Color Filters in Filter Photometry STANCIL S. COOPER, S t . Louis University, S t . Louis, Mo.
light-sensitive element, and from transmittance or transmittancy factors of 6lter and solution, respectively, as a function of wave length. The method of evaluating a transmittancy factor of a solution for nonmonochromatic light, produced by filter transmission, can be employed to select the filter that will allow the least transmittancy factor to be obtained by a specific solution without having the filter for a test. The Cenco-Sheard Spectrophotelometer and Cenco-Sheard-Sanford Photelometer were used.
The selection of the proper filter to be used with a specific colored solution, light source, and lightsensitive element is often difficult when the selection is attempted on the basis of a comparison of transmittance curves of filters and transmittance or transmittancy curves of solutions. A method is given here for evaluating the transmittancy factor for a specMed light source, filter, solution, and light-sensitive element from data which can be obtained for the characteristics of the combined light source and
tively. k is a factor which is less than 1 and depends on the character of the filament (k is 1 for black body radiator and approximately 0.3 for the gray body radiator, the tungsten filament). Thus, as the temperature of the filament rises, t.here is progressively more energy in short wave-length radiation (11, p. 7). Approximately white light (approximate equal intensities of all visible wave lengths) should be emitted by a filament a t a temperature of about 5000' -4. Filament's operate considerably below this temperature, so that these light sources yield radiation which is more intense in red than in blue wave lengths. The intensity of radiation from a heated filament is dependent on a power of the voltage, I = Vn, where n is between 3 and 4 (11, p. 4). An accurate control of the voltage applied to a heated filament results in a constant distribution of energies in the emitted light.
P
HOTOELECTRIC filter photometers are widely used as aids in quantitative analysis, especially in routine analytical procedures involving the application of colorimetric analysis. These photometers employ as light-sensitive elements the photo; emission cell (or cells) or the photronic (photovoltaic) cell (or cells). Several excellent reviews of these instruments are available (,??, 3, 8-16). The instruments use color filters to select the quality of light for a particular determination (1). In the operation of a photoelectric filter photometer one usually determines the magnitude of some quantity, such as the current output of the photocell, or some value which is proportional to this quantity, either value of which is proportional to the total light from a fixed light source which emerges after passing through a selected filter and a solution of known thickness, and then compares this to the magnitude of the same quantity obtained with light from the same source after it has passed through a system like the first but without the colored material. The ratio of the second magnitude to that of the first is interpreted to be the fraction of the incident light transmitted by the colored material. This ratio depends on a number of factors: (1) the character of the colored material, (2) the character of the color filter used (fraction of light transmitted by the Hter as a function of nave length), (3) the character of the light source (distribution of intensities as a function of wave length), and (4)the character of the instrument which responds to the light emerging from either absorbing system (sensitivity of phototube or photronic cell to light of various wave length). For the best quantitative results, conditions should be so arranged that the greatest change in transmittancy factor per unit change in concentration of colored material can be brought about. For a particular colored material and an instrument of fixed light source, 1, 3, and 4 are &xed and any difference in transmittsncy factor is to be brought about by a change in filter character. If the characteristics of the light source, of the photo or photronic cell, of the filter, and of the solution are known, it should be possible to ascertain the transmittancy factor of a particular combination. I n other words, for a given concentration and depth of a definite colored substance, the filter could be selected, without a direct test, which would give the least transmittancy factor when a definite light source and phototube or photronic cell are used. The distribution of energy in the initial light depends upon the type of source. Most light sources are heated filaments.
The relative response of both phototubes and photronic cells as a function of wave length is given by Gibb ( 2 , p. 88). Partridge (13, p. 207) gives the specific photoelectric sensitivity for photocells with alkali metal-sensitive elements. Muller (11, p. 5 ) gives the characteristics of photronic cells. The selection of the proper filter to be used in a particular photoelectric filter photometer for a specific solution is sometimes difficult, especially when one has on hand a very limited number of filters from which to choose. Manufacturers usually provide a set of filters with each instrument sold, but these filters are necessarily few in number. In selecting the proper filter one should choose the one which will give the greatest charge in instrument reading per unit change in concentration of solution. If enough filters were on hand with each instrument, this could be easily ascertained by a direct test; however, often a worker has only a small number of filters to choose from and it would be very desirable to be able to make a selection from a list of filters not immediately available. The material presented here is intended to aid in the select'ion of filters by a use of their published transmittancies and is not intended to take the place of a direct test when filters are available. In this work the photronic cell in the Cenco-Sheard-Sanford Photelometer No. 12,338 was studied, employing data determined by the Cenco-Sheard Spectrophotelometer, No. 12,317, with illuminator No. 12,333. Although this study includes only the use of photronic cells, the principles presented should be applicable t o other types as well.
