Table Ill.
421 105 21 1 31 6 42 1
Error in Quantitative Estimation of Silver
04002.1 057 040 1 3 1 0 1 4
22
1 9
2 7
109 5 4 6 2 4 3
5 2
5 3 4 6 6
7 8 9 2 4
Beer’s law. In tlie case of the 1-hour readings, concentration is the only variable which is significant with respect to error. In the cnsc of the 24-hour Samples, dithiol batch is another significant variable. The variance due to error is miich larger in the case of the 1-hour readings than in the case of the 24-hour readings. This is probably due to the fact that in the 24-hour case we are reading absorbance a t a peak, which is not true of the 1-hour readings (Figure 2). On the other hand, the fact that dithiol batch becomes a significant variable in the 24-hour solutions tends to cancel out the apparent increase in precision gained by waiting the longer time. The error variance shown in the analysis of variance table refers to the error in determination of absorptivity. Analytical chemists will be more concerned with tlie error in determination of silver concentration. This was estimated in the following way. Since the dithiol complex does not obcy Beer’s law, a calibration curve must bc constructed to relate absorbance t o concentration. This was done by plotting the mean absorbance of the four determinations a t each concentra-
-
~,k, qc-5 -;
Figure 3.
Calibration curves
tion level against concentration and estimating the best curve through these points. The curves for the two sets of readings are shown in Figure 3. Next, the concentrations corresponding to the individual absorbance readings were read off the calibration curve. This resulted in four estimated concentrations corresponding to each known concentration. The standard deviation was calculated for each set of four estimated concentrations, using the known concentration as the mean and four degrees of freedom, since the mean is known and not calculated from the samples. The relative standard variation was also calculated by dividing the standard deviation by the mean and multiplying by 100. Results are shown in Table 111. The absolute standard deviation increases with increasing concentration, while the relative standard deviation is relatively constant. The mean of the
five coefficients in Table I11 was chosen as the best estimate of the relative standard deviation and hence the precision of the method. This was 6.4% for the I-hour samples and 5.470 for the 24hour readings. LITERATURE CITED
(1) Cave, G. C. B., Hume, D. N., A N A L . CHEW25, 1503 (1952). (2) Clark, R. E. D., Analyst 62, 661 (1937). (3) Ibid., 83, 396 (1958). (4) Clark, R. E. D., Neville, R. G., J. Chem. Edztc. 36, 390 (1959). (5) Farnsworth, M., Pekola, J., ANAL. CHEM.26, 735 (1954); 31, 410 (1959). (6) Feigl, F., 2. anal. Chem. 74, 380 (1929). (7) Sandell, E. B., “Colorimetric,, Determination of Traces of Metals, 2nd ed.. D. 544. Interscience. New York. (8) I b d . , p. 549. RECEIVEDfor review August 31, 1960. Accepted November 23, 1960.
Ebulliometric Apparatus for Studying Number-Average Molecular Weights of Polymers CLYDE A. GLOVER and RUTH R. STANLEY Research laboratories, Tennessee Easfman Co., Division of Easfman Kodak Co., Kingsport, Tenn. An ebulliometric apparatus was needed, which would be simple to operate and would enable rapid, accurate, and reproducible measurement of the boiling point elevation of dilute polymer solutions. The apparatus consists of an ebulliometer of the Menzies-Wright type combined with an 80-junction, copper-constantan thermopile, which serves as the temperature-sensing element. The output of the thermopile is ‘fed through a d.c. microvolt amplifier to a strip chart recorder, where it is continuously
recorded. The sensitivity of the temperature reading is of the order of 0.015 millidegree. Use of the apparatus to obtain data for calculating, by conventional methods, an ebulliometric constant and the molecular weight of a polymer is illustrated. A limited statistical study is given to indicate the precision of the method.
