Analysis by Infrared Spectroscopy A New Method Applied to Mixtures of Nitroparaffins J. RUD NIELSEN AND DON C. SMITH' University of Oklahoma Research Institute, Norman, Okla.
A method of analysis by infrared spectroscopy is described, which is applicable, if Beer's law holds, and a set of wave lengths can be found such that at each wave length only one component of the mixture has strong absorption while the other components have weak absorption. This method gives a high degree of accuracy with a minimum of computational work. Its application to certain ternary mixtures of the four lowest nitroparaffins is described.
with a minimum of computational work. This method is applied here to certain ternary mixturcs of the four lowest n i t r o p a r a h , and i t can be generalized so as to apply to mixtures of any number of components. Various experimental factors, which must be considered in aocurah analytical work, are also discussed.
Apparatus The infrared spectrograph used was practically identical with that described by Wright (9). The 60" rock-salt prism had facea 10 by 8 cm. and the collimating arabolic mirror had a focal water-cooled Nernst glower length of 91.4 cm. (36 inches). operating on a voltage-stabilized line served as the source of radiation. A Weyrich compensated vacuum thermocouple served as receiver. The arimary galvanometer deflectiom were amplified by a balance photovoltaic cell device. The pri-
1
R
ECENT improvements in apparatus and technique have made it feasible to apply infrared absorption spectra to the analysis of mixtures of chemical compounds (1, 2, 3, 9). In several industrial laboratories isomeric and other mixtures of compounds which are difficult to differentiate by other means are now analyzed in this manner. Infrared methods of quantitative analysis of binary mixtures are particularly simple and can be applied even when the mixtures do not follow Beer's law. Wright (9) has discussed several procedures suitable for industrial use. When more components are present it may be possible to find for each compound a wave length a t which that compound has strong absorption while all the other compounds have negligible absorption. When that is the case each component can be determined separately by the simple methods used for binary mixtures (1). Unfortunately, this condition can seldom be realized with sufficient accuracy, and the general methods of analysis of multicomponent mixtures involve much time-consuming computational labor. I n many cases, however, a set of wave lengths can be found such that a t each wave length only one component of the mixture has strong absorption while the other components have weak absorption. I n $he present paper a simple and practical method of analysis is described which is applicable to such cases, provided Beer's lam holds, and which gives a high degree of accuracy 1
Present addreno, Naval Rsseuoh hboratory, Washington, D. C:
4
2-Nit ropropone t =0.06mm.
1
1 - 1
FIGURE1. PARTOF
A
RECORD OF THE INFRARED SPECTRUM OF %NITROPROPANE
Wave length region 12.45 to 10.06p. Up er trace reoorded with no oeU in radiation'path, lower tracea wit% 0.06-rnm. cell in path
.
,+
IN D u sTR IA L A N D EN G IN EER IkG
610
Infrared Absorption Spectra of Nitromethane, Nitroethane, 2-Nitropropane, and 1-Nitropropane The four lowest nitroparaffins were selected for this work because of their commercial and scientific importance (6). These
compounds are all similar, two of them being isomers, and their boiling point range is rather narrow, necessitating lengthy fractionation for complete separation. Since the only available data on the infrared absorption spectra of the nitroparaffins were the early measurements by Coblentz
IN
Vol. 15, No. 10
( 4 ) on nitromethane and nitroethane and the data of W e b and Wilson (8) for gaaeous nitromethane, the first step in the present work waa a careful investigation of the spectra of the four compounds in the liquid state. The materials, which had been purified by fractionation in a long column, were kindly supplied by the Commercial Solvents Corporation. Figure 1 shows a portion of a record obtained with liquid 2nitropropane. The upper curve is obtained with no absorption cell in the light path. The vertical distance between this curve and a line drawn through the zero positions gives the emission intensity, IO,as a function of wave length. The lower curvea are obtained with a cell of 0.07-mm. thicknese filled with 2-nitropropane placed in front of the entrance slit. From these curvea and the corresponding zero linea the intensity of the transmitted radiation, I , is determined. In Figure 2 the per cent transmission, 100 I/ZO, has been plotted against wave length. Since these curvea are used here only for choosing the wave lengths most suitable for analysis, the per cent transmission has not been corrected for background radiation nor for losses due to the cell windows. The following characteristic bands were chosen as the most favorable for analysis: nitromethane 10.909,nitroethane 10.069, Znitropropane 11.749, I-nitropropane 8.159. A glance a t the curves will show that a t each of these wave lengths the compound indicated has intense a b sorption, whereas none of the other compounds absorbs strongly. This choice allows the detelc mination of each compound in a mixture with any of the three others. For some mixtures a different choice would permit a more sensitive analysis, but would not lend itself so well to the extension of the work to four-compgnent mixtures. The most intense bands, those occurring around 6.59, cannot be used here, since they are common to all n i t r o p a r a h .
