stein, H. J., C‘un. J . Chem. 35, 1060 (1957). (33) Ramsel-, S . F., Phys. Rev. 77, 567 (1950): 78, 699 (1950); 83, 540 (1951); 86, 243 (1952). (34) Reilly, c. -1, ; \ s a L C H E W 30, 839 (1958’1. (35) Saika, A Slichter, C. P.,J . Chem. Phys. 22, 26 (1954) (36) Tiers, G. 1- D J . Phys. Chem. 6 2 , 1151 (1‘358). ~
~
(37) Varian Associates, ,%SAL. CHEM.28, X o . 12, 23A (1956). (38) Ibzd., 29, S o . 9, lOlA (1957). (39) Ibzd., Yo. 12,,p. 45A. (40) Varian Associates, Technical Information Bull., Vol. I, S o . 3, 1955. (41) Killiams, R . B., ASTN Special Tech. Publ. 224, 168-94 (1958). (42) Williams, R. B., Ann. N. Y . Acad. of Sci., 70, Art. 4, 890 (1958). (43) Williams, R. B.,Molecular Spec-
troscop\ Conference of the Hidrocarbon Research Group of the Institute of Petroleum, London, Feb. 27, 1958; to be published by Pergamon Press and in Spectrocham. Acta.
(44) Zimmerman, J. R., Foster, 31. R , J . Phys. Chern. 61, 282 (1957) (45) Zimmerman, J. R., Lasater, J. A., rlSTI1.l Tech. Publ. 224, 195-203 (1958). RECEIVEDfor review Ma: 19, 1958. Accepted hugust 22, 1968.
Gas Analysis by Optical Interferometry DONALD N. HANSON and ARTURO MAIMONI’ Radiation laboratory, University o f California, Berkeley, Calif.
b The theory and experimental techniques used for analyzing mixtures of hydrogen-nitrogen and deuterium-nitrogen over the entire range of compositions are given. The optical interferometer i s a reliable gas analytical tool capable of yielding accurate results in binary mixtures, and the deviations from linearity of the data for index of refraction vs. composition can be adequately explained from molar refraction theory and the predicted deviations from ideal gas mixing behavior. The index of refraction for deuterium for white light is slightly smaller than that of hydrogen:
x
1.80
A
calibration of a n optical interferometer as a tool for gas analysis has been carried out. The work was done in connection with a n experimental program in which liquor-vapor equilibrium data were obtained for the system hydrogen-nitrogen (9) and deuterium-nitrogen ( I O ) , and it was desired to have gas analysis equipment for fast, accurate, routine analysis. The accuracy to which sample compositions was desired was better than 0.1% for the vapor samples and better than 0.05yo for the liquid samples. After a preliminary investigation of other analytical methods, such as Orsat techniques, velocity of sound, effusion, and thermal conductivity, it was established that the above lacked either accuracy or reliability. However, the possibility of using a n optical interferometer was apparent once the knom-n indices of refraction of the pure components were compared against the sensitivity limits stated by the manufacturer (Carl Zeiss, Jena). It was also known that the relation RATHER EXTEXSIVE
l Present address, Radiation Laboratory, University of California,Livermore, Calif.