In the operation of the Photelometer one obtains first a galvanometer setting (measure of the current from the photronic cell) when light from a heated filament passes through a selected filter and a cell containing solvent, and second, the corresponding setting with a colored solution and the same filter in the light path. The setting for solution and filter is divided by that for the filter and solvent to obtain the transmittancy factor for the colored solution to light through the filter used. If, for instance, the intensities of light emitted by the heated filament are 11, , , , , , , , , , . . , ln(= 1,) for wave lengths A,, A 2 . A,, and the corresponding sensitivities of the photr thepe wave lengths are al, U Z .. . . . .
The distribution of energy in the light emitted by a heated filament is given by the Plank equation, k CIA-' E = ____ &AT - 1 where h is the wyave length in millicrons, and c1 and CP are constants having values of 3.70 X loz3and 1.433 X lo7, respec-
254
255
V O L U M E 19, NO. 4, A P R I L 1 9 4 7 t h a t the response factors of the cell to light from the filament are llal, 12az . . . , . . . , , . . . Inan(= Imam). These factorsmay be designated by bl, bz , . . . . . . . . . . , b, ( = bm). If the composition of the light is constant, then li, In . . , , . . . . . . . . 1, are fixed and the relative response factors for the cell and light source will be hi h,, -, bz b, - . . . . . . , . . . . . , . b, where b, is the response factor for a cerb, tam wave length, &. If b, is selected as the maximum response factor, then b, = b,, and each relative response factor lies between 0 and l. Let these relative response factors for the light source and cell be pi, p 2 . . . . . . . . , , , . . , . p,( = p m ) . If the transmittance factors for the filter are fl, fz . . . . . . . . . . . . fn( = fm) and the transmittance factors for the solution employed are 81, sz . . . . . . . . . . sn(= sm) for light of wave length Am, the current from the photronic cell IS measured by
-
..
PiJl
+ Pzfi: + . . + Pnf" ,
=
Table 11. Solutions Employed and Filter or Filters Used with Each Solution Solution Solution Concentration Employed NO. of Solution o-Phenanthroline F e + + 11 5 micrograms of Fe per mi. 1 microgram of F e 12 per ml. Potassium chromate 14 to 17 174,,80,40, and 20 micrograms of C r per ml. Potassium dichromate 13 174 micrograms of Cr per ml. Chromium chloride 18 4 mg. of C r per ml.
Filter or Filters Used Cenco blue and green Cenco blue and green Cenco blue Cenco blue Cenco blue, green, orange, CG 511, 430, 348, 243, 241, a n d 243 512 Same as for chromium chloride Same as for chromium chloride Cenco orange, CG 348, 243, 241, 512 and 243
+
Chromium sulfate
19
4 mg. of C r per ml.
20
2 mg. of C r per ml.
Copper sulfate
21
5 mg. of C u per ml.
m = n
+
pmfm for filter alone in the light path m = l
and
+ pzse + . . . . . . . . +
E X P E R I M E N T A L AND DISCUSSION pnSn
=
m = n
pmsmfor solution alone in the light path m = l
The measure of current when both filter and solution are in the light path is, then, PlfiSl
+
p2s2j2
+ . . . . + pnfnsn *
=
m - n
E
PmfnSm
m - 1
From this the transmittancy factor for the solution through thelparticular filter is m = n
E
Pmfmsm
m = l T s = m = n
-
PlJlSl p1.A
+ pzfzsz + . . . . + pnfnsn + pzf2 + . . . + ,
,
, ,
Pnfn
Pmfm
m = l
Table I. Filter
Glass Color Filters Employed
Make a n d KO. of Filter
1 Cenco, 87,309.A-410P Cenco, 87,309B-425P Cenco, 87,309C-625P 5 Corning 511 6 Corning 430
2 3
[7
Corning 348
8 9
Corning 243 Corning 241
10
Corning 243
+ 512
Name Blue Green Orange Violet Dark shade bluegreen H . R . red shade yellow H.R. signal red H.R. pyrometer shade red H . R . signal red didymium
+
Designation Here Cenco blue Cenco green Cenco orange CG 511 CG 430
Thickness, llm. , 1.31 2 .07 7.34 1 09 4.05
CG 348
1 99
CG 243 CG 241
4.90 4 75
CG 243
+ 512
5 . 0 0 for 512
-4t any wave length, ,A, a measure of the current is p, when no filter or solution is in the light path, pmfmwith the filter alone, and pmsmJvith solution alone in the light path. The transmittance factors for the filter are: blfi' - bz f 2 . . . b"fn, and since fi, bi bz bn fz . , , f n are independent of the individual values of b,, these transmittance factors should be the same when measured in any spectrophot,ometer, provided the light source used for measurement of each factor is monochromatic. Similar reasoning shows that the values of sl, si: . . . sn are independent of the instrument used t o measure them. This implies that the thickness of the filter and solution be definite, since f, and s, depend on the thickness of the material as well as on its composition. Since the response factors, b,, for the cell and light source are a function of the cell, a,! and light source, ,l they should be evaluated for each combination of light source and cell used (11, p. 7 ) .
