SOLETIOKS FOR COLORIMETRIC STAKDARDS. 11. THE RELATIOPL’ O F COLOR TO COXCENTRATION FOR AQUEOUS SOLUTIOKS OF CERTAIN IYORGXSIC SALTS &I. G . MELLON
Judging from the lack of information, at least in chemical periodicals, regarding the use of numerical specifications of color, one is led to concludc that the average chemist, rather than having learned to think in these terms, is still attempting to specify colors descriptively, so that an object exhibiting a blue hue, for example, is designated simply as being a light, dark, medium, Alice, sky, azure, or some other type of blue. Recently, two committees, composed of representatives from the various fields of activity interested in colorimetrics, published comprehensive reports describing methods of measuring and specifying colors1*z. Following their suggestions, one may formulate a definite numerical specification of a given color on either the monochromatic or trichromatic system. The present paper is presented in the hope of aiding, in some small measure, the development among chemists of an appreciation of the possibility of applying these methods. In the first paper of this series3 data for various solutions were presented in the form of curves representing percent transmittancy as a function of wave length. The readings from which the curves were constructed had been obtained by determining, a t the wave lengths indicated, the percent of incident light transmitted by the various solutions, relative to that transmitted by the pure solvent. Such curves, in themselves, may be sufficient for certain purposes as a n indication of the properties of the system measured; but in case one wishes to know the relative brilliance, colorimetric purity (saturation), and dominant wave length of the system, or the percentages of elementary red, green, and violet excitations constituting the color, further calculation is necessary. An example is given below of how this is done for a given solution, together with the collected data :or several solutions of different concentrations. Method of Calculation The data presented here were all determined by means of calculations based on the curves previously published, and include only the inorganic solutions of Amy mentioned in the first paper. An inspection of the original curves, involving measurements made with a Keuffel and Esser spectrophotometer, indicates that the readings did not cover the whole range of wave lengths from 400 to 700 mp, due to the fact that the relative visibility for different wave lengths becomes quite low toward either the red or violet end, rendering the readings in these regions Troland et al.: J. Optical SOC.America-Rev. Sei. Instruments, 6, 527 (1922). Gibson et al.: J. Optical SOC.America-Rev. Sei. Instrudents, 10, 169 (1925). Slellon and Martin: J. Phys. Chem.. 30, 161 (1927).
I932
M. G . MELLON
too uncertain to be very reliable. However, in making calculations, such as those presented belpw, one can scarcely neglect the effect of the violet excitations for wave lengths below 44omp, where readings on the Keuffel and Esser instrument are difficult to make. I t is necessary, therefore, to extrapolate the curves previously presented in order to include the whole region between 400 and 7 0 0 mp. An inspection of the published curves indicates that, in some instances at least, such an extrapolation becomes a little too much of a guess to leave one entirely comfortable; but, on the other hand, failure to make such extrapolations, which finally involves the omission of certain elementary color excitations (particularly serious in the violet region), leads to absurd results when one attempts to construct a curve coordinating some given value with concentration for a solution such as cobaltous chloride. In order to indicate just what was done in this direction before calculating the present data, there is included in Tahle I the value of the transmittancies which it seemed might reasonably be used as extrapolated values for the ends of the curves. Since the method for calculating the values used in specifying a color seem not to be generally known, illustrative calculations have been made for an ammoniacal solution of cupric sulfate having a concentration of two hundredth molar. The following steps indicate the general procedure involved : I. Extrapolate (if necessary) the spectral transmission curve, as described above, constructed from the two sets of values read directly on the Keuffel and Esser color analyzer. For the solution of cupric sulfate these values (wave length and percent transmittancyj are given in columns I and 2 of Table 11. Obtain, by means of the special slide rule available for the Keuffel 2. and Esser spectrophotometer, a t intervals of even I O mp, the values given in columns 3, 4, j, and 6 of Table 11; that is, calculate the elementary color excitation values for red, green, and violet and the value of the relative brilliance. With considerable more effort, these values may be calculated without the special slide rule.’ 3 . Obtain the sum of the values in each of columns 3 , 4, and 5 . Then reduce these sums to percentage form by dividing the sum for each column by the sum of all three. Multiplying the results by I O O gives the percents of red, green, and violet. 4. Obtain the dominant wave length and the percent colorimetric purity by means of t,he color triangle available for such work, using the percents of red and violet calculated above. 5 . Obtain the sum of the values in column 6 and divide by the sum of the luminosity values for “average noon-day sunlight” (10.6856)~in order to calculate the percent relative brilliance. Ferry: “Physics Measurements”, 1, 239 (1926)
* See Ref. 2 , Table VI.