R
field of polymers has resulted in an increased desire for an understanding of the factors APID growth in the
which influence the physical nature of these materials. One of the most important of these factors is the numberaverage molecular weight. Bonnar, Dimbat, and Stross (4) recently published a thorough review of the methods for determining this property. Four general methods have been used: ebulliometry (11, 12, 15), cryoscopy ( l ) , osmometry (3, 8, 14-16)’ and vapor pressure lowering (1.3). Each method, however, has certain known disadvantages or limitations. After consideration of these methods VOL. 33, NO. 3, MARCH 1961
447
and their limitations, ebulliometry seemed to offer the best opportunities for further refinement and simplification. The object of this norb, then, was to develop an ebulliometric apparatus that 11ould be simple to operate and capable of giving accurate and reproducible values for the boiling point elevation produced by dilute polymer solutions. Significant iniprovemcnts in ebulliometric techniques have been made sincc Beckman's (9)publication in 1889 on the measurement of boiling point elpvation. More recently, electrical devices surh as thermistors (5, 9) and thermopiles (11, l a ) , usually used in a differential manner, have replaced the vapor pressure thermometers suggested by llenzim and Kright (10). In this work. a lIenziPs-Wright type of ebulliometer and an 80-junction thermopile were combincd nith a stable recording electrical systcni to giw an apparatus with 11hich a laboratory technician can make measurements from which a p o l p r r molecular weight can be calculated in approximately 4 hours nith no more than 1 hour of actual operator time.
sever:il Iiwt input valucs to check the purity ot the solvent and the performance of the apparatus. Following this. several successiw portions of tristearin (Eastman grade, crystallized from toluene, melting point 72" C.) were added and the elevation produced by each was recorded a t the same heat input value used to establish the zero line. E.m.f. values nere obtained by visual averaging of the recorder chart readings a t the final heating rate. The value for the constant x a s obtained hy Equation 1. - , (solute) X A e.m.f.
Thermopile
c -
Figure 1 .
Ebulliometric apparatus
Measurement of the thermopile output is simplifird by use of a direct current microvolt amplifier (Leeds & Sorthrup stabilized d. c. microvolt amplifier Xo. 98358). The signal from the amplifier is recorded continuously with a strip chart recorder (0- to 5-mv. Speedomax). PROCEDURE
APPARATUS
The ebulliometei section of the apparatus is showi in Figure 1. Its design is based on that described by Rsy (If) ; however, several changes were made : The ground-glass joint was eliminated from the bottom of the apparatus; provision was made for draining the apparatus by use of vacuum and a hypodermic probe; and the vacuum jacket was replaced with a vapor jacket (not shown), which normally contains the same liquid as that used in the ebulliometer. The vapor jac.kf)t and the ebulliometer are connected to prevent prewure differentials, and the system is vented to the atmosphere through a 20-liter surge tank and a 4-foot section of 0.3-mm. capillary tubing. Boiling is induced in the ebulliometer by a 5.5-ohm (measured a t 110" C.) heater containing approximately 6 feet of S o . 30 (B & S gage) platinum wire coiled on a helical glass core of I-mm. borosiliratc glass rod. The hentcr is operated from a 12-volt a x . source through a variable transformer. During opcratiori, the cntirc apparatus is cowrcd n-ith aluminum foil, n liii.11 acts as a shirk1 for both lieat and light. The temperature-scnsing dement is an 80-junction, copper-constantan thermopile which is made from 0.001 5-inchdiameter wire insulated with a synthetic oleoresin. The method and twhniques used in construction of the thmnopile are described in detail in another paper ( 7 ) . The s i r e for the leads leaving the ebulliometer is the same as that used in the thermopile. \\lien the thermopile i q placed in the ehulliometcr, each set of junctions is cmhedded in w r y fine glass beds. n-hich act as a heattransfer medium while holding the junctions in a fixed position. 448
ANALYTICAL CHEMISTRY
Optimum operating conditions were established for the ebulliometer and the solvent to be used by finding the solvent volume which gave the best pumping action of the Cottrell pump and the heating range over which the thermopile output was constant. These two factors are interrelated to some extent; however, the solvent volume which gave good pumping at the lowest heat input was used. I n this particular apparatus, use of 15 ml. of solvent and a heat input range of 5 to 20 watts gave good operation. Once established, these conditions remained constant. Next, to relate boiling point elevations, as indicated by increases in thermopile output, to molecular weight. a constant, K,, was established for the ebulliometer and the solvent by measuring elevations produced by several portions of n c-ompound of known molecular weight. As Figure 2 shows, a "zero" line for the solvent (Eastman-grade toluene , rcdistilled) was recorded a t
wt. of solute (mg.)