To test the validity of the equation for the transmittancy factor, Ts, a series of nine filters (Table I) was applied to six different colored solutions. Three of the solutions were tested in two or more concentrations. Transmittancy factors were calculated by means of the above equation for Ts, using data determined by means of the Cenco-Sheard Spectrophotelometer for fm, sm, and p,. These calculated values for Ts were then compared to those determined experimentally by using the solution with the proper filters in the Cenco-Sheard-Sanford Photelometer. These instruments employ the barrier layer type photronic cell. Table I1 shows the solutions employed and the filter or filters used with them. Values of the transmittance factors, fm, of the various filters listed in Table I and of transmittancy factors, sm, of 1-cm. depth of the solutions listed in Table 11 were determined as functions of wave length with the Spectrophotelometer in the conventional manner. The relative response factors, p,, for light source and cell were determined as follows: The Photelonieter light source was arranged before the entrance slit and the Photelometer photronic cell inserted in the Spectrophotelometer. With a definite light intensity and width of apertures, the wave length (600 millimicrons) was determined for which the cell produced the maximum current. The entrance slit was set a t 1 mm., the wave band a t a width of 5 millimicrons, and the light intensity adjusted by use of the diaphragm to give a galvanometer reading of 95 t o 100 a t 600 millimicrons. With these factors fixed the wave-length selector was turned backwards to the least value for which a noticeable galvanometer deflection could be observed. As the wave-length selector was turned forward in units of 5 to 10 millimicrons, values of the galvanometer deflections for each setting were recorded. These values are proportional to the response factors (Ilal, l z a a . . . , . Inan). The maximum galvanometer deflection for this run was divided into the deflection for each wave length t o give the relative response factors for the cell and light source ( p l , p , . . p n ) . The latter values are plotted in Figure 1 as curve P of plate A, where relative response is given as per cent of the value at 600 millimicrons. The general practice was followed of introducing a blue filter in the light path for wave lengths below 400 millimicrons and a red filter for wave lengths above 650 millimicrons (because of the reflection grating employed in the Spectrophotelometer) . Transmittance factors, fm, of the various filters (except for 7 and 9) are plotted as per cent transmittance against wave length in millimicrons in plate A. Relative response factors, p,, times the corresponding transmittance factors for the respective filters are plotted as per cent filter-response, pmfm, against wave length in plate B. Transmittancy factors, sm, for some of the solutions employed are shown in plate F as per cent transmittancies against wave
A N A L Y T I C A L CHEMISTRY
256
80-
60-
40-
!-
z
W
u
20-
a
300
400
500
300
400
500
700
600
800
900
50
40
z a
30
0
v,
2 20 I-
z
w
CI:
10
W
n
100
600
so0
eo0
WAVE LENGTHS, MILLIMICRONS Figure 1. Photronic Cell Response, Transmittance, and Filter Response Factors as Functions of Wave Length Plate A. P, per cent relative response factors for photronic cell and Cenco Photelometer light eource 1 to 10. Per cent transmittance of filters Cenco, 87,309: 1 (A), 1.31 mm.; 2 (B), 2.07 mm.; 3 (C), 7.34 m m . Corning Glaes: 5, CG 511, 1.99 mm.; 6, CG 430, 4.05 mm.; 7, CG 348, 1.99 mm.; 8, CG 243, 4.90 mm.; 9, CG 241, 4.75 mm.; 10, CG 243 CG 512, 5.00 m m . Plate B. Per cent filter response (numbers correspond to filters of plate A)
+
lengths, where curve numbers correspond to the solution numbers in Table 11. The product of the filter response factors, p,f,, and the transmittayc-- factors, sm, of the solutions yields the filter-solution response f zctors, p, fms,. These values for certain filters and solutions arc shown in plates C, D, E, and I as per cent response against wave length. In plates C and E the per cent filter response curves for filters 1 and 2, respectively, are shown to give a comparison to the filter-solution-response curves. I n order to evaluate the fraction transmittancy of a solution employed with a definite filter and light source it is necessary to obtain the sum of the ordinates (filter-solution response factors) m - n
pmfmsm nb E 1
for curves such as 2 P l l and 2P12 of plate E and divide this by the sum of the ordinates (filter response factors), m - n Pmfm
m = l
for the filter curve such as 2P of plate E. Since all curves are plotted with the same unit of wave length (10 millimicrons per centimeter), the ratio of the area under curves such as 2 P l l and
.
