V O L U M E 2 7 , NO. 3, M A R C H 1 9 5 5
459
&
o’60
/ I
0.50
9 0.40 L .k2
DISCUSSION AND APPLICATION OF METHOD
/
W
s4
Oa30
0.90
0.10
1
9
3
4
5
6
7
8
, CONCENTRATION, VOL. %
Infrared absorbance of alcohol and ether
Figure 2.
analysis. The net absorbance (total absorbance minus rrll absorbance) of the various standards a t the two selected positions was plotted against concentration t,o obtain the working curves (Figure 2).
- - - At
8.00 microns in 10-cm. cell A t 6.90 microns in IO-cm. cell
The relationship of concentration to absorbance for both ether and alcohol a t both 6.9 and 8.0 microns appear t o follow a straight’ line and therefore the working curves have been drawn as straight lines. The various points lie very close t,o the lines, indicating that the weighing pipet method of preparing infrared gas standards for ether and alcohol is valid. T o test the applicability of the method, four known samples of ether and alcohol in air were prepared by introducing known amounts of both ether and alcohol in the gas cell as described above. The infrared absorbance of the prepared samples was measured a t 6.9 and 8.0 microns and the values were calculated to per cent ether and alcohol using the method of successive approximations (3). The results obt,ained are listed in Table I and $how good agreement between the values added and the values found. ACKNOWLEDGMENT
cell was calculated as follow (all n.ork as done a t 760 mm. of pressure and 25” C. or 298’ K ) : Per cent of ether or alcohol by volume =
n.t. X22,400_____ X 100x298 11.K.-x v 273
where Wt.
The authors wish to acknowledge the assistance of W.J. Huff, who weighed the pipets on a microbalance. hppreciation is further expressed to J. D. Armitage, Robert Frye. C. J. Bain, and A . J. Clear of Picatinny Arsenal for help rendered in the publication of this report.
= weight of ether or alcohol in pipet in yranis
M.W. = gram molecular weight of ether or alcohol V = volume of gas cell in cubic centimeters ralculatcd from
its geometry (fo,md to be 117.6 cc. for the cell used)
I n this n-ay various standards of ether and alcohol were prepared. The infrared spectrograms of the gas cell without ether or alcohol, and of the prepared standard samples were obtained on papilr \vith alisorhmce markingr using a Pwicin-Elmer douhlebeam inf‘rarrbd sprctrophotometer (Figure 1). The 6.0-micron ether liand and the 8.0-micron alcohol band n-ere selected for
LITERATVRE CITED
a n d Saier, E. L..J .Ippl. P h y s . , 17, 450-6 (1946). ( 2 ) S i e d e r l , J. E., a n d Xiederl, J., “Organic Q u a n t i t a t i v e LIicro.” pp. 46-7, \17iley, S e w York. 1042. (3) Pristera, F., B p p l . Spectroscopy, 7, Xo. :3, 116-31 (1953).
(1) Coggeshall,
K, D.,
R E C E I V Bfor D review October 1 4 , 1 0 5 3 . Accepted October 27, 1954. Presented at the Annual Xeeting of the Society f u r Applied Spectroscopv. T r w Tork, S . Y . , May 2;. 1954.
Instrumental Variability of a Model 7 Coleman Photonephelometer HUBERT J. KEILY
and
L. B. ROGERS
Department o f Chemistry and Laboratory o f Nuclear Science, Massachusetts Institute o f Technology, Cambridge, Mass.
Instrumental variability is attributed to variations. in the blanks used to set the instrument sensitivit). and to a tendency for the readings to drift to lower values. By modifying the manufacturer’s operations and making frequent checks against standards, a standard deviation for individual measurements of 0.28 reading unit at the normal instrument sensitivity has been estimated.