between the index of refraction of a gas mixture and the composition is approximately linear, although it was not known if the linearity could be assumed to hold within 0.0370, as all previous data on mixtures are of lower accuracy and very few extend over the entire range of comparison. Edwards determined the sensitivity of his apparatus by filling both chambers with dry, carbon dioxide-free air and obtaining the interferometer reading while pressures were different in the two chambers ( 2 ) , This reading, together with the known index of refraction of air, gave him the desired value of interferometer sensitivity. He then prepared a carbon dioxide-air mixture containing 2.52% carbon dioxide, and found that the calculated index of refraction agreed with that found experimentally. h1ohr analyzed flue gases containing from 4 to 14% carbon dioxide for carbon dioxide and oxygen, calibrating his interferometer by standard gas absorption techniques (11). He declared his accuracy to be 50.5% and the index of refraction to be linear in this range. Cuthbertson and Cuthbertson measured the indices of refraction of mixtures of oxygen and ozone, analyzing their mixtures either by the volume increase upon decomposition or by chemical absorption ( 1 ) . The scatter in their data ran from 1 to 370, and the range of compositions investigated n-as limited to about 7y0ozone. The best values for the dependence of index of refraction on composition are those of T’alentiner and Zimmer (13). They measured the index of refraction of synthetic gas mixtures, which they made by measuring accurately the amounts of pure components and mixing thein inside their blending apparatus. Their data extend over the eritire composition range, with an average deviation of about 0.5%. They found a small deviation
from linearity for the system hydrogencarbon dioxide, which was almost completely masked by the scatter. Therefore, the assumption of linearity of variation in index of refraction with composition is seen to require a more careful investigation if uniform accuracies of the order of 0.03% are required. Actually, this study has shown that, for the systems investigated, small deviations from linearity do occur but can be predicted from the deviations from ideal gas behavior of the gas mixture. EXPERIMENTAL
Operating Procedure. The experimental procedure recommended by t h e manufacturer was modified t o allow the use of relatively small gas samples and application of vacuum techniques. The interferometer was connected to the vacuum system manifold and reference gas - cylinders as shown in Figure 1. The absolute calibration of the interferometer was obtained with monochromatic light of 5461 A. The calibration consists of obtaining the micrometer readings that correspond to the successive bands that pass through the ocular as the micrometer screw is rotated, and is usually expressed in the form of a calibration table in which values of the band number, h, are listed us. the corresponding values of R - Ro. where Ro is the reading corresponding to the zero-order band-obtained with white light when both gas chambers are evacuated. These readings correspond to equal increments in thickness of the compensating glass plate, and correspondingly to equal increments in index of refraction difference between the unknown and reference substances. Although the band-number calibration thus obtained holds only for a particular wave length of light, it can be used with white light if only a measure of equal increments in refractive index difference is required. The procedure for making a nieasurement is as follows. The system is first VOL. 31, NO. 1, JANUARY 1959
77
evacuatad until the thermocouple gages, 9 and 10, shorn a pressure smaller than 5 microns, a t which point the gas sample may be introduced into the system. The hydrogen content of the sample deteriiiines the reference gas and chamber to be used. Take the case of a sample that is known to contain about 507, hydrogen, and is to be read against nitrogen gas as reference. The sample is introduced into chamber L, for a gas of low index of refraction, while the reference nitrogen is introduced into chamber H , for a gas of high index of refraction. If the amount of sample is not sufficient to bring up the pressure in L to atmospheric pressure, additional gas may be pumped out from the line by manipulating stopcocks 2 and 3 and the mercury level in L. The pressure in the gas cell is shown by the height of the mercury column over the mercury seals, 11. When the gas is a t atmospheric pressure, and enough gas is left in L for the purging procedure that is t o be described, stopcock 3 is closed and the line is evacuated for admission of the reference gas into chamber H. Chamber H is filled by closing stopcock 1 and opening valve 7 by the reference nitrogen cylinder. When both chambers have been filled with gas, a waiting period of about 1 minute is allowed for the gases to reach approximately the same temperature in the gas cells. The pressure is then raised in chamber L by admitting mercury, until the gas bubbles out through the mercury seal. The pressure in L is now above atmospheric; the mercury qeal is lowered until the gas inside the chamber is directly connected with the atmosphere through the long glass capillary (about 1 mm. in diameter), which minimizes the diffusion of air into the interferometer tubes. The same procedure is repeated for the gas in chamber H , and a period of 2 minutes is allowed for temperature equilibration before the interferometer is read. The interferometer reading is obtained by lining up all the clearly visible bands of the upper spectra with the most prominent band of the reference spectra, denoted band 4 in Figure 2. For each of the successive bands in the upper spectra there is a corresponding reading which is identified by the subscripts 1, 2, 3, or 4,according to the relative intensity of the lines; 4 corresponds to the blackest line, 1 to the most colored, and 2 and 3 to intermediate degrees of blackness. The reading of any individual band is accomplished by rotating the micrometer screw (almays in the same direction t o minimize the possible effects of backlash in the mechanism). The above procedure is carried out for two reasons: t o compensate for possible errors in the absolute calibration of the interferometer, and to obtain a set of independent readings of the same quantity, readings which are later brought t o a common basis in the calculations. The distribution of color in the different bands of the upper spectrum is valuable in the identifica78
ANALYTICAL CHEMISTRY
Interferometer.