The numerical value of K , as determined ten times within the concentration range to be used in numberaverage molecular weight determination-Le., below approyimately 0.003 molal. These determinations gave an average value of 1107 with a standard deviation of 1.4%. After operating conditions and K , were established, the ebulliometer was mashed by boiling with several fresh portions of solvent. The apparatus xtts then ready for use in molecular weight determination, e x e p t for a preconditioning step which physically prevents adsorption of the sample on the surface of the ebulliometer. A 100-mg. portion of the sample t o be determined was added to the ebulliometer and the boiling point elevation recorded as in the caw of tristearin. \Then equilibrium was reached, the c.bulliometer was emptied and fresh solvent was added without washing the apparatus. To determine the number-average molecular weight of a polymer, several portions of the sample, usually totaling 100 to 300 mg. depending on the molecular weight, were added successively to the preconditioned ebulliometer and the elevation produced by each was recorded (Figure 3). The irregularities which appear in the recording a t the higher heat input values were possibly caused by foaming and suprrheating of the solution. The e.m.f. values a t the final heating rate were used in all calculations. To relate these elevations to molecular weight, the change in e.m.f. per milligram !vas plotted against the weight (in milligrams) of each portion of the
w
Time ____) Figure 2.
(1)
E.m.f. chart for tristearin in toluene
sample added. The curve was then extrapolated to zero concentration. Such a plot is shown in Figure 4. The number-average molecular weight was obtained from this intercept by Equation 2.
I
2 RESULTS
The number-average molecular weights of over 300 polymer samples, chiefly polyethylenes, were determined. The values varied from a few hundred to about 75,000. Limited studies of precision were made a t only three molecular weight levels (Table I). A statistical consideration of these data indicated that the precision a t each of the levels studied was practically the same. The precision should logically decrease as molecular weight increases. This apparent anomaly could be the result of differences in homogeneity of the samples and should not be expected to hold in all cases. DISCUSSION
The importance of the heating rate is shown by the fact that the apparent boiling point of a solution is more sensitive to changes in heat input than is that of the pure solvent. Further, this effect varies for different solutions. To eliminate errors which might be introduced in this way, a series of decreasing heat input values is used for each boiling point measured. Values for the boiling points of all solutions involved in a determination are then taken a t heating rates below which any of the solutions are sensitive to heat input. There is some doubt as t o the numerical validity of the ebulliometer constant, K,, when established by the use of tristearin because of a "solute effect" previously noted in this laboratory (6). Observations indicated that the magnitude of K , (or Kb) for some solvents was dependent upon the molecular weight and the nature of the solute used to establish the constant. Any error introduced by the use of tristearin, however, is constant. The need for preconditioning the apparatus was shown by evidence that, in some cases, the polymer was adsorbed to some extent on the glass surfaces of the ebulliometer. In this way, the effective weights of early portions of the sample were reduced. Apparently, with this apparatus, 100 mg. of any polymer is sufficient to "saturate" the surfaces involved. This phenomenon is being more thoroughly investigated. In the meantime, the preconditioning step is recommended. Consideration of the data obtained
w
13.0~~.
Time Figure 3.