D
URISG the course of a study on the nephelometric deter-
mination of sulfate (4), the need arose for an evaluation of the variability contributed to the measurements by the instrument alone. The Model 7 Coleman Photonephelometer used in the study measures the light scattered a t right angles to the direction of illumination by means of two barrier layer cells. The instrument, which is linear in its response t o scattered light, may be operated as either a direct or a null-reading device. Unknown turbidities may be compared ~1ith standaids, supplied by the manufacturer, which are suspensions of an inorganic salt in a highly viscous organic polymer (3). Each one is labeled with a particular Xephelos number which has been assigned with reference t o a master standard. Thus, t h e light-scattering piop-
erties of the standards, and the samples subsequently measured with reference to them, are enipirically related. I n this way, a correlation of readings in Sephelos units between laboratories should he possible. Essentially, t h e standards provide a means of reproducibly establiehing the instrument sensitivity, which is defined as the slope of the linear relationship between the instrument reading and the 90’-scattered light intensity. This relationship ibQ referred to below as the instrument-response curve. RESULTS
Using the procedure outlined by the manufacturer for the null method of operation ( 1 ), the instrument was adjusted using a standard 38 and a distilled water blank. [ A modification ( 6 ) of this procedure is now recommended by the manufacturer. 1 Five other standards were then run as “samples” in a random order which was determined by a chance selection of a 5 X 5 Latin square ( 6 ) . A different Latin square was used for the data in each table. Table I indicates the values taken after a single initial adjustment of t h e instrument with standard 38. The readings tor each
460
ANALYTICAL CHEMISTRY
Table I. Readings Obtained after Single Initial Adjustment of Instrument Sensitivity at Normal Value with Standard 38 (Distilled water used as blank) CoefNominal Stand- ficient ard of Value of StandAverDeviVariard‘ Individual Readings age ationb ationc 4 3.7 3.6 3.6 3.9 3.7 3.7 0.12 3.3 9 8.5 8.2 8.4 8.4 7.8 8.2 0.28 3.4 18 19.6 19.9 19.6 19.6 19.4 19.6 0.20 1.5 37 41.7 41.9 4 1 . 4 41.1 41.1 41.4 0.36 0.9 78 84.2 83.4 82.8 82.1 81.8 82.9 0.52 0.6 a Nominal values are Nephelos numbers assigned to standards by manufsctnrer.
* Estimated standard deviation of individual measurements,
C
Coefficient of variation, u =
8
=
In order to make a precise adjustment of the instrument sensitivity, a blank with a constant lighbscattering ability is required. Zero would have been ideal, but in lieu of such a blank, the sensitivity level was adjusted with two standards using the following procedure. With the blank adjustment com letely inoperative, standard 38 was made to read 38.0 with the 8 T D knob. Next, the second standard, which had a nominal value of 9 (not the same one included in the tables), was adjusted to read 10.0 with the BLK knob. This could be done because its value was slightly higher than 10 before this adjustment. A second adjustment with each standard was usually all that was required to provide an instrument-response curve which passed through the values 10.0 and 38.0. Table IV shows the values obtained for the five “samples” when using the above procedure for setting the instrument, together with an adjustment with the STD knob using standard 38 before each reading. The BLK knob needed no further attention.
a 100 7,
X
standard have been recorded in their chronological order of measurement; but, because of the Latin square arrangement, the time intervals between individual values for a given standard were not necessarily constant. A drift toward lower values is observable, particularly for the high standards. This drift could be due to photocell fatigue and/or decrease of the intensity of light source. The power supply was a &volt storage battery. A recheck of the standard 38 a t the completion of the series showed that its value read 35.9.
With the instrument in the authors’ laboratory, the slope of the instrument-response curve was varied from 0.3 to 3.2 times the normal value, on the basis of the fact that standard 38 could be made to read any value from 11.4 to 122. These values were only approximate because of the tendency to drift, which lowered both limits simultaneously. By reducing the galvanometer sensitivity (maximum galvanometer setting was used with the null method of operation), the lower limit could be reduced still further. However, for the measurement of low turbidities the gain in sensitivity over the normal-Le., 1X-value was of principal interest. Therefore, the standards were read a t 3X sensitivity and then converted to normal sensitivity. The resulting average values of 4.2, 9.3, 20.4, and 41.8 show good agreement with the data in Table IV. Standard 78 could not be read because the full scale limit of the instrument is 130.
