable with yolks of commerce than with whole eggs. This is to be expected in view of the fact that the yolks measured contained variable amounts of whites. Since a large fraction of the total solids of whole eggs and an even larger one in case of yolks is fatty matter emulsified in the continuous aqueous phase, it is remarkable that the refractometric method works a t all. Since it does, there is evidently a relationship between the total fatty matter and the water-soluble matter, as is the case in cows' milk where a high fat content is accompanied by a high protein content and vice versa. An examination of the data obtained in this study revealed an indication of a seasonal variation in the case of yolks and to a less extent in the case of whole eggs. The determined
values for total solids of late June eggs were lower than those calculated by means of the equation, and to a smaller extent early March eggs showed calculated total solids lower than those actually determined. However, the number of specimens analyzed was insufficient to give more than a general trend. Further study is necessary to determine the extent of this seasonal variation. For the benefit of those who may wish to apply the data a t temperatures other than 25" C., temperature coefficients were determined by measurements upon 7 specimens of whole egg and 7 specimens of dry yolk. These showed that there is a straight-line variation between the temperatures of 20" C. (68" F.) and 30" C. (86" F.) The method cannot be applied outside of this temperature range. In the case of the refractive index of whole egg, 0.0001 should be added (or subtracted) for each degree Centigrade above (or below) 25" C. (77" F.) in order to reduce the reading to the 25" C. (77" F.) basis. The corresponding correction for dry yolk refractive index is 0.0002. While the number of cases studied is small, the application of the equations derived from them to 1932 spring eggs and yolks gave such satisfactory results that it was decided to publish the results herein given as a rapid method for the estimation of the total solids content.
Acknowledgments The author is indebted to M. E. Pennington for the suggestion of this study, to A. W. Thomas, in whose laboratory the work was done, and to the Borden Company for its material codperation.
Literature Cited (1) Almquist, H. J., Lorenz, E'. W., and Burmeater, B. R., IND. ENQ.CHEM., Anal. Ed., 4, 305 (1932). (2) Assoc. Official Agr. Chem., Official and Tentative Methods, 3rd ed., p. 244 (1930). (3) Holst, W. F., and Almquist, H. J., Hilgardia, 6, 45 (1931). (4) Pennington, M. E., J. Biol. Chem., 7, 109 (1910). RECEIVED August 13, 1935.
A Short Method for Calculating Delta D in a Crystal Growth Process J
RIOSES GORDON,' University of North Dakota, Grand Forks, N. D.
I
N ORDER to predict the screen analysis of the product
from the analysis of seed it is necessary to calculate AD, the increase in size of opening (mesh) through which a crystal will pass after the growing process is completed. McCabe (9, S) does this by integrating the following equation graphically : where W , and D,give the screen analysis of the seed W , = weight of crystal product
(
Values are assumed for AD, a curve of 1
>:,
+-
against
W , is plotted for each value of AD, and the area under each curve measured. The A D giving the proper value for W, is then used in calculating the final screen analysis. The purpose of this paper is to eliminate the cut-and-try 1
Present address, University of Minnesota, Minneapolis, Mian.
graphical integration by substituting for it a rapid method of finding A D . The method will be illustrated by applying it to the example on the crystallization of potassium chloride worked out by McCabe ( I ) . The screen analysis of the seed (D. and WE) is given. Calculations made from solubility data show that 155 pounds of product will be obtained per 100 pounds of seed. From these data A D may be calculated as follows: To integrate Equation 1 it is necessary to obtain an expression for D, in terms of WE. This is done by plotting D, against W, and drawing the best straight line through the points. (The straight line is an approximation, since the cumulative screen analysis plot will curve a t either end, but the approximation is sufficiently accurate for practical purposes.) This will give
D, = b
+ mW,
(2)
where b is the intercept on the D, axis and m is the slope.