mary galvanometer and the amplifier were mounted on a lar e Mueller support (6,7)placed on a basement f i r . The secon8ary galvanometer was mounted on a sma& Mueller support about 2.5 meters from the recording camera. The deflections could also be read on a scale. The fixed-thickness absorption-cells and the precision variablethickness cell used will be described elsewhere.
WAVELENGTH
c,H E M I s T R Y
MICRONS
u;
v-
60.
40-
NITROMETHANE
20-
I
I
IO
,
I
9
,
I
8
,
l
,
l
I
7 6 5 4
Analytical Procedure A consideration of the boiling points suggested the following analytical problems as being of particular importance in the control of nitroparaffin production:
NIT ROETHANE
A. The determination of nitroethane and 2nitropro ane in nitromethane. B. TRe determination of Znitropropane and nitromethane in nitroethane. C. The determination of 1-nitropropane and nitroethane in 2-nitropropane. D. The determination of Znitropropane in 1nitropropane.
-7
01'
Ib
'
1'3
'
G
'
III
'
IO "
9 ' 8 ' j . d i " 4'
32
FIGURE 2. INFRARED TRANSMISSION CURVESFOR FOUR LOWEST NITROPARAFFINS
I
In each case a concentration range of the minor components from 0 to 7 per cent by volume was considered. BINARYM ~ T ~ E sProblem . D is typical of seven problems studied. Figure 3 shows a record obtained with known solutions of 2-nitropropane in 1-nitropropane, covering a small region around 11.749 where 2-nitropropane has a strong absorption band. Experimental results of this kind furnish the basis for all methods of infrared spectroscopic analysis, although these methods may differ considerably in the manner in which the experimental data are obtained or utilized. Common to all of the methods for analysis of binary mixtures is the use of "working curves"-i. e., plots of the ratio (or the logarithm of the ratio) of two deflections (or differences between deflections) against concentration.
October 15, 1943
ANALYT CAL EDITION
The necessary data may be taken from a record such aa Figure 3 or may be obtained by visual observation. The I detailed procedure is largely I I a matter of experimental circ u m s t a n c e and preference. Unless the detecting and recording devices of the spectrograph are extremely stable, a single measurement cannot be trusted to be sufficiently accurate. Hence, the wave11 7 p length interval concerned must be scanned several times, or the instrument must be set on the correct wave length and several m e a s u r e m e n t s taken to obtain an average. FIQURE 3. SMALL PART OF A RECORD SHOWING The number of readings reABSORPTION AROUND quired is determined by the 11.74~ OF MIXTURES stability of the instrument and OF %NITROPROPANE IN NITRO PROPANE the accuracy desired. It is believed that in general the most accurate readings are obtained by setting the instrument on the correct wave length rather than by scanning, since in the latter procedure the exact positions o i the deflection zero may be doubtful except at the ends of the region scanned. With the instrument used in the present work the data obtained by averaging three or four deflections with the instrument a t rest were found to be more accurate than readings obtained with comparable effort in other ways. This procedure was accordingly adopted. It was possible for different observers to check galvanometer deflections of 100 mm. to within 0.2mm. Working curves for two binary mixtures are shown in Figure 4 in which the extinction, log Zo/Z, for a suitably chosen wave length is plotted against the concentration of the minor component. The extinction is preferred over other functions of the deflection ratio, since when the solutions obey Beer's