Table 11. Readings Obtained Using Repeated Adjustment of Instrument Sensitivity at Normal Value with Standard 38 and Distilled Water for Blank (Each group of readings taken on different day) Nomi. nal Value Standof ard, AverDeviard Individual Readings age ation Group Stand4.5 A 4 4.6 4.3 4.2 4.2 4.4 0.18 9 8.6 8.9 9.2 9.4 8.6 8.9 0.36 18 21.3 20.8 20.9 20.9 20.6 20.9 0.26 37 42.2 4 2 . 8 4 2 . 3 42.5 42.8 42.5 0.28 78 86.1 86.7 86.1 8 6 . 6 87.1 86.5 0.42 B 4 3.4 3.4 3.4 3.2 3.4 3.4 0.09 9 8.6 8.3 8.4 8.5 8.5 8.5 0.11 20.6 20.2 19.9 20.1 20.0 18 20.2 0.27 37 42.9 42.7 42.2 42.4 43.1 42.7 0.37 78 87.9 87.4 87.4 87.8 87.6 87.6 0.23 ~
~~
Coeffioient of Variation 4.1 4.0 1.2 0.6
0.5 2.6 1.3 1.3 0 9 0.3
In Table 11, each measurement was preceded by a check or readjustment of the instrument sensitivity with standard 38, with the result that the drifting of the readings toward lower values was avoided. However, when the average values obtained for the same standard on different days were compared by means of the l-test (6),the difference between them, with the exception of standard 37, was shown to be greater than could be accounted for by the variability within the data taken on a particular day. R7ith standards 4 and 78, the differences were “very highly significant”-i.e., the probability that the differences were due to chance variations alone was jess than 0.1%. These results suggested that the blank adjustment, which was made with unfiltered distilled water, was influencing the slope of the instrument-response curve. To show the effect of a high blank, standard 4 was substituted for the distilled water as the blank, and, as before, standard 38 was made to read 38.0. Table I11 indicates the measurements taken. It is evident that the high blank caused a tilting of the instrumentrresponse curve about the value of the standard chosen for setting the instrument sensitivity.
DISCUSSION
The null method of operation was used in preference to the direct-reading method because, even a t the normal sensitivity, it was twice as sensitive as the direct-reading method a t full galvanometer sensitivity. For example, standard 38, which could be
Table 111. Readings Obtained Using Repeated Adjustment of Instrument Sensitivity at Normal Value with Standard 38 and Standard 4 Used as Blank Nominal Value of Standard 4 0.0 9 7.0 18 19.2 37 42.2 78 89.4
Individual Readings 0.0 0.0 0.0 7.4 6.9 7.4 18.6 18.4 18.2 42.2 42.2 42.4 90.9 90.4 90.9
Average 0.0
7.1 18.6 42.2 90.2
...
7.2 18.6 42.2 90.4
CoefStand- fioienb ard of DeviVariation ation
...
0.23 0.37 0.09 0.62
...
3.2 2.0 0.2 0.7
Table IV. Readings Obtained Using Two-Standard Method for Establishing Instrument Sensitivity and Hypothetical Blank (Each group of readings taken at normal sensitivity on different days) Nominal Value of Group Standard A 4 9
B
I8 37 78 4 9
18
37 78
4.0 8.9 19.9 41.7 85.2 4.3 9.5 20.6 41.7 85.4
Individual Readings 4.2 4.1 4.4 9.4 9.2 9.3 19.9 20.2 20.1 41.9 4 2 . 0 41.9 85.6 85.4 85.6 3.9 4.6 3.9 9.4 9.1 9.1 20.4 20.1 2 0 . 0 41.8 42.2 42.1 85.8 85.9 86.3
Average 4.6 4.3 9.9 9.3 20.4 20.1 42.4 42.0 85.4 85.4 3.6 4.1 9.3 9.3 19.9 20.2 4 2 . 4 42.0 85,Q 85.9
Standard Deviation 0.24 0.36 0.21 0.26 0.17 0.39 0.18 0.29 0.29 0.32
Coefficient of Variation 5.6 3.9 1.1 0.8 0.2 9.5 1.9 1.4
0.7 0.4
V O L U M E 2 7 , NO. 3, M A R C H 1 9 5 5
461
adjusted to read 38.0 by the null method, gave a maximum value of only 20.3 by the direct-reading procedure; after 0.5 hour oj instrument operation, the maximum reading was 16.6. Only when the null method was used a t the 3X sensitivity (standard 38 made to read 114.0) was maintenance of the sensitivity difficult, owing to the downward drift of the readings. The cause of this drifting was not investigated, but it was noted that an initially high maximum value could alwavs be obtained after the instrument had been inoperative for a short time. A comparison of the instrument with three other Model 7 Photonephelometers was made, using standard 38 and the null method of operation. Each instrument had a widely different inherent maximum sensitivity. The instrument used in this study proved to be capable of four times the sensitivity of one of the instruments tested. The condition of each instrument was not investigated, but each was relatively new and apparently undamaged.