Thermocouple Vacuum G a g e
L
-
Reference G a s Cylinders
Figure 1.
Flow diagram of optical interferometer
tion of the zero-order band, as described below under band shift. After a preliminary set of readings is taken, the mercury is allowed to rise in chamber H , thus purging the gas in the gas cell with the gas contained in H. A new reading is taken on the zeroorder band. The same procedure is followed with the gas contained in reservoir L. This purging procedure allows for the detection of any lack of homogeneity of the gases in the chambers caused by incomplete evacuation, slow leak, diffusion, or, in the case of the calibration blends, incomplete mixing in the blending apparatus. While the reference and unknown gases are being purged, the necessary pressure and temperature readings are made. Aftcr the readings are taken, the mercury seals are raised until the tips of the capillary tubes are under mercury, and stopcocks 1, 3, and 4 are opened so as to pump out all the gas in the system. After the pressure has decreased to below 100 microns, a new reading is taken to establish the reading corresponding to the zero-order band when both chambers are evacuated. This zero reading is fairly constant, although it seems to be somewhat dependent on room temperature.
Band Shift. The use of white light permits easy identification of the zero-order inteiference band, whereas this identification is impossible to make with monochromatic light. For this reason white light is used almost universally when the interferometer is used for analytical purposes. However, owing to the difference in the dispersive powers of the glass in the compensating plate and the substances in the sample reservoirs, the distribution of energy in the upper spectra shifts gradually with increasing difference in index of refraction, changing the chromaticity of the different bands
until the zero-order band no longer corresponds to the two dips in light intensity that appear black but may be displaced from it by one or more bands-Le., the zero-order interference fringe is now colored. The position of the zero-order band was determined during the calibrations of the interferometer with gas blends of known composition, by purging the blend with reference gas while following the position of one of the bands by rotating the micrometer screw. For the above example, where the unknown sample was in chamber L , the procedure would be as follows. Stopcocks 1, 3, and 4 are closed after the introduction of the gases in the chambers. Valve 7 is opened until the reference gas pressure, indicated in the compound gage, is slightly above atmospheric. Valve 6 is closed and stopcock 3 opened. Valve 7 is opened. Then valve 6 is opened slightly while the movement of the bands in the interferometer field is followed. The band shift is established by the change in the relative color intensity of the band. Thus, for the above example, if the blackest band is followed, it will gradually become more colored, and when both chambers are filled with essentially the same gasreference nitrogen-the band will be found to lie one band to the left of the blackest band, which for this case is known to be the zero-order interference band. Figure 2 shows the pattern of relative color intensity of the different bands vs. composition and interferometer reading, and was used to determine the position of the zeroorder band for unknown samples. Similar plots were obtained for the hydrogen-nitrogen samples read us. reference nitrogen and for the deutcrium-nitrogen mixtures. This method of obtaining and plotting the band shift is similar to the one recommended by Karagunis et al. (6),and allows for the identification of the zero-order band regardless of how colored it may be.
This gives n2 - 1 rT nz+2 P
1v=--
(3)
which can be simplified by the introduction of e = n - 1
(4)
Since e is a very small quantity compared with unity (e = 299.8 X lop6 for nitrogen), its square can be neglected, so that we obtain -2 rT N=-e3 P
or P ,\,
*'\ \A.
30
1000
500
I500
INTERFEROMETER
Figure 2.