2P12 to that under 2P would give the same result as the ratio of ordinate sums-that is, m - n
Pmfmsm m - 1
Ts=,,,,%
Pmfm m = l
= area under solution-filter response curve
area under filter response curve
The results of such evaluations &s compared to direct measurements of the per cent transmittancies as determined by the Photelometer are given in Tables I11 and IV. Table V givee deviations of these values from those measured by the Photelometer. When the recommended light source is used with the CencoSheard Spectrophotelometer, values obtained below approximately 325 and above approximately 760 millimicrons should not be used in a quantitative way. The Photelometer light source operates a t a lower temperature than that of the Spectrophotelometer and thus furnishes relatively less blue and more red light, so that quantitative measurements by the Spectrophotelometer with the Photelometer light source can be extended somewhat
V O L U M E 19, NO. 4, A P R I L 1 9 4 7
2.57
Table 111. Area of Filter Response and Filter-Solution Response Curves with Comparison of Per Cent Transmittancies Calculated from Area Ratios and Measured Values on Photelometer Jolu- Filter KO.X xon Filter response curve, X P 'Jo. Area, filter-response curve, mp %
1 1P 684
2 2P 2237
3 3P 1961
5 5P 495
6
6P 3075
7 7P 7583
8 8P 2868
9 10 9 P 1OP 1748 2102
18 hrea, filter-solution response curve, XP-18, mr % Transmit- From areas tancy, By Photelometer
156 508 795 22.8 22.8 40.5
94 929 2167 1385 19.0 30.2 28.5 48.3
1116 930 64.0 44.3
23.9 33.7
40.8
18.8 30.3
31.6
49.2
66.0
19 Area, filter-solution response curve, XP-19, mp % Transmit- From areas tancy, By Pbotelometer
118 17.2
390 585 17.5 29.8
69 743 14.0 24.2
1525 20.2
1102 38.4
943 682 54.0 32.5
18.0
17.8 29.3
13.3 24.3
23.8 38.6
30 Area, filter-solution response curve, XP-20, mp % Transmit- From areas tancy, By Photelometer
260 866 988 164 37.9 38.8 50.4 33.2
1427 46.4
37.7
38.9
.. .. ..
.. .. ..
%
%
%
31
Area, filter-solution response curve, XP-21, mp % Transmit- From areas tancy, By Photelometer
50.5 32.9 1136 57.9
..
..
44.1
66.1
32.7
2953 39.0
1659 1240 57.8 71.0
1136 54.0
46.8 41.3
58.1 72.1
54.2
.. .. ..
5436 1496 71.6 52.1
730 41.7
1178 56.0
It is often difficult to Belect the be& filter for use with a particular solution by a comparison of transmittance curves of filters with the transmittancy curves of the solution. I n fact, often the filter selected by such a comparison of curvee is not the best possible from a given list. Transmittance curves of filters (plate A) and transmittancy curves for solutions (plate F) do not contain the effect of light source and character of photronic cell. Filter response curves (plate B) picture the combination of the three effects: light source, photronic cell, and filter, and are the curves which should be compared with the transmittancy curve of a solution in order to make a filter selection.
For example, compare the two solution curves 11 and 12 (for two concentrations of o-phenanthroline-ferrous ion) of plate F with curves 1 and 2 of plate A and Table IV. Area of Filter-Solution Response Curves and Comparison of Per with 1P and 2P of plate B. The central Cent Transmittancies Calculated from Area Ratios and Measured Values on maximum for the two filters, 1 and 2, Photelometer from plate A is 410 and 525 millimicrons, respectively. One is, therefore, unable Filter and .Gii,Filterto choose between the two filters for use Sesponse Curve, with these solutions. The filter response 11 12 13 14 15 16 17 Solution, Y curves in plate B show the maximum 1. Area 1P Area, filter-solution response curve response for these filtens for use in the 1PY, mp-% 195 508 137 179 460 376 268 Cenco-Photelometer is about 450 and f384 mp Transmit- From areas 28.5 74.3 20.0 26.2 67.2 54.9 39.2 tancy, By Photelometer 540 millimicrons. From this compari28.9 74.9 20.3 25.6 68.0 54.5 39.7 % son filter 1 can be chosen as better than filter 2 for this solution. Curves of Area, filter-solution response curve ?. hrea 2P ?237 mp % 2PY, 9 ~ - % 898 1768 .. .. .. , . plate C and E and the data in Table 40.2 79.0 .. . . .. .. ,. Transmit- From areas IV justify the selection on the basis of tancy, B y Pbotelometer the filter response curves in plate B. 40.0 78.8 .. .. .. .. .. % Filter 1 with solutions 11 and 12 in the Photelometer gave per cent transmittancies of 28.9 and 74.0, respectively, whereas filter 2. under the same conditions, gave values of 40.0 and 78.8. farther into the red and not so far into the blue regions. The Consider solutions represented by curves 18 and 20 of plate lower limit, under these conditions, is approximately 350 and the F and filters 1 and 5. Plate A shows the central maximum of upper limit is about 790 to 800 millimicrons. The relative reeither of these filters is 410 millimicrons. Curves 18 and 20 reveal a maximum absorption in the region of 410 millimicrons. sponse factors for the photronic cell and Spectrophotelometer On the basis of these curves alone one cannot choosq between light source (operated a t 70 amperes) is about 2 and 5% for 325 the filters. Filter response curves for filters .1 and 5 (curves and 760 