193.3
SOLUTIONS FOR COLORIMETRIC STANDARDS
TABLE I Values used for perceu transmittancy for the ends of curves for various solutions (extrapolated if necessary) Solution
Concn.
cuso4
w
Red End 4
I
at
623 mp
M/S
”
”
660
,,
MI16 M/3
CU(NH~)~SO~
(IiHd2Cr04
at 548
j
”
700
W4oo
30
”
700
”
”
440
rooat j I o
W3oo M/6oo
M/4
I
at 486
1)
If
MI16
”
”
w 3 2
”
”
M/ IO0
14, 4
1,
,I
f,
,,
66
at
5 00 joo
89 I ’
”
453 440
96
”
loo a t 410
1)
It
4i0
1
at 450 550
420
loo at 400
”
loo ” 610
\ ’ I ”
Mj400
1
I
at 450
I O O at j o o ”
”
680
’’
”
630
7 1 at 7 0 0 j6
I’
’’
M /16
87
”
”
31/32
98
”
”
100
M/8
K2Cr20;
f!
I
M/200
coc12
2,
&I/IO0 MI200
W 8
Co(KHs)sCls
700
8
2
M/I200
FeCL
,I
hI:6
&I,/I 2 M/60
at
j90
))
1)
j8j Si5
”
”
RI/joo
>!
))
& 600 ‘I/
- 2
,)
550 550
I934
11. G . 1IELLON
TABLE I1 rolorimetric data for a two hundredth molar solution of tetrammino-cupric sulfate Elementary color excitation values Relative Red Green 1-iolet Brilliance
T
_-
IOOC,
_-
___
IO0
~
IO0
__
~
_-
IO0
97 87 78 68 59 49 39
__ ~
__
0.91
-_
’
51.20
1
81.40 0.6j 93.00 1.39 81.40 3.10 5.95 8.02 9.43
2.26 3 .7? 11.80 3 .03 13.20
__
29.60’ I 33.70
__
__ 0.0119
Wave length X Rei. Uril. ~
__ ~
5 . I2 7.39 1 1 .66
o ,0168 o o2j9 0.03;o
17.03
o.oj28
21.82
30.60
0.0;50
12.10
0.0998
36 .oo 48.92 61..+j 73.40 j0.68 60.92
67.j0 50.30
5.50
0.1230
2.89
0.1440
12.00
1.41
0.1360
1.96
9.39
0.70
O.IIj0
9 6
4.2;
7.02
0.33
0.0928
j o , 10
7 0
j . 2 0
0.15
0.0698
3.56 2.36 I .I1
0.07
3 8 29
3,54 2 .83 2 .28 I .78
2 4
I.jO
2 1
I .24
2
I
6 19 7
28
I3
5 .lo
f!
5 1
0
.oj
o.oj03
38.40 28.16
0.03
0.0358
2 0 .‘$I
0.01
0.02jI
0.84
--
0 , O I 79
0.48 0.26
--
0.0125)
--
0.0097
0.13
1 4 , j6 I O .j 6 i .i-l 5.92 4.46
0.83 0.68
0.0;
__ __
o.ooj2
2 2
2 4
0 . jo
0.03
--
0.0038
0.01
-__ __ __
0 , 0 0 2j
I .62
0.0014
0.92
0.0008
0.53
0.0004
0.27
2 0
2 ;
0.34
3 ’ 3 6
0 22
4 0
0.09 0.06 0.06
46 5 1
0.14
~
13 - 6 9
__ __ __
0 .00.;4
0 0004
3.40 2.43
0.27
___
~_
I .I732
607 . o j
Purity j0r;
6 . .rc;
I1
.or;
jIi.4
inp
6. To calculate the values in colunin ;niultiply each wave length indicated by the corrwponding value for relative brilliancr. The sum of these values is t h m divided by the sum of the values for relative brilliance t o obtain the wave length of the spectral centroid (or center of gravity).
S O L C T I O S S FOR COLORIMETRIC STASDARDS
I935
Having made such a set of calculations, the color then may he definitely specified by giving, for the trichromatic system, the percents of red, green, and violet or, for the monochromatic system, the percents colorimetric purity and relative brilliance, together with the dominant wave length. Having made such a calculation, it should be kept in mind, hoivevw: that the colorimetric specification so obtained holds only when the object is illuminated by “average noon-day sunlight.” Similar calculations can be made, of course, for other sources of illumination, providing one knows their spcctral distribution curves. The special slide rule would not be applicable then, since its values are based on determinations for average noon-day sunlight. Relation of Color to Concentration If one were to inquire of most chemists what happens colorimetrically on adding niore solvent to a given colored solution, they would probably reply that the process of dilution renders the color paler or less intense. Similarly, the more concentrated of two colored solutions is frequently rcfrrred to as having the deeper color. I n view of the newer specification of color, such an answer is not entirely sathiring; one is led to seek the effect of dilution on the various numerical value.