2500
2000
READING
e = - -3- N P 2 rT
I
,
30C3
The interferometer, however, measures
R
- e,)
h = a(e,
Band shift for hydrogen-nitrogen mixtures read vs. reference hydrogen
(7)
where Pressure and Temperature Measurement. Barometric pressure mas read on a Fortin-type U. S. Signal Corps barometer, and tabulated corrections provided by the manufacturer were made for temperature and local gravity. The error in the pressure measurement is of the order of AO.1 mm. of mercury. Temperature was measured by means of a copper-Constantan thermocouple, 5 feet of which were wound around the gas cells inside the interferometer case. with the assembly insulated with 2 inches of glass fiber. The latter made for very slow changes in the temperature of the gas cells, while the I\-inding of the thermocouple wire around the cells minimized the effects of thermal conduction along the thermocouple wire. The thermocouple mas read with a Type K-2 Leeds & Northrup potentiometer, and was calibrated a t the sodium sulfate point and against an NBS certified thermometer. The error in teniperature measurement was smaller than 0.01O
The above pure gases were mixed in a specially designed blending apparatus (3).
-
Sample Hydrogen Deuterium Nitrogen
A
0 2
...
0,004 0.004 0,004
o:o22
= interferometer sensitivity
h e, e,
= bandnumber = n - 1 for the reference gas = n - 1 for the unknown gas
THEORY
whereas we are interested in the values of
The equations used for data reduction in routine analysis are described here, as well as the equations relating the deviations in linearity of the index of refraction us. composition to the nonideal mixing behavior of real gases. Equations Used for Data Reduction. The Lorentz-Lorenz molar refraction is known to give, t o a good approximation, the changes in index of refraction with pressure, temperature, and composition, and was used t o reduce all the interferometer readings to standard conditions. It is defined by
ho = a K e d (8) where the subscript 0 refers to some standard reference state like 0" C. and 760 mm. of mercury. The values of h can be transformed into values of ho by [ ( e o ) ?-
=
n
JI p
= = = =
*
760 P,
--
273
P,
molar refraction index of refraction molecular weight density
p =
(9)
For the parhicular case in which P, = P, = P; T,= T, = T, Equation 9 can be simplified to
=
=
760
(10)
2.7822 ( T I P ) h/a
Thercfore, one obtains ho = 2.7822 (T/P)h
The density can be eypressed in terms of the ideal gas density given by P r;r .TI
(11)
Equation 11 expresses the functional relationship between the values of h, P , T,and h,and was used to bring all data to the same standard conditions. For P, # P, but T , = T , = T , then
+
h, = 2.7822 ( T I P ) h (1 -
where
P T r
T 273
F~(TIP)(er - e,) = 2.7822 (TIP)( e , - e , )
\\-here
S
e,
e oT2 . - 760
[(eo)7 - (eo),]
c.
Purity of Gases Used. The gases n-ere purified by passing the raw commercial gas a t high pressure and a t a slow rate through a bed of activated charcoal held a t a low enough tpmperature to remove most of the higher boiling impurities from the raw gas; thus, for nitrogen purification, the bed was held a t dry-ice temperature, \yhile for hydrogen and deuterium purification, the bed was cooled with liquid nitrogca. This method of purification seemed to be effective, as evidenced by the following mass spectrographic analysis of typical samples of purified gases. (The amounts of impurities recorded are the maximum limits of impurities in the sample, assuming that the mass spectrograph has zero background.)
a
= = =
Gas, 70 h'Z 0.009 0.01 99.974
pressure absolute temperature gas constant, expressed appropriate units H2 99.997 0.37
...