millimicrons, respectively. Above 800 millimicrons the 1P and 5P of plate B) are unsymmetrical with maximum response response factors are low, and it is doubtful if values above this values at 455 and 440 millimicrons, respectively. This indicatee a smaller transmission measured on the Cenco Photelometer wave length are reliable even with a light source such as that of through either solution 18 or 20 and filter 5 than for the same :he Photelometer. The photronic cell has a small response in solutions through filter 1. Data in Table I11 for these solutions t,hese extreme regions and if i t is employed with filters which and filters confirm the selection. If a choice is to be made be:ransnit these wave lengths, this response is utilized and must be tween filters 2 and 6 for use with solutions 18 and 20, a comconsidered. Although the values of the response factors for high parison of transmittance (plate A) and transmittancy curves (plate F) gives little ground for choice, especially since the and low wave lengths are not accurate, their values are small and transmittance of filter 6 is still large a t 410 millimicrons. Filter therefore their contribution to the total response is never large if response curves (plate B) for these filters show the central maxifilters are used which transmit in the visible. These inaccuracies mum for 2P is nearer the maximum absorption for solution 18 will be carried over to transmittance and transmittancy factors of and 20 than is the corresponding value for 6P, and therefore filter 2 should allow the least transmittancy for either solution. This filters and solutions, respectively, if measured by an instrument selection is confirmed by values in Table 111. 2mploying the photronic cell. Ordinate sums (and therefore sreas) of both filter response and solution-filter response curves :overing these regions will be subject to larger errors than those :overing the visible region. This should be especially noticeable Table V. Deviation of Per Cent Transmittancies as Calculated by Area Ratios from Measured Values if filter and solution show large transmittancies in these extreme Filter 1 2 3 5 6 7 8 9 1 0 Tegions. No. of values ,of % Table V shows the average of transmittance values as obtained transmittancies, calculated from from curve areas as compared to measured values when each of area ratios 1 0 5 4 3 3 4 1 4 ;he several filters Vere employed. Filters 2 and 6, transmitting Total deviation from measured value, shiefly in the visible, show 1.0 part per 100 deviation, and with parts per 100 19.0 6 . 5 ' 3 . 1 7 . 3 1 . 5 35.5 3 . 8 15.2 2 . 0 filters 3 and 10 added (both show greatly repressed transmittanAverage deviation from measured :ies in the far red) the deviation is only 0.8 part per 100. Howvalue, parts per wer, filters l and 5 (transmitting into the ultraviolet) show devia100 1.9 1.3 0 . 8 2.4 0 . 5 8.9 0.9 3 . 8 0.6 Average deviation from measured (excluding 7 and 9) = 1.3 parts per 100 fions of 2 parts per 100 and filters 7, 8, and 9 (transmitting into -he infrared) show deviations of 4.4 partssper 100 40
58.2
..
68.2
51.6 39.5
55.7
.
I
A N A L Y T I C A L CHEMISTRY
258
PLATE E
W
W
g24
v)
z
0
W
t x
% w
B v) a t-
16
I-
z W
Z
c,
W
a w e
0
a
a
W
n 300
4 00
5bO
400
WAVE LENGTHS,MILLIMERONS
300
400
600
500
70 0
WAVE LENGTHS,MlLLlMlCRONS
500
700
600
800
900
WAVE LENGTHS, MILLIMICRONS Figure 2. Transmittancies of Solutions and Response Factors as Functions of Wave Length Plates C and D. Per cent response through Cenco filter 87,309 A, 1.31 mm. l P l l through filter and solution 11 1P12 through filter and solution 12 1P13 thiough filter and solution 13 1P14 through filter and solution 14 1P16 through filter and solution 16 Plate E. Per cent response through Cenco filter 87,309 B, 2.07 mm. 2Pll through filter and solution 11 2P12 through filter and solution 12
Selection of filters by a visual comparison of filter response curves with transmittancy curves of solutions is approximate only; therefore a more reliable method is desirable. Reference to Tables 111and IV shows that it is possible to calculate the per cent transmittancy of a solution measured by a filter photometer with photronic cell by the equation for Ts as developed above. This method of computing the transmittancy can be made into a method for selecting the best filter for a particular solution. The response factors for photronic cell and light source and the transmittancy factors for a known depth and concentration of the solution in question may be combined with published values of transmittance factors of various filters in the same manner as is shown for chromium chloride in plate I. If transmittance data for dl the filters considered here had been taken from published values, filter 5 would have been selected as the best one to be used with solutions 18, 19, and 20 and the photronic cell, because of all the filters the least transmittancy is calculated when its data are employed (see Table 111). The method employed for the calculation of a transmittancy factor of a solution for light transmitted by a particular filter may be illustrated by the data in Table VI for wave-length intervals of 10 millimicrons.