Emf. chart for polyethylene in toluene
with this apparatus gives a choice of several methods of treatment, all of which are discussed by Bonnar, Dimbat, and Stross (4). Since one of the aims of this work was the simplicity necessary for routine operation, however, a graphic solution, and that in its simplest form, was used in this study. Although i t is not essential to the use of the method, it is of interest to consider the magnitude and accuracy of the temperature measurements involved in this work. The electrical system of the apparatus was calibrated with a Leeds & Northrup Type K-2 potentiometer. Experience has shown that the e.m.f. can probably be read to 0.05 pv., which, based on the reported output of a copper-constantan junction, is 0.012 millidegree, and certainly to 0.125 pv. or 0.030 millidegree. These values refer to accuracy in e.m.f. (or temperature) reading and not to over-all accuracy of the determination. From these calibration data the total elevation of 24.6 pv. obtained in the example shown in Figure 3 represented a total elevation of 0.006" C. The most sensitive temperature readings reported to date for this type of work are 0.015 millidegree by Smith (It?) and 0.02 millidegree by Lehrle and Majury (9). CONCLUSIONS
The increase from a 20-junction thermopile, as described by Ray ( I I ) , to an 80-junction thermopile makes possible a greater sensitivity in temperature measurement. The increased thermopile output enables the use of a commercially available amplifier and recorder, and this stabilized electrical system gives a continuous record of the data. These changes have resulted in an ebulliometric apparatus that is equal in sensitivity to those previously reported and is simple in design and operation.
I
0 04 ' 0
,
1
50
100 150 Mg. Polyethyleoe/lS
1
1
1
200
250
300
MI. Toluene
Figure 4. Relation between boiling point elevation and concentration of polyethylene in toluene
Table I. Precision in Determination of Number-Average Molecular Weights of Polyethylenes in Toluene
Detn. No. 1 2
3 4 5
18,600 17,100 18,600 18,700
19,100
, 22 ,400 25,000 26 , 100
24,400 25 ,200
34,500
32,800
34,200 34,500
35,400
6 17.600 7 17,500 34,280 18,170 24,620 Av. 1,386 942 756 Std. dev. or 4.2y0 or 5.6y0 or 2.7%
ACKNOWLEDGMENT
The authors express appreciation to
D. C. Sievers for his interest and suggestions; to L. D. Moore, Jr., and J. E. Guillet for their cooperation in supplying polymer samples and assisting in evaluation of the data; and to K. W. Reeser for the glass work necessary in the study. VOL. 33, NO. 3, MARCH 1961
449
(6) Glover, C. A., Hill, C. P., Ibid., 25, 1379 (1953). (7) Glover, C. A , Stanley, R. R., lbid., 33,477 (1961). (1957). (8) Harris, I., J . Polymer S C ~ 8, . 353 ( 2 ) Beckman, E., 2. Physak. Chenz. 4, 532 (1952). 11889). (9) Lehrle, R. S., Majury, T. G., Ibid., ( 3 j Billmeyer, F. W.,Jr., J . Am. Chem. 29. 219 11958). SOC.7 5 , 6118 (1953). (10) ’Rleneies, A. IT. C., Wright, P.L., Jr., (4) Bonnar, R. U., Dimbat, U.,Stross, J . Am. Chem. SOC.43. 2314 (1921). F. H., “Sumher-Average Molecular (11) Ray, N. H., Trans: Faraday SOC.48, Weights,” Interscience, Sew York, 1958. 809 (1952). (5) Dimbat. 11.. Stross. F. H.. A I ~ A L . . ,CHEJI. (12) Smith, H., Ibid., 5 2 , 406 (1956). 2 9 , 1517 (195‘7). LITERATURE CITED
(1) Ashley, C. E., Reitenour, J. S., Hammer, C. F., J . ilm. Chem. SOC. 7 9 , 5086
(13) Tremblay. R., Sirianni, A. F., Puddington, J. E., Can. J . Chem. 36, 725 (1958). (14) Trementozzi, Q. *4., J . Polymer Sci. 23,887 (1957). (15) Tung, L. H., Ibid., 24, 333 (1957). (16) Uberreiter, K., Orthman, H. J., Sorge, G., Xzkrornol. Chem. 8,21(1952). RECEIVED for wview August 3, 1959. Resubmitted December 5, 1960. hccepted December 5, 1960. Division of Analytical Chemistry, 135th Meeting, iZCS, Boston, Mass., April 1959.