DP 0,009 99.63
...
in
PJPd
(12)
Thus, if the pressures in the two gas chambers are not identical, an appreciable correction has to be applied, n hich involves the absolute values of interferometer sensitivity and index of refraction of the reference gas. Equation 12 can be used, however, t o determine either the absolute sensitivity or the absolute value of eo for VOL. 31, NO. 1, JANUARY 1959
79
a gas, if the other value is known, Thus, for determining the value of the sensitivity, both chambers are filled with a gas of known index of refraction, the pressure in both chambers is determined, and since ho = 0, a =
ZC
+
~ho b
=
(14)
where xc is the calculated mole fraction. It is interesting to note that the value of the coefficient, s, is not a constant for a given gas mixture; thus, it is 0.0068616 for the hydrogennitrogen data read us. reference hydrogen, and 0.0068476 for the data read us. reference nitrogen, showing a discrepancy of 0.204% in the absolute values of the slopes. This discrepancy can be partially explained by assuming slightly different lengths for the two gas chambers, but the difference between the two tubes required to account for the discrepancy would be 0.5 mm. An alternate explanation for the difference between the two slopes is the possibility that the lines of index of refraction versus composition may have a small degree of curvature due to deviations from ideal gas mixing behavior. It is fortunate that for this case the second virial coefficients of the pure components and the interaction coefficient have been experimentally determined, making it possible to calculate the density of the mixtures as a function of composition, values which can be substituted into the molar refraction equations to obtain correct values of index of refraction of the mixture. Molar refraction theory predicts that the molar refraction of a mixture is a linear combination of the molar refractions of the pure components. For a binary mixture it is = Nix1
+
(15) where S, is the molar refraction of the mixture, S1 and N z are molar refractions of the pure components, and z1 and xz, the respective mole fractions, For a gas mixture one has N m
m em M - = el
Pm
-21
P1
N2~2
Mz xz + e2 P2
(16)
N*:
mix without interaction, Equation 2 can be substituted above to obtain (e,), =
e121
+
6232
ANALYTICAL CHEMISTRY
(17)
edvI -
h
h,
X
0
I
X
Figure 3. Diagrammatic plot of index of refraction vs. composition
where the subscript I applies to ideal mixtures. Combining Equations 16 and 17, we have
X = 5461 A e =
TI
-
1 = 139.65 X IO-'
e = n - 1 = 299.77 X 10-6 eH2 = 160.12 X 10-6
to obtain the values of e,, - (em),. Thus, additivity in the molar refraction, when combined with the proper density values for the mixtures, predicts a small deviation from linearity for the index of refraction. The maximum deviation of 8.3 X lo-* occurs a t 45% hydrogen, and should be large enough to be reflected in a difference in the slopes of the lines expressing composition us. refractive index. This is indicated in Figure 3, which shows the over-all pattern of index of refraction us. composition, and in which the deviations from linearity are greatly exaggerated. RESULTS
This expression can be simplified by making the substitution
where
V is the molar volume, to obtain
The values of the molar volume of the mixture can be calculated from the virial equation PV R -T = l +By
where the second virial coefficient is given by B,
=
+
+
B~ZL' 2Bi2~1~2 B2rz2
(22)
The following values have been given in the literature for the second virial coefficients in the system hydrogennitrogen: Reference Keyes(7) Hildebrand
BH, +14.54
Bsn
B12
-2.78
(3) f14.5 -6.2 Calcd. from data in Perry (12) f13.7 -10.5 Lunbeck.and +13.70 -4.71 Roerboom
+13.7
(8)
Theoretical
+11.5
(8)
If the components are ideal gases and
0
H2 :
2.7822 T h / ( P , - P,)(eo),
(13) For routine analysis, the calibration consists of obtaining the empirical relationship between composition of the sample and band number, Index of Refraction of Real Gas Mixtures. The experimental results can be expressed in terms of a straight line, within the limits of experimental error. The equation of that line is of the type
80
tion 21 were combined with these values of e obtained from the International Critical Tables (5) a t :
Values used in calculations
+14.11
The values of
-6.05 +13.33
V obtained from Equa-
The results of calibrating the interferometer with gas blends of known compositions are partially illustrated in Figures 2 and 4, while the complete set of data is tabulated in the original reports (9, 10). Figure 2 presents the general trend of interferometer readings us. gas composition, and was used mostly in the determination of band shift and as a help in selecting the zero-order interference fringe. The line presented in Figure 2 has a slight curvature, which is due almost entirely to the lack of linearity between interferometer readings and band numbers. If a plot were made of composition us. band numbers, it would appear as a straight line having the follorving equations: Hydrogen-nitrogenmixtures read vs. reference hydrogen: xC = 0.99774 - 0.0068616ho (23) Hydrogen-nitrogen mixtures read us. reference nitrogen: xC = 0.0068476ho - 0.00014 (24) Deuterium-nitrogen mixtures read US. reference hydrogen : = 0.986567 - 0.0067845ho (25) Deuterium-nitrogen mixtures read vs. reference nitrogen: xc = 0.0067705ho - 0.000135 (26) XC
In the above equations r, is the mole fraction of hydrogen (or deuterium) calculated from the measured value of hoe The values of x - x,-that is, mole fraction of hydrogen in the synthetic mixture as obtained in the blending apparatus minus mole fraction calculated from the above expressions-are illustrated in Figure 4 for hydrogen-nitrogen mixtures read us. reference hydrogen.