Plate F. Per cent transmittancies of solutions in 1-om. cell 11. o-Phenanthroline Fe+* 5 microgram of Fe per ml. 12. o-Phenanthroline Fe++: 1 microgram of Fe per d. 13. Potassium dichromate, 174 microgram of Cr per ml. 14. Potassium chromate, 174 microgram of Cr per ml. 16. Potassium chromate, 40 microgram of Cr per ml. 18. Chromium chloride, 4 mg. of Cr per ml. 20. Chromium sulfate, 2 mg. d Cr per ml. 21. Copper sulfate, 5 mg. of Cu per ml.
+ +
Column 2 is the per cent relative response of photronic cell to Photelometer light source (section of curve P, plate A ) ; column 3 contains the transmittance factors for filter 2 (see Table I and curve 2 plate A); and column 4 contains the transmittancy factors for a 1-em. depth of solution (see Table I1 and curve 11of plate F). The product of the values in columns 2 and 3 for each wave length gives the filter response values in column 5 and the product of these filter response values and the corresponding values in column 4 gives the filter-solution response values in column 6. Values in columns 5 and 6 are plotted as curves 2P and 2Pl1, respectively, in plate E. Two methods were used to evaluate the transmittancy factor, Ts. I n one method the factor is obtained by dividing the sum of the filter-solution response values in Table VI (ordinates for each 10 millimicrons of curve 2 P l l in plate E) by the sum of the filter response values in Table VI (ordinates for each 10 millimicrons of curve 2P in plate E). Employing the two sums as 90 9 listed in the table, Ts = = 0.404 as compared to 0.400 as measured by the Photelometer. Applying the same method to solution 12 and fdter 2, the value of T s for this combination is calculated to the 0.790 as compared to a measured value of 0.788. This method gives values of Ts in close agreement n-ith the measured values if the ordinates are taken a t close enough wavelength intervals, This is especially important when filter response or filter-solution response curve is irregular. To avoid the difficulties presented by the above procedure a second method was
2eg
259
V O L U M E 19, NO. 4, A P R I L 1 9 4 7
PLATE
H
dops'p20
WAVE LENGTHS , MIL L IM IC RONS PLATE I
lOPl8
w ln
A
I2-
z
0
a
v)
E
500
400
300
WAVE L E NGTHS ,MILL I MICRONS
8-
I-
z
d V
a w
4-
a 300
400
500
600
700
800
900
WAVE LENGTHS, MILLIMICRONS Figure 3. Transmittance of Filter and Response Factors as Functions of Wave Length Plate G. Curve 51, per cent transmittance of CG filter 511 (1.99 mm.) from literature (Corning Glass Works) Curve SIP, per cent filter response for 51 Plate H. Per cent response through CG filter 511 (1.99 m m . ) Sip18 through filter and chromium ehloride (4 mg. of Cr per ml.) 51P19through filter and chromium sulfate (4 mg. of Cr per ml.) 5iP20 through filter and chromium sulfate (2 mg. of Cr per ml.) Plate I. Per cent response through solution 18, chromium chloride (4 mg. of Cr per ml.) and filters 2P18 through solution and Cenco 87,309 B (2.07 mm.) 3P18 through solution and Cenco 87,309 C (7.34 mm.) 5P18 through solution and CG filter 511 (1.99 mm.) 6P18 through molution and CG filter 430 (4.05 m m . ) 1OP18 through solution and CG filter 243 (4.90 mm.) 512 (5.00 mm.)