law a straight line is obtained which minimizes considerably the work required for determining and checking the working curve. It requires only about 5 minutes to fill the absorption cell and measure its extinction. On a routine basis the instrument can be set on the correct wave length and the straight-line working curve checked at two points in about 16 minutes, and the analyses then follow a t the rate of about ten per hour. The working curve should be checked occasionally, since it may shift owing to changes in transmission of the absorption cell with deterioration of the rock-salt faces, accumulation of dirt, etc. For these and several other binary mixtures investigated the error of the analysis never exceeded 0.1 per cent of total sample. The smaller concentrations could have been measured more accurately with a cell of greater thickness; the range of measurable concentrations could have been increased by using a thinner cell. TERNARY MIXTURES. The analysis of a mixture having two minor components is made in three steps: (1) the presence of one minor component is neglected, and the approximate concentration of the other minor component is determined by the procedure for a binary mixture; (2) the approximate concentration of the neglected component is then determined in a similar manner; and, finally, (3) the approximate concentrations of the two minor components are corrected for the error caused by the neglected component in each case.
jb
61 1
small absorption. A working curve is made for a bine mixture of component 1 in the major component a t this wavexngth, the extinction of the ternary mixture is measured, and the a p proximate value 15, for the concentration of component 1 is determined from this working curve. The more nearly equal the a b sorption of component 2 and the major component are, the mom nearly correct will Z1 be. A wave len h, A', is chosen a t which component 2 has stron absorption an com onent 1 and the major component have w e d absorption. A woriing curve for component 2 is made and the approximate concentration Q of component 2 in the mixture is determined. Finally, the corrected concentrations c1 and g are determined by
2
where e:, e;, and e; are the extinction coefficients a t the wave len th, X', of the major component and of minor components 1 a n f 2 , respectively; and e:, e; and are the extinction coefficients a t X'. Equations 1 are derived in thenext paragraph.
TABLE I. DETERMINATION OF %NITROPROPANE AND NITROETHANE I N NITROMETHANE Mixture
C2 - N P
c~~
% ' by rolums A-1
7.03 A>orreot'l7.00
3.05
5.03 4.96 6.25 5.20 4.99
5.10 5.07 4.93 5.01 4.89 5.00 5.00
A-2
3.00
5.08 A&rrect" 5 . 0 0
A-3
01
2.96 3.06 3.22 2.94 2.92 3.02 A6orreot" 3 . 0 0
I
1
I
6.99 7.09
7.03 7.12 6.87 7.02
7.00
I
I
I
J 7
CONCENTRATION I N PERCENT
FIGURE 4.
BY VOLUME
WORKINQ CURVES
A . For determination of 2-nitroparaffin in I-nitropsrathn.
One first chooses a wave length, A', a t which minor component 1 has strong absorption and the other two components have
E.
len th 11..74@.. Slit 0.60 mm. Cell thickness 0.071 mm. of 1-nitroparaffin in 2-nitro ara5n. length 8 . 1 5 ~ . Elit 0.25 mm. Cell thiokneea 0.Oh mm.
For Lerminatzon
Wave
Wave
612
-
-
The small factors (e: - €:)/(e; e:) and (e; - ei)/(e: e:) need be determined only once. The former may be conveniently obtained by dividing the slope of the working curve, already made, for determining component 1 in the major component into the slope of a working curve, made with the same cell and a t the same wave length, A’, for determining component 2 in the major corn onent. The other correction factor may be determined s d a r1y.