’i 60
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lnftmiy oi 90.-scmer8d In Arbitrary U n l h
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Figure 1. Hypothetical instrument-response curves established with standard 38 at normal sensitivity _ _ _ Ideal curve obtained with zero blank
- Effect of unknown blank; ard 38
not subtracted from stand-
- - _ _Effect of subtraction of known blank from standard 38 It is evident from the tables that the nominal values of the standards as assigned by the manufacturer are not exact. Obviously, standard 37 had a greater light-scattering power than standard 38, which was used to adjust the instrument. Thus, correlation of data, even within a particular laboratory, will be poor if the instrument sensitivity is adjusted with different standards without regard for their true values relative to one another. The linearity of the instrument-response curve has been assumed without investigation, and subsequent use of the instrument with chemical systems ( 4 ) has brought forth no reason to doubt this assumption. One year after the data in Table I V were taken, a replication of the work was done with the same five standards. The average values obtained were 3.8, 9.1, 20.5, 42.1, and 84.5, respectively. For each standard, a “betm-een and within treatments” analysis of variance (6),involving all the data used to obtain the three averages-for example, the averages 20.1, 20.2, and 20.5 for standard l&showed no significant difference between themi.e., the probability was greater than 5% that variations were due to chance alone. The standards used above had been in frequent use by several workers during the 1-year interim period. This indicates the very satisfactory stability of t h e Coleman Nephelos standards.
I n order to limit the instrumental variability to a minimum, the light-scattering power of the blank must be known relative t o the standard used to establish the instrument sensitivity. The dashed line in Figure 1 represents an ideal instrument-response curve a t IX sensitivity as obtained with standard 38 and a blank with zero scattered-light intensity. The full line in Figure 1 shows the effect of using a blank, the value of which is assumed to be unknown and therefore cannot be subtracted from standsrd 38. As in Table 111,where standard 4 was used as the blank, the slope of the curve has been increased. Because of the negative intercept, samples with light-scattering abilities less than those of standard 38 have readings which are lower than those on the ideal instrument-response curve, whereas those with more light-scattering ability are higher. -4s indicated by the dotted line in Figure I, the subtraction of a known blank from standard 38 has the effect of “nulling” out its light-scattering power without changing the sensitivity (slope) of the instrument. Unfortunately, in chemical systems, a prior knowledge of the value of the blank relative to the standard used to establish the slope of the instiument-response curve is unavailable. As shown in Table IT, slight variations in the turbidity of distilled water caused significant changes in the sensitivity setting. ‘The procedure, using two standards to establish the instrument-response curve as described for Table IV, is really a method for defining a hypothetical blank the value of which is unknown but constant with respect to standard 38. Later work (4) with optically clear solutions, which were obtained by filtration, showed this hypothetical blank to be essentially zero. In order to show that the separate variances (square of standard deviations) calculated for each standard might be combined to provide an estimate of the instrument error, the Bartlett test ( 5 ) for the homogeneity of variances was applied to the data in Table IV. This test indicated that, regardless of the level of the light-scattering ability of the standards, the variances did not 821. T h e r e differ significantly among themselves [P%(XO) fore the standard deviations in Table IV were pooled, and provided an estimated standard deviation for individual measurements of 0.28 reading (or Nephelos) units a t the normal (1X) instrument sensitivity. In general, the instrumental variability is independent of the level of turbidity being measured, and depends upon the p r e cision with which the slope of the instrument-response curve can be established. However, as indicated by the coefficients of variation shown in the tables, the percentage of error contributed by the instrument depends upon the level of turbidity being read. Where the instrument sensitivity was three times the normal value, an improvement in precision was achieved in the measurement of very low turbidities a t instrument sensitivities greater than normal. However, for turbidities with values greater than 10 Nephelos units a t 1X sensitivity, no particular advantage seems to accrue from the use of greater sensitivities than normal. ACKNOWLEDGMENT
The authors are grateful to Mallinckrodt Chemical Works and to the Atomic Energy Commission for partial support of thL work. LITERATURE CITED (1) Coleman Instruments, Inc., RIaywood, Ill., “Operating Direc-
tions for Model 7 Coleman Photo-Nephelometer,’’ Bull.
D-199 (1948). (2) Ibid., Bull. D-199A (September 1951). (3) Humes, C. H., Ind. Lab., 3, No. 11 (1952).
(4) Keily, H. J., and Rogers, L. B., submitted to ANAL.CHEM. (5) Villars, D. S.. “Statistical Design and Analysis of Experimenta for Development Research,” Wm. C. Brown Co., Dubuque.
Iowa, 1951. RECEIVED for review July
29, 1954.
Accepted November 9, 1954.