Spectrophotometric Determination of Microgram Quantities of Vaporizable Water from Solids Using Karl Fischer Reagent DUMAS A. OTTERSON lewis Research Center, Nafional Aeronautics and Space Adminisfrafion, Cleveland, Ohio
b Karl Fischer reagent is used as the basis of a colorimetric method capable of 0.5-pg. sensitivity at 475 mp for the determinaiion of water. Water in a solid is determined after its isolation by heating in a stream of dry nitrogen, collecting in a cold trap, and transferring to the reagent. Results of water determination in BaClz. 2Hz0 samples containing 1 1 to 26 pg. of water show that the average error is about 2 pg.
D
a n investigation a t the Lewis Research Center of the Xational Aeronautics and Space Administration, i t became necessary t o determine the amount of water adsorbed on salt crystals. Recent literature contains methods for the determination of water that appear to be very sensitive, S e s h (9) used methylene blue as a color reagent to determine as little as 30 pg. of nater in mineral oil. An attempt to adopt this reagent for our purposes produced insensitive results due to a necessary modification-namely, the suspension of methylene blue in dry acetone. The sensitivity of Karl Fischer titrations has been increased by Meyer and Boyd ( 7 ) to about 5 p g . for liquid samples and by Bastin. Siegel. and Bullock ( 2 ) to 3 p g . Bruckenstein ( 3 ) measured the n-ater in acetic acid by adding and measuring the amount of acetic anhydride that reacted spectrophotometrically. H e determined about 90 Mg. of water. Keidel (5) developed a n extremely sensitive method based on the electrolysis of water that is especially suited to steady-state conditions and that can be used to determine as little water entering the system as 7 X IO-* 450
URING
0
ANALYTICAL CHEMISTRY
gram per minute. Armstrong, Gardiner, and Adanis ( 1 ) used this method to determine microgram quantities of water in paper. However, their calibration curve shovied a number of points that are in error as much as 9 pg. Sivadjian (10) presented a unique method for the determination of water called hygrophotography. As yet, we have not been able to appraise its value for the purpose a t hand. This paper gives a method in n hich Karl Fischer reagent is used as a color reagent by measuring the change in absorbance that accompanies its reaction with water. The sensitivity is 0.5 pg, of water. I n addition, a method is presented in which water can be transferred from a solid sample to a collcction apparatus from nliich it can be accurately transferred for measurement. The method is trsted using BaCl? 2H20 as a standard. The main difficulty encountered in this work is the exclusion of c.;tranrous v,-ater while the sample is added to the system, but this would be encountered in virtually every method of similar sensitivity. Some of the difficulties n-ill be described in detail n i t h the hope that the reader may gain sufficient insight to solve the unique problems presented by his work. SPECTROPHOTOMETRIC METHOD FOR WATER
The color change of Karl Fischer reagent from reddish brown to yellon. has been used to indicate the end point of its water titration (8). This color change might also be used as the basis of a colorimetric method in which the change in color intensity that accompanies a minute nater addition is meas-
ured. Preliminary tests with diluted reagent readily indicated that this color change is eytreniely sensitive. The need to protect the reagent JTas indicated by the fact that the reagent in an unprotected absorption cell was completely converted to the yellow color (in about 5 minutes) by the water absorbed from the air. Sleeved rubber stoppers for serum bottles have been used to protect Karl Fischer microtitrations (6). Experience a t this laboratory shows that these stoppers can adequately protect the contents of an absorption cell containing Karl Fischer color reagent. The use of hypodermic syringes and needles permits addition of the reagent and the water to be determined to such stoppered cells. It mas very difficult to add color reagent to the color cell in such a way as to repeat the absorbance reading. TYater on the vialis of the color cell, the stopper, needles, and syringe rarely appeared to be the same for subsequent color reagent additions. This difficulty suggested the techniques used in this work. A known volume of color reagent was added to a stoppered color crll. K h e n the w t e r in the cell had reacted completely, the absorbance was recorded. The water to be studied was then added. The cell was shaken and the absorbance measured. The change in absorbance depends on the amount of water added. Apparatus. A Beckman Model B spectrophotometer is used t o make the absorbance measurements a t 475 mp. Color cells with the usual square opening and a 1-em. path are used. The contents are protected from airborne water (Figure 1) with a sleeved rubber stopper for a serum bottle
