termination of oxygen in niobium showed that baths containing from 25 t o 75y0 nickel yielded good results. A similar study on tantalum showed that baths containing from 25 to 5070 nickel gave good results, the bath to sample ratio in each case being approximately 1O:l. In both cases, the range of the results was far more satisfactory in the case of the mixed bath than with platinum alone. Though nickel alone tends to volatilize a t temperatures above 1800' C., the platinum-nickel bath shows no signs of volatilization until 2200O For analysis of vanadium, niobium, and tantalum, a 40% nickel bath was prepared and used with the platinum flux method. Studies on the bath to metal ratios necessary for the use of this bath are shown in Figure 1. The minimum bath to metal ratio for vanadium is 1:1, for niobium, 5:1, and for tantalum, 6 : l . The bath to metal ratios were maintained by periodic addition of nickel with subsequent outgassing. The use of the platinum-nickel bath nermitted the analvsis of 25-30 metal samples, before it" was necessary to change the crucible, which was approxi-
c.
mately double the number analyzed with platinum alone. There is, however, little volume decrease between the platinum-nickel bath and the platinum alone, because of the lower density of the nickel. The increased number of analyses would appear to be caused by increased solubilit,y of the samples and graphite in the bath. Procedure. After the bath was outgassed and the system calibrated ( I ) , the crucible was preheated for 1 minute, the platinum-wrapped sample was introduced, heating was continued for 3 minutes, the power was shut off, the system was swept for 4 minutes, and the final oxygen content was calculated from the change in conductance.
p.p.m. of oxygen content in the sample, except for the higher oxygen values on tantalum metal. Multiple analyses of the samples showed a relative standard deviation for vanadium of about 3%, and a relative standard deviation of about 5% for niobium and tantalum.
RESULTS
(3) Elbling, P., Goward, G. W., Ibid., 32, 1610 (1960). ( 4 ) Kaliman,'S., Collier, F., Ibid., p. 1616.
The pentoxides of the Group V-A metals were analyzed and the results of these analyses are shown in Table I. A comparison of the results obtained by the vacuum fusion and by the inert gas fusion methods on the Group V-A metals is also given in Table I. As can be seen, the results were in good agreement in the range from 100 to 1000
ACKNOWLEDGMtNT
The authors thank V. A. Fassel and his coworkers for the vacuum fusion results. LITERATURE CITED
(1) Banks, C. V., O'Laughlin, J. W., Kamin, G. J., ANAL. CHEM.32, 1613
(1960).
(2) Beck, E. J., Clark, F. E., Ibid., 33,
1767 (1961).
(5) Potter, J. L., Murphy, J. E., Heady, H. H.,Ibid., 34, 1635 (1962). RECEIVED for review February 11, 1963. Accepted April 4, 1963. Division of An-
alytical Chemistry, 141st Meeting, ACS, Washington, D. C., March 1962. Contribution No. 1283 from the Ames Laboratory of the U. s. Atomic Energy Commission.