ANALYTICAL EDITION
NOVEMBER 15, 1935
For the data in the problem being considered the values of b and m are found to be 0.09 and -0.0006, respectively. Substituting Equation 2 in 1we obtain
which expanded gives
(3)
387
Since AD is so small, the term containing AD3 mlty be neglected. The turn containing ADz may be considered to be only a correction factor which can be estimated by using AD = ADt, thereby converting Equation 3 again into a linear rather than a quadratic or cubic equation. The. integrated form of 3 becomes
Solving for AD we obtain
As a first approximation the last two terms in parentheses are negligible. Equation 3 then becomes Wp = S,"*(l + b 3fA D8 t )dW,
where AD6 is the tentative value of AD. This integrates to (4)
Solving Equation 4 for AD,, changing to the common logarithms, and substituting for b mWa the values De, and Dag, where DsO = intercept of straight seed line at W = 0, and D., = intercept of straight seed line at W = W , we obtain
+
(5)
Substituting in Equation 5 the values for W,, W., m, Dualand D;, we obtain AD, = 0.0102
Substituting in Equation 6 the values for m, W,, W., Da,, and Dai we obtain AD = 0.009, which is the value found by McCabe ( I ) . The steps then are as follows: 1. Plot the screen analysis of the seed and draw the best straight line through the points. This gives Da = b mW8. Values for Da,,D ~ Jand , m are read from this curve. 2. Obtain ADt, a tentative value for AD, from Equation 5 . 3. From Equation 6 obtain the final value for AD.
+
Literature Cited (1) Badger and MoCabe, "Elements of Chemical Engineering," p. 409,New York,MoGraw-Hill Book Co., 1931. (2) McCabe, W. L., IND.ENQ.CHEM., 21, 30 (1929).
(3) Ibid., 21, 112 (1929). RECEIVED June 1, 1936.
Spectrophotometric Determination of Copper in Ores and Mattes J. P. MEHLIG, Oregon State College, Corvallis, Ore.
2'
H E colorimetric method for the determination of copper based upon the formation of the blue copper-ammonia complex ion [Cu(NH&]++ by the addition of an excess of ammonium hydroxide to a solution of cupric ions has been known and used for many years (2, 8). While it has given satisfaction, it has the disadvantage of requiring the preparation of a series of standard solutions of copper for comparison and there is a question as to the permanency of these standards. With the development of photoelectric colorimeters it is now possible to dispense with the use of standard solutions. About 2 years ago such an instrument called the photelometer was devised by Sanford, Sheard, and Osterberg (7) and recently similar instruments have been described by Eimer and Amend ( I ) , by Yoe and Crumpler (9), by Zinzadze (IO),and by Muller (6). In using them the intensity of light transmitted by a colored solution is correlated with the concentration of the constituent responsible for the color. It is necessary to use a suitable light filter in order to provide light of the proper wave length. The spectrophotometric method for copper depends upon the fact that the percentage transmittancy of light of a given wave length for an ammoniacal copper solution is a function of the copper concentration. It is possible to construct a reference curve by plotting percentage transmittancy a t a given wave length of a series of standard solutions of ammonia-
cal copper sulfate against the known copper concentrations and then by use of this curve to convert the percentage transmittancy of an unknown ammoniacal copper solution into concentration of copper. A similar procedure was followed by the writer in determining manganese in steel (4). Once constructed, such a curve may readily be used permanently, but the labor involved in its construction is an objection to it. Since Beer's law has been shown (6,9) to hold for ammoniacal copper solutions up to concentrations of almost 1 gram of copper per liter, the concentration of copper in a given solution can be calculated from the fundamental Lambert-Beer equation
I
=lo
x
10-elc
in which IO represents the intensity of the incident light of given wave length which enters the solution, I the intensity remaining after its passage through the solution, 1 the length in centimeters of the solution, c the moles of absorbing substance per liter of solution, and e a constant which is a measure of the absorption due to a single molecule and is called the molecular extinction coefficient. The above equation may also be written log
I
T~
=
-eZc