rc '
1
I
1
I
1
1
I ,006
I
4
A A
A
A A
i
A A
IO
c
I
I .Ol% CALCULATED FROM
I N COMPOSITION A
.0°4
i
,002
eqn. 18 H,- N, VS. REF. N, AH,-N, VS. REF. -H, 1
t
0
I
.2
I
I
.4
I
I
I
.6
,
.8
-
1
I I.o
XMOLE FRACTION H,
L
A EARLY BLENDS
LATE I BLENDS 1 .2
I
.3
.4
.5
.6
1
X MOLE FRACTION
-
.8
.7
.9
J.006
1.0
Figure 5. Comparison of theoretical and experimental values of h - (hm)I
H,
Values of x - x , vs. composition for hydrogenFigure 4. nitrogen mixtures read vs. reference hydrogen
In Figure 4 distinction is made between the points obtained before the blending technique was perfected and the values obtained later. While only one of the later values shows deviations larger than 0.001, most of the earlier blends fall outside this range. The scatter of the points shown in Figure 4 is due to the errors in making the blend in the blending apparatus and the errors in reading the interferometer, so that it is actually difficult to assign a definite value to either one of the two sources; however, the scatter for most of the "good" points is less than 0.0005. Index of Refraction of Deuterium. Internal Consistency of Data. From Equations 23 and 25 and the value of sensitivity of the interferometer (band numbers per unit index of refraction difference), one can obtain the difference in index of refraction between pure hydrogen and pure deuterium. The index of refraction of deuterium for white light is slightly smaller than that of hydrogen: 1.80 x 10-6. Equations 23 through 26 were calculated for best fit to the experimental data; however, the following internal consistency test can be made. If the coefficients for the hydrogen-nitrogen data are corrected for the difference in index of refraction between hydrogen and deuterium, one can obtain the corresponding coefficients for the deuterium-nitrogen system. This test was made with the following results: For blends read v s . reference nitrogen: Coefficient of ho for best fit to deuterium-nitrogen blends = 0.0067705 Coefficient of ho from hydrogennitrogen data, corrected = 0.0067709 For blends read us. reference hydrogen: Coefficient of ho for best fit to deuterium-nitrogen blends = 0.0067845 Coefficient of ho from hydrogennitrogen data, corrected = 0.0067847 Comparison of Calculated and Ex-
perimental Values of Index of Refraction. As indicated above, the nonideal gas mixing of real gases leads to a small deviation from linearity in the curves of index of refraction us. composition. It is desirable t o compare the calculated and experimental values of index of refraction. At this point, however, the information available is not sufficient to show if the deviations from linearity predicted from molar refraction agree with the experimental data, as the absolute sensitivity of the interferometer is not known with sufficient accuracy to convert e values into h values. Alternatively, if the point of intersection of the lines of slopes SI and s2 (Figure 3) were known, the calculated and experimental values could be brought to the same basis. However, as the maximum deviation from linearity occurs a t 45y0 hydrogen and the fit of Equations 23 and 24 to the data is good a t this concentration, it was decided to assume that the lines intersect a t 2 = 0.45. This is the only assumption that was necessary for the following calculations. From this assumption and from the slopes given in Equations 23 and 24, it is possible t o calculate the value of h2 - hl, from which the values of interferometer sensitivity, a, and average slope, s, follow. Thus, the value of s was found to be 0.0068553, with a corresponding value of interferometer sensitivity of 0.91102 band number per index of refraction difference X 106. Once s is known, values of h corresponding to the different concentrations of the synthetic mixtures can be calculated and compared ith the experimental findings, giving Figure 5 , which ~ ) the ~ shows values of k - ( 1 ~ for experimental blends and the values of h - @,,,)I obtained from the values of e, - (e,)r and the interferometer sensitivity. The agreement between the two sets of values is good.