TABLE
Vol. 15, No. 10
INDUSTRIAL A N D ENGINEERING CHEMISTRY
OF NITROMETHANE AND %NITRO11. DETERMINATION PROPANE IN NITROETHANE
Mixture
% by uolume B-1
7.11 7.15 7.15 7.09 0.98 Av. 7.10 “Correct” 7 .OO
3.00 3.23 3.23 3.11 3.18 3.15 3.00
B-2
5.13 5.32 5.32 5.15 5.25 Av. 5.23 “Correct” 5 . 0 0
5.26 5.40 5.27 5.20 5.19 5.27 5.00
2.98 3.25 3.26 2.93 2.90
7.21 7.20 7.20 6.91 7.08 7.12 7.00
B-3
Theoretical Beer’s law states that the absorption of each component of a mixturc is indcpcndent of the presence of the other componenb, or, more precisely, that the extinction sufTcred by a beam of monochromatic light on passing through a layer of the mixture is a linear function of the concentrations of the individual eomponents.
Let Figure 5 represent an absorption cell filled with a liquid mixture. Let Zo represent the intensity of the incident radiation, Z: the intensity of the radiation transmitted by the front window, I’ the intensity of the radiation having passed throu h the liquid, and Z the intensity of the radiation transmitted by t%e Wed cell. If the liquid mixture obeys Beer’s law,
‘2-NP
C~~
analysis the working c w e a would need to be redetermined only occasionally, say, after sets of ten or twenty analyses.
+ . .. . . ) I (2) where 2 is the thickneea of the liquid, eo, cl, c?, . . .are the concentrations of the individual components of the mixture, and co, el, . . . , are their extinction coefficients. If the concentrations 1’
I;
I
x
10-(eoCo
+
(IC1
+
CICt
Q,
are expressed in moles per liter and 2 in centimetcrs, the e’s are called molecular extinction coefficients. In this paper the concentrations will be expressed in per cent by volume.
In Tables I, 11, and 111 are given the results of five entirely independent andyscs of each of eight ternary mixtures. The symbols A-1, A-2, etc., designate the different mixtures. The symbols C N M , C N B , CI N P , and CI N P are used to designate the concentrations of nitromcthane, nitroethane, I-nitropropane, and Znitropropane, respectively.
-
TABLE
I
-
OF 1-NITROPROPANE 111. DETERMINATION
AND
>
NITRO-
ETHANE IN 2-NITROPROPANE
Mixture
‘l-NP
CN1
% C-1
4.03 3.85 3.02 4.11 3.90 Av. 3.97 “Correct” 4 . 0 0
€I# uolume
2.01 1.81 2.12 2.12 1.96 2.01 2.00
h a m 5. ABSORPTION CELL(SCHEMATIC) Definition of l o , I:, Z’, and Z
Substitution of the relations
c-2
I: and Ar. 1.92 “Correct” 2 . 0 0
3.01 4.00
where Ti and T2 are the transmission factors for the front and back windows, into Equation 2 and taking logarithms gives log (Zo/l)
While 26 of the 80 measured concentrations deviate from the “correct” values by 0.15 per ccnt by volume or more, only 9 of the observed concentrations deviate from the average by that amount. Thie indicates that some of the values listed as “correct” are somewhat in error. If all 80 measurements are considcred, and if the fact that they are not all measurements of the same quantity is neglcrted, an over-all standard deviation for a single measurement of 0.093 per cent by volume is obtained. The time required to determine the working curves was about 45 minutes, and each analysis took about 15 minutes. In routine
Tilo Z/T2
=i
I’
(e&
+ e1ci +
+ . . .) I - log Ti - log7Tz
€2~2
or, with obvious abbreviations,
E
(EA
+ + +. .. . I 2 + K eici
et&
(3)
We shall call Equation 3 the “cell equation”. E is the extine tion for the given wave length used, and K is a positive quantity which will be called the “cell constant”, since it depends largely upon the nature nnd condition of the windows of the ccll. K varies in a gradual manner with the wave length. The extinction ,on the other hand, are rapidly varying coefficients, eo, el, er, functions of the wave length, which are different for d8erent com-
. . . ..