Semimicro Determination of Molecular Weight with a Dew-Point System ANGEL0 DE ROS, OLlVlERO FAGIOLI, and PIER0 SENSI Research laboratories, lepetit S.p.A., Milan, Italy
b A new method for the semimicro determination of molecular weight is described. The method is based on the fact that the observation of the dew point provides a very accurate estimation of the beginning condensation and of the ending evaporation of the solvent on a surface whose temperature varies slowly, in the presence of the vapor of the solution a t constant temperature. If a number of cells containing solutions of different molarities are used sirnultaneously with a common condensing surface, the disappearance of the various solvent films follows the order of the molar dilutions, even where the differences among the concentrations are very small. The method described presents the following features: ease of performance, possibility of repeating the measurements many times, good precision and accuracy, use of small quantities of substance (2 ml. of solution from 0.1 to 0.2M), quantitative recovery of the substance whose molecular weight has been determined, and the possibility of using substantially all the solvents having boiling points between 40' and 120" C. 1054
ANALYTICAL CHEMISTRY
M
is usually determined by methods based on the variation of the vapor pressure of a solution relative to the pure solvent (cryoscopy, ebullioscopy, isopiestic, osmotic methods), the determination of vapor density, or functional group analysis (1). The more recent ones, which are microscale methods, utilize improvements in temperature measurements, such as amplified thermocouples and thermistors with low thermal capacities, high speed, and sensitivities not previously attained. These methods are very useful because of the small amount of substance required, but are rather delicate (2-7). The problem of determining molecular weight using small quantities of substance is very important in organic chemistry, and in spite of the considerable amount of work cited, the problem seems not yet definitely solved. In this paper a new method, based on vapor pressure lowering of a solution, is described which can provide, in a semimicro scale, an easy and quick determination of molecular weight with good accuracy and with the possibility of using a very large number of solvents. The method is based on the fact that OLECCLAR WEIGHT
the observation of the dew point provides a very accurate estimation of the beginning condensation and of the ending evaporation of the solvent on a surface whose temperature varies slowly, in the presence of the vapor of the solution a t costant temperature. If a number of cells containing solutions of different molarities are used simultaneously with a common condensing surface, the disappearance of the various solvent films follows the order of the molar dilutions even where the differences among the concentrations are very small. EXPERIMENTAL
Apparatus. The apparatus is shown schematically in Figure 1. The cell block, A , is formed by a cylinder of copper electrolytically plated with platinum, 10 cm. in diameter and 3 cm. high. The six cells on the top surface are 2 cm. in diameter and 1 cm. deep, and are placed a t the corners of a regular hexagon. The center of each cell is 3.2 cm. away from the axis of the block. To the undersurface of the block, a 1-watt heater, B , is screwed. The ground-glass disk, C, is 12 cm. in diameter and 0.23 cm. thick, with plane parallel surfaces. The bottom
surface was carefully ground with 3micron grain corundum. The aluminum disk, D,is 10 om. in diameter and 0.5 em. thick, and is connected by an arm to an externally rotatable spindle, E. The assembled apparatus, Figure 2, shows the relative positions of the components. The differential thermocouple, H , whose two elements are connected to the block, A , and to the disk, D, is a copper-constantan one which gives an e.m.f. of about 38 pv. per OC. and has a resistance of 4 to 5 ohms. The e.m.f. of the thermocouple is amplified by a driftless d.c. amplifier (not shown). A Anorescent lamp is arranged so that the halos on the ground glass are easily visible. The apparatus, except for the latter two components, is enclosed in a thermally insulated polyethylene vessel with a transparent Plexiglas cover. Materials. All solvents and solutes used in this study were C. Erba pure products. Analytical checks were in agreement with the literature data for the pure products. Procedure. Five solutions of the chosen standard substance in the appropriate solvent are prepared. Usually these are 0.20, 0.17, 0.14, 0.11, and 0.08M. Two milliliters of each are introduced into five of the cells in order of their molarity. The solution containing the substance of unknown molecular weight is introduced into the sixth cell. The unknown molarity must he within the range o? the five known ones. The ground surface of the glass disk is attached to the cell block by placing silicone grease spots on three small symmetrical areas on the edee of the block. The heater is then sGtohed on, and the temperature of the block slowly and uniformly rises to a temperature slightly above room temperature. The temperature difference, At, between the heated block and the cooling disk for obtaining the best measurements depends mainly ~~~~
~~~~~
~~~
~
~~~~
~
n
At a uniform temperature and a t
Figure 1 . Schematic diagram of the dew-point apparatus for determining molecular weight
~~
A.