It may be concluded that, a t least for the hydrogen-nitrogen system, the assumption of additivity of molar refraction is a good approximation to fact, and that the probable deviation corresponds to an error of less than 0.01% in composition. Sources of Error. The assumption of ideal gas behavior, as applied in Equations 1 through 13, introduces some error in the values of ho; however, for the gases used (hydrogen and nitrogen) and the usual range of temperature and pressures (15" to 30" C., 740 to 750 mm. of mercury), the degree of error introduced is well below the limit of accuracy of the interferometer with gas chambers 50 cm. long. The tolerances of error in the measurements of temperature and pressure are not very stringent provided the gases in the two chambers are a t exactly the same pressure and temperature (see Equation 12). For hydrogennitrogen mixtures, with 50-cm. gas chambers, it is necessary to measure concentrations below 60% hydrogen against nitrogen gas as reference, and mixtures containing more than 40% hydrogen against hydrogen gas as reference, thus obtaining a certain amount of overlapping in the region near 50%. For mixtures containing 60% hydrogen read us. reference nitrogen, the value of ho is about 89, and the errors in temperature and pressure corresponding to an error of O . O l ~ o in composition are 0.045" C. and 0.12 nim. of mercury. For loner values of ho the allowable tolerances are correspondingly increased, as evidenced in Equation 11. Thus, the errors in the measurement of pressure and temperature are almost negligible compared with the lack of reproducibility in the interferometer readings, which at best is about 0.5 unit in drum reading or about 0.02% in composition. The interferometer is satisfactory as an analytical instrument, however, and allows for fast, accurate analysis of gas mixtures. The time required for analysis is of the order of 30 minutes VOL. 31, NO. 1, JANUARY 1959
81
per sample, but most of that time is actually involved in pumping out the lines and involves no loss of operator time. ACKNOWLEDGMENT
The authors are indebted to Leonard Fick for his assistance in obtaining some of the early calibration results. LITERATURE CITED
(1) Cuthhertson, C., Cuthbertson, M., Phzl. Trans. Roy. SOC.London A213, 1 (1914).
(2) Edwards, J. D., J . Am. Chem. SOC.
39, 2383 (1927)* ( 3 ) Hanson, D. N., Maimoni, A., cHEM. 31, 158 (1959).
.~NAL.
Hildehrand, J. H., Scott, R. L., “Solubility of Nonelectrolytes,” ACS Monograph 17, 3rd ed., Reinhold, New York,
(4)
1950. ( 5 ) “International Critical Tables,” Vol.
VI1, P. 7 , LfcGraw-Hill, yew York,
1930. (6) Karagunis, G., HaTxkins, A,, Damkoler, G., 2. physik. Chem. A151, 433 (1930).
(7) Keyes, F. G., in “Temperature,” pp. 45-59, Reinhold, New York, 1941. ( 8 ) Lunheck, R. J., Roerboom, J. H., Physica 17, 77 (1951).
( 9 ) Maimoni, A., Univ. Calif. Radiation Lab. Rept. UCRL-3131 (September 1955). (10) Maimoni, A., Hanson, D. K., Zbid., UCRL-3169 (October 1955). (11) Mohr, O., 2. angew. Chem. 25, 1313 (1912). (12) Perry, {; H., “Chemical Engineer’s Handbook, 3rd ed., p. 205, hlcGrawHill, New York, 1950. (13) Valentiner, S., Zimmer, o., Ber. deut. physik. Ges. 15, 1301 (1913).