+
employed for the evaluation of Ts. The filter response and filtersolution response curves are plotted on the same graph (see plate E) and the area under each curve obtained. The transmittancy factor is given by under filter-solution response curve TS = area area under filter response curve
-
area under curve 2P11 (plate E) area under curve 2P (plate E)
I n Table I11 the area under curve 2P is given as 2237 millimicron % and in Table IV the area under curve 2 P l l is given as 898 millimicron %. The ratio of these areas is Ts = 0.402 as shown in Table IV. The areas may be easily obtained by counting squares, by the use of a planimeter, or by weighing. -411 the areas listed in Tables 111, IV, and VI1 were obtained by making the plot on millimeter coordinate paper and then counting squares. The error in this method of obtaining an area is about 0.5 to 1%. Transmittance data for all the filters considered here are not available in the literature. Data for the transmittance factors of Corning Glass filter 511 (CG 511) of 2.15-mm. thickness are available (6) and may be used to establish transmittance factors for a thickness of 1.99 mm. and for the thickness of the CG 511
filter 5 used in this work. I n calculating the factors a t the new thickness it must be remembered that Lambert's law applies t o internal transmittance. Since about 470 of the light is lost a t each face of the filter, the over-all transmittance factor is 0.92 of the internal transinittame factor for each wave length. Making use of this relation and of Lambert's law, the transmittance factors for a 1.99-mm. thickness of CG 511 were calculated from the given values of a 2.15-mm. thickness filter. These values are shown as curve 51 of plate G. Curve 51P of the same plate is the filter response curve for this filter and the curves in plate H are the filter-solution response curves for this filter and solutions 18, 19, and 20. Table VI1 shows that the agreement is excellent between the per cent transmittancies as measured with the Photelometer and a CG 511 filter of 1.99-mm. thickness and those calculated from the reported transmittance factors for this filter. A spectrophotometer trace (6) from Corning Glass Works for CG 511 filter of 1.99-mm. thickness for a different melt than the corresponding filter described here gave transmittance values which did not differ by more than 0.6 in percentage from the corresponding values determined for the filter in this laboratory. Therefore, transmittancy factors of solutions employing the filters from the two different melts should be almost identical. Another spectrophotometer trace ( 6 ) , for, Corning Glass iilter CG 430 of 3.015-mm. thickness from a different melt than the CG 430 filter of 4.05-mm. thickness described here, gave transmittance
ANALYTICAL CHEMISTRY
260 Table VI. Data at 10-Millimicron Intervals, Illustrating Method of Calculating a Transmittancy Factor of a Solution for Light Transmitted by a Filter Wave Response Length, Factor. mr Pm, % , P 240 16.2 50 19.8 24.2 60 28.9 70 80 33.6 38.8 90 45.2 500 10 51.4 20 57.5 30 65.0 72.4 40 78.9 50 86.5 60 88.5 70 96.5 80 94.2 90 100.0 100 93.1 10 90.8 20 77.5 30 66.4 40 52.5 50 90 37.9
-
Transmittance Factors, Filter 2,
Transmittancv Solution Factor;11,
fm
pnfmt
am
0.008 0.014 0.037 00 .. 01 85 41 0.230 0.311 0.380 00 ,. 44 11 73 0.385 0.324 0,250 00 .. 11 28 85 0.082 0.051 0.029 0,018 0.010 0,008 0.006 0.004
TE
0.226 0.194 0.174 00 .. 11 42 77 0.124 0.118 0.111 00 ,. 11 17 95 0.304 0.487 0.675 00 .. 78 97 30 0.910 0.950 0.970 0,980 0.990 1,000 1.000 1.000
- l:i,\
Filter,
Rzdgse,
$$:&,
2P pmlmsm 2 P l l
0.1 0.3 0.9 25 .. 14 8.9 14.1 19.5 2 37 . 81 27.9 25.6 21.6 11 26 .. 44 7.7 5.1 2.7 1.6 0.8 0.5 0.3 0.1 Sum 2 2 4 . 9
-
0 0.1 0.2 0 . 46 1.1 1.7 2.2 42 . 78 8.5 12.5 14.6 11 03 .. 80 7.0 4.8 2.6 1.6 0.8 0.5 0.3 0.1 90.9
-
-= 0.404
Ta 0.402 from area ratios and 0.400 as measured by Photelometer (see Table IV).