Cells bearing platinum-plated copper block 1-Wall electric heater C. Ground-gbrr dirk 0. Aluminum cooling disk 8.
on the boiling point of thesolvent (b.p.). The following formula has been found empirically, and it is useful for solvents boiling in the range 40" to 120" C. and a t a room temperature between 18' and 25' C. : At = (0.0147) (b.p.) - 0.347
equilibrium, in each cell the solvent is not present outside of the solution because its vapor pressure is greater than that of the solution. The solvent can be present in equilibrium with the solution only when its temperature is such that its vapor pressure is equal to that of the solution. To obtain this condition, the cooling disk is carefully put on the glass, with the external knob, and after 15 seconds it is raised and returned to the rest plate. Condensation halos of the solvent appear on the glass in correspondence to the cells and will tend to disappear as the glass disk gradually returns to the temperature of the block (Figure 3). From the time of disappearance of the first halo, corresponding to the solution of highest molarity, begin the measurements of the time of the consecutive disappearances of the other halos. If At has been appropriately chosen, the maximum disappearance time varies from 3 to 15 minutes except for the highest boiling solvents used (water, butanol) for which the time may be as much as 40 minutes. The halos can be made more visible if some form of appropriate lighting is provided and a lamp can accordingly be placed outside the vessel; reflections of light can be prevented by a black scrcen placed on the Plexiglas cover. The disappearance times of the solutions of standard molarities are plotted against the molarity values;, the disappearance time of the solution of unknown molarity, reported on the graph, will give by interpolation the value of molarity (Figure 4). If the order of the molecular weight to he determined is completely unknown, preliminary tests can be made to find out the appropriate concentration range. For that, three standard solutions having molarities of 0.20, 0.10, and 0.05 are placed in three of the six cells, and the other cells are provided with solutions of the unknown product in concentrations varying by a known factor-for instance, 2. The described procedure is repeakd several
............
Figure 2.
Main part of the dew-point apparatus
E. Spindle connected with the external knob F. Rest support for cooling dirk G. H.
Plexiglas bare Thermocouple
Figure 3. Example of disappearance of condensates of six solutions of various molarities
....
.......
.
alcohol as solvent, and Table I1 gives the results for three substances using ethyl alcohol as solvent. The precision and accuracy data are also given in the tables. The relative standard deviation of the determinations is very low and the relative error for the molecular weights is in no case greater than 1.5%. The molecular weights obtained for some substances in other solvents are given in Table 111. For the most of them the relative error is less than 3%; only occasionally it is greater. As in these last cases the relative standard deviation is never greater than *2%, the fact that the relative error is greater than 3% can be attributed to phenomena of association. I n fact, these discrepancies lead to molecular weights greater than the theoretical ones. The sensitivity of the method depends mainly upon the smallest thickness of condensate which can be perceived on the glass disk. This thickness is approximately of the order of wavelengths in the visible range. Consequently, the amounts of heat required for evaporation and condensation are small, relative to the thermal capacities of the system, and therefore they cause substantially no disturbances to the regular pattern of heating and cooling of the glass. The thermal capacity of a glass disk weighing about 80 grams is
1000 v)
0
5u
-
MOLARITIES
900
w
v)
w'
800
EI-
-+-t-
700 \
\\
FOUND 0,1210 0.1225 0,1165 0,1200
I 0,1170
600 500 400 300
200
100
MOLAR CONCENTRATION Figure 4. Example of five determinations of molecular weight of benzophenone in ethyl alcohol For precision and accuracy data, see Table II
times with various concentrations of unknown product until the disappearance of a t least one of the halos of the unknown sclution occurs between two of the standard solutions. RESULTS AND
I.