RECEIVED for review January 31, 1958. Accepted August 21, 1958. Work performed under the auspices of the U.S. .itomic Energy Commission under Contract No. W-7405-eng-48.
Mass Spectrometric Analysis MolecuIar Rearrangements FRED W. McLAFFERTY Eastern Research Laborafory, The Dow Chemical Co., Framingham, Mass.
,Structure determination b y mass spectrometry has been hampered b y the relatively unpredictable possibilities of molecular rearrangement. Classification of such anomalies as more random or more specific rearrangements is proposed. The former appear to involve a higher energy reshuffling process in which various atoms or groups are equilibrated in the molecule. The latter can yield either specific ions of high abundance through formation of a sterically favorable transition state or more stable products. Further classification according to whether the ions and neutral species involved contain an odd or even number of electrons has been useful in correlating these rearrangements. Mechanisms are proposed for several rearrangement classifications.
P
the greatest drawback to unequivocal molecular structure assignment from a mass spectrum is the possibility of molecular rearrangement during ion formation-Le., ion fragments are found in the mass spectrum that cannot be formed by simple cleavages of a bond or bonds of the molecule -such as C2H6+ in the spectrum of CH&H(CH&. Examination of a large number of spectra shows that rearrangements are very common. There are few molecules (other than diatomic) that do not exhibit this phenomenon in their mass spectra to some extent. Further information on the nature of these rearrangements would also help to elucidate the effects of bomROBABLY
82
ANALYTICAL CHEMISTRY
bardment of molecules with high energy particles. Some striking similarities have been shown between radiolysis and mass spectrometry (6, SS), including recent evidence for similarity in rearranged products (43). The relative abundance of a rearranged ion depends on the relative activation energy and stability of products of the rearrangement reaction, as compared to other possible reaction paths. Many mechanisms have been postulated to explain the variety of rearrangements observed in various individual spectra (14, 18, 19, 24-26, 30, 34, 35, 40, 41, 47-49, 52, 65). The chief similarity of these proposals is that all involve intramolecular rearrangement of the molecule-ion. To bring these diverse observations together for comparison on a common basis, it is proposed that these rearrangements can be classified according to the amount of randomization in the molecule, with further characterization as to whether there is an odd or even number of bonding electrons in the original ion and products. Some rearrangements appear t o involve a relatively high degree of activation of the molecule, with considerable exchange of atoms. I n other molecules the rearrangements are of lower energy and much more specific, and are usually caused by the strong influence of a functional group. Field and Franklin (15) have pointed out recently that the activation energy for molecular ion decomposition or rearrangement is small compared to the neutral molecule, and that the rate
of rearrangement depends on the energy and entropy of the activated state required for the process. Thus the more randomized rearrangements are ones where several reaction paths are nearly equal in energy and entropy requirements so that a number of rearranged ions are possible, usually of reduced abundance. The more specific rearrangements usually have one path more favorable than the rest, so that the rearranged ion(s) may be dominant in the spectrum. Xost of this paper is devoted t o the latter specific rearrangements, because the former have been considered previously. EXPERIMENTAL
Except where otherwise noted, the mass spectra were obtained on a 90” sector-type instrument (8) equipped with a heated inlet system (7) usually run at 200” C. These were part of the file of 4500 mass spectra a t the Spectroscopy Laboratory, The Dow Chemical Co., Midland, Mich., examined for this study. Percentage figures in parentheses refer to the relative abundance of the particular peak in relation to the total ion abundance. The samples giving spectra containing anomalous rearrangement peaks were checked for impurities in many cases by vapor phase chromatography. RANDOM REARRANGEMENTS
Random rearrangements are characterized by a more general reshuffling and isomerization of the excited molecule-ion. This often leads t o a family