values calculated for 4.05-mm. thickness, which did not differ by more than 1.201, from the corresponding values determined in this work. Area under filter response curves for the filters from the two melts were measured to be 3075 and 3026 millimicron yo. Per cent transmittancies for solutions 18, 19, and 20 for light through CG 430 filter of 4.05-mm. thickness represented by the Corning Glass Works spectrophotometer trace are calculated t o be 30.5 24.1, and 46.3 respectively, as compared to calculated values for the CG 430 h e r used here of 30.2 24.2, and 46.4 and the corresponding values (30.3,24.3, and 46.8) as measured by the Photelometer with CG 430 filter. Thus, in three cases data on separate melts of filter glass by different instruments in different laboratories have allowed calculated transmittancy factors for the system: tungsten filament light source, filter, solution, and photronic cell, which agree exceptionally well with the measured transmittancy factors for these combinations. This indicates that one could make a selection of the proper filter to be used with a particular solution without having the filters on hand for a trial, if thickness and internal or external transmittance data were available for the filters on the market. Either internal or external transmittance data for Blters can be used by the method presented here, as long as the effect of change of filter thickness is not desired. Data for one batch of filter glass may not exactly match that of another batch of the same glass; however, the difference should not be great enough to invalidate the above treatment. The method presented here will allow the selection of the proper filter rather easily from an extended list not immediately a t the disposal of a worker. The data he must provide are (1)combined characteristics of light source and photosensitive element as a function of wave length, and (2) the transmittancy factors for a definite thickness of the solution in question. With transmittance factors for deiinite thickness of filters given, their transmib tance-wave length curves can be compared with the corresponding curve for the solution in question, and several filters may be chosen for use with the solution. I n this selection a suitable filter will show its maximum transmittance a t or near the minimum transmittancy of the solution. The several suitable filters can be treated in a manner similar to that used for filter 2 and solution 11 and illustrated in plate E, or as shown in plate I for several filters and solution 18. The
best filter for use is the one allowing the least transmittancy for a given concentration of solution. I n c m two filters show approximately the same transmittancy for a certain concentration of solution, data for another concentration should be applied to the two filters. The filter allowing the greatest change in transmittancy per unit change in concentration of solution is the filter to be chosen. The above approach should prove helpful in understanding the principles involved when nonmonochromatic light, obtained by filter selection on a continuous light source, is used in measuring a transmittancjr factor. There are a t least four factors involved in addition to depth and concentration of medium: (1) character of light source, (2) character of lightrsemitive instrument, (3) character of filter, and (4) character of solution employed. The principles presented should apply to instruments employing either the photronic or photoemission cells. The requirement of either is a knowledge of the combined or separate characteristics of the light source and photocell. The procedure should also be applicable to visual colorimetry, but the situation is more involved because of the uncertainty of the relative sensitivity of each eye employed in the measurement. Relative visibility factors (4, 7 ) for the normal eye to light of equal energy for all wave lengths is available, but since the light source actually used is rarelv of this kind, these factors can be hehful only and may not serve as a reliable guide in the selection of the proper filter tjo be used on a specific solution in visual colorimetry.
Table VJI. Comparison of Observed Per Cent Transmittancies of Solutions with Corresponding Values as Calculated from Measured and Reported (6) Transmittance Factors of Corning Glass Filter 511 of 1.99-Mm. Thicknese
Area from reported transmittance factors, mp % Transmit- From areas, reported factancy, tors From areas, measured fac1 cm., % tors Measured, Photelometer with CG 511 filter
Filter-Solution Response Filter Solution Solution Solution Reaponse 18 19 20
394
72
50.4
130
..
18.3
12.8
32.9
18.8
13.3
32 P
19.0
14.0
33.2
.. ..
ACKNOWLEDGMENT
The author wishes to thank E. A. Doisy for the use of the Spectrophotelometer. Thanks are also extended to C. F. Henkel of Corning Glass Works for submission of Spectrophotometer recordings for certain thicknesses of some of the Corning Glase filters used. LITERATURE CITED
(1) Ashley, 9. E.Q.,IND.ENQ.CHEM.,ANAL.ED., 11, 72-9 (1939). (2) Gibb, T. R. P., “Optical Methods of Chemical Analysia”, p. 88. New York, MoGraw-Hill Book Co., 1942. (3) Gibson, K.S.,Inst~umsnts,9,309,335 (1936). (4) Gibson, K.S.,and Tyndall, E. P., Sei. Papers Bur. Standards, No.4,475 (1923); Bur. Standards BUZZ.,19, 131 (1923). (5) Henkel, C. F.,Corning Glass Works, private communication. (6) Hodgman, C. D., “Handbook of Chemistry and Physios”, 27th ed., p. 2161, Cleveland, Ohio, Chemical Rubber Publishing Co., 1943. (7) International Critical Tables, Vol. V, p. 436, New York, McGraw-Hill Book Co., 1929. (8) Lange, B., Chem.-Ztg., 62,737 (1938). (9) Mellon, M. G., IND. ENQ.CHEM.,ANAL.ED., 11,80-5 (1939). (10) Mtiller, R. H., Ibid., 7, 223-6 (1935). (11) Ibid., 11, 1-17 (1939). (12) Orastein, L. S., -Xoll, W. J. H., and Burger, H. C., “Objektive
Spektralphotometrie”, Brunswick, Germany, Frederick Vieweg und Sohn, 1932. (13) Partridge, H. M., IND.ENG. CHSM., ANAL.ED., 2, 207-11 (1930). (14) Yoe, G. H.,and Crumpler, T. B., Zbid., 7,281-8 (1935). (15) Zinradre, C., Ibid., 7, 280-1 (1935).