Determination of the Molecular Weight of Some Substances in Methyl Alcohol a t Two Different Molarities
Standard reference substance: urea
DISCUSSION
Determinations of molecular weight of different substances were made using 10 different solvents-namely, water, methanol, ethanol, butanol, methyl acetate, ethyl acetate, acetone, carbon disulfide, chloroform, and benzene. An appropriate reference substance was used for each solvent: urea for the first four, phenanthrene for the next five and benzophenone for benzene. For each solvent, five solutions of known molarity varying from 0.2 t o 0.08 of the reference substance were prepared. The molecular weight found is the mean of five consecutive determinations except in the case of methyl alcohol and ethyl alcohol, for which five determinations a t one molarity (0.15) and five determinations at another molarity (0.12) were made. Figure 3 shows the curves for the determination of the molecular weight of benzophenone in ethyl alcohol (molarity 0.12) using urea as the reference sibstance. Table I gives all the values obtained in the determination of the molcwlar weight of three substance? at two differmt mo1aritit.i iising m ~ t h p l
1056
Table
ANALYTICAL CHEMISTRY
Substance
Theor.
Benzoic acid
0.150
Molarity Found
Theor. 0.1490 0.120 0.1475 0.1485 n. 1485
n
Mol. wt. 122.12 p-Nitrobenzaldehyde
147.5
0.1482 Mean Rel. std. dev. i l ,5% Mol. wt. calcd. 123.601.2% Rel. error
+
0.1495 0.120 0.1490 0.1510 0.1490
0.150
n imo
Mean 0.1497 Rel. etd. dev. 1.1Yo Mol. wt. calcd. 151.42 Rel. error +0.2%
Mol. wt. 151.12 Benzophenone
0.1510 0.120
0.150
0.1500 0.1510 0.1522
pnn .M_---
Mol. wt. 182.21
n. ifin7 n ifiin
Rel. std. dev. =!= 1.5Y0 Mol. wt. calcd. 181.01 Rel. error -0.7t5
Molarity Found 0.1195 0.1215 0.1210 0.1200 0.1215 0.1207 Mean Rel. std. dev. f1.3% Mol. wt. calcd. 121.41 Rel. error -0.6% 0.1205 0.1200 0,1185 0.1175 0.1235 Mean 0.1200 Rel. std. dev. =!= 1.8% Mol. wt. calcd. 151.12 Rel. error 0.0% 0.1237 0.1225 0.1220 0.1180 0.1218 0.1216
Mean Rel. std. dev. =!=l. ~ Y O Mol. wt. calcd. 179.80 Rel. error -1,370
Table II.
Determinaticn of the Molecular Weight of Some Substances in Ethyl Alcohol at Two Different Molarities
Substance Methylurea
3201. wt. 74.08
Tartaric acid
Mol. wt. 150.09 Benzophenone
Mol. wt. 182.21
Table 111.
Solvent Water
Standard reference substance: urea Molarity Molarity Theor. Found Theor. Found 0.1495 0.120 0.12001 0.150 0.1500 0.1190 0.1485 0.1175 1 0.1485 0.1175 0.1475 0.1165 Mean 0.1485 Mean 0.1181 Rel. std. dev. = k l . l % Rel. std. dev. f 3 . 0 7 o Mol. wt. calcd. 74.63 Mol. wt. calcd. 75.22 Rel. error +0.7% Iiel. error 1.5% 0.1510 0.120 0.1172 0.150 0.1520 0.1200 0.1525 0.1220 0.1525 0.1200 0.1475 0.1205 Mean 0.1511 Mean 0.1199 Rel. std. dev. f1.8% Rel. std. dev. 1 2 . 2 % Mol. wt. calcd. 148.99 Mol. wt. calcd. 150.09 Rel. error -0.7% Rel. error 0.0% 0.15C 0.1490 0.120 0.1210 0.1500 0.1225 0.1475 0.1165 0.1490 0.1200 0.1485 0.1170 Mean 0.1488 Mean 0.1194 Re]. std. dev. =!=3.0% Rel. std. dev. 1 2 . 3 % Mol. wt. calcd. 183.67 Mol. wt. calcd. 183.12 Rel. error +0.8% Rel. error +0.5%
+
Accuracy Data in the Determination of Molecular Weights of Some :Substances in Eight Different Solvents
Standard substance Urea
Butyl alcohol Methyl acetate
Urea
Ethyl acetate
Phenanthrene
Acetone
Phenanthrene
Carbon disulfide
Phenanthrene
Chloroform
Phenanthene
Benzene
Benzophmone
Phenanthrene
Molecular weight Solute Theoretical Found Methyl urea 74.08 76.4 Tartaric acid 150.09 160.1 Glucose 180.15 174.9 Methyl urea 74.08 74.5 210.22 Benzil 205.5 Benzoic acid 122.12 122.7 p-Nitrobenzaldehyde 151.12 155.2 Azobenzene 182.22 184.1 Benzil 210.22 216.1 p-Nitrobenzaldehyde 151.12 155.9 Benzophenone 182.21 183.7 Benzil 210.22 211.2 Benzoic acid 122.12 121.8 p-Nitrobenzaldehyde 151.12 156.4 Benzil 210.22 205.8 Azobenzene 182.22 188.4 Benzophenone 182.21 189.8 Benzil 210.22 218.1 p-Nitrobensaldehyde 151.12 153.2 Benzophenone 182.21 184.9 Phenanthrene 178.22 181.6 Benzil 210.22 212.7
Relative error,
Ye
+3.1 +6.7 -2.9 $0.5 -2.2 +O. 5 f2.7 +1.0 +2.8 +3.2 $0.8 +0.5 -0.3 +3.5 -2.1 $3.4 +4.2 f3.7 +1.4 +1.5 f1.9 11.2
approximately 15 to 20 cal. per "C.; mg., and the heat exchanged in the with the most unfrtvorable solvent distillation is 5 0.75 cal. such as water, the quantity of conFor an accurate determination, the densate-6 disks of Z-cm. diameter and cooling of the glass must be carefully 0.5 micron or less of thickness-is 125 controlled; over-cooling leads to the
formation of drops while, if cooling is poor, condensation could not happen. For an accurate measure of the temperature difference between the cellsbearing block and the cooling disk, a system of thin differential thermocouples is used. They are connected to an indicating instrument via a chopper amplifier and a lock-in detector which readily indicates temperature changes of the order of 0.05" C. The temperature difference between the copper block and the cooling disk has been standardized for the various solvents. The condensation and evaporation of thin films of liquid on a solid surface depend principally upon the nature of previous treatments of the surface. Cleanliness is extremely important and in the absence of this condition, the measurements give abnormal results. The ground glass must be in good contact with the block. This provides a hermetic closure and ensures that the temperature distribution over the glass during the thermal cycle is such that the solvent halo gradually and regularly decreases in diameter and disappears (Figure 2). The measurements can be easiIy reproduced on the same solutions as many times as desired and all the solutions can be recovered unaltered at the end of the experiment. The method has been applied to the determinations in the range of molecular weights below 500. S o experiments have been carried out for high molecular weight substances, but the range of concentrations used seems to indicate a limitation. ACKNOWLEDGMENT
The authors thank G. G. Gallo for helpful discussions and Sergio Terni for technical assistance. LITERATURE CITED
(1) Bonnar, R. U., Dimbat, M., Stross, F. H., "Number-Average Molecular Weights," Interscience, New York, 1958. (2) Dimbat, M., Stross, F. H., ANAL. CHEM. 29, 1517 (1957). (3) .Knight, A., Wilknis, B., Davies, D. K., Sicilio, F.. Ana2. Chim. Acta 2 5 . 317 (1961j. ' (4) Muller, R. H., Stolten, H. J., ANAL. CHEM.2 5 , 1103 (1953). (5) Newmayer, J. J., Anal. Chim. Acta 20, 519 (1959). (6) Simons, E. L., ANALCHEM.30, 979 (1958). (7) Wilson, A., Bini, L., Hofstader, R., Ibid., 33, 135 (1961). RECEIVED for review January 23, 1063. Accepted April 12, 1963.
VOL 35, NO. 8, JULY 1963
1057