ANALYTICAL EDITION
October 15, 1943
pounds. To characterize them unambiguously it is necessary to specify the resolution of the instrument as well as the temperature of the absorbing liquid. For most liquids the extinction coefficients are nearly constant over a temperature range of a few degrees. The working curve8 shown in Figure 4, and all the other working curves obtained for binary mixtures of the nitroparaffins, are straight within the experimental error. Thus, it may be concluded that mixtures of the nitroparaffins obey Beer's law with considerable accuracy in the infrared. In fact, these working curves may be regarded as graphs of the cell equation
-
... . . .
obtained by substituting ~0 = 100 cl, ct = c8 = 0, in Equation 3. From Equation 4 it is seen that the sensitivity of the analysis incresscs with the difference between the extinction coefficients of the two comuonents and also with the cell thickness. The difference in extiiction coefficients depends upon the choice of wave len th, and eo limits the value of 2 which can be used without maiing E too large to be measured accurately. Hence, in chooeing the wave len&h for an analysis it is important to keep co small and (el to).large. If the validity of Beer's law has been established for a mixture, only two points are required to determine the working curve. If the same cell is always used so that I is constant, the slope remains constant, and the working curve need be checked at only one point for shifts due to changes in
-
K.
+ +
I n view of the relation ~0 c1 c2 = 100 per cent by volume, the analysis of a ternary mixture requires extinction measurements a t only two wave lengths, h' and h". They are chosen in such a manner that el is large while 62 and €0 are small at A', wheress e, is large and c I and €0 are small a t h". If the extinctions and the cell constants have been measured at these wave lengths, two cell equations can be written down. Marking the quantities memured a t A' and A" by single and double primes, respectively, the solution of these equations is
c1
-
(E' - K'
- 100 (E:
e:
1) (e:
- e:)
(e:
- e:) €):
- (E' - K" 2
- (e: -
(e;
)€:
- 100 e: 1) (6;
- e;)
2
and an analogous expression for a. If the very slight dependence of the cell constant upon the corn osition of the mixture is neglected, K' 100 e,' 2 is equal to l$, the extinction of the cell filled with the major component;
+
also,
Substitution of these and the analogous relations into the expressions for c1and c2 gives
el = 1Ol-J(E' .- - E:) ( E ; - E:) (E: E:) (E: - E:)
-
- (E" - E:) ( E : - E:) - (E: - E:) (E: - E:)
(6)
and an expression for q which may be obtained by interchanging subscripts 1 and 2. I t is essential to choose wave lengths A' and A" in such a manner that, with a given inaccuracy in the extinction mearsurements, the inaccuracy in the computed concentrations will be as small as possible. A simple analysis, which will not be given here, shows that one should strive to satisfy tho following conditions: (e: - e:)* +.(e; - e:)* ftnd (e,! e@*+ (e; - e:)* should beas e,) (e: - e:). (e: e): (e: large as possible, and (e, should be as small, numerically, as possible. When the previously described procedure for selecting the wave lengths is used, these conditions tend to be fulfilled. The expressions for the concentrations may then be simplified as follows:
-
-
+
-
€4)
61 3
or
where E1 and Z: are the values for the concentrations obtained from the measurements of E' and E" by means of the two-component working curves. Similarly,
The relative error introduced by using these approximation formulas is:
The value of this quantity was about O.OOO9 for Problem B. Thus, the systematic error introduced by the simplification waa less than 0.1 per cent of concentration E:. In the two other c a w of analysis of ternary mixtures of the nitroparaffins this error was even smallcr. I n all theso cases this systematic error was negligible compared to the inaccuracy caused by the errors of obscrvation. The crror introduced by the simplification leading to Equations 7 and 8, when expressed as a percentage of the concentration to be determined, is independent of this concentration. Hence, the method outlined here is not limited to mixtures for which the concentrations of the components to be determined are small
Background Radiation
- e:)
The existence of stray radiation inside the spectrograph is revealed by the fact that the measured intensity, I , differs from zero for wave lengths for which the absorption is virtually complete, as indicated by the flattening of the bands. This may be seen in the transmission curves of Figure 2 for the strong absorption bands a t about 6 . 5 ~ . Even when a glass shuttcr was used it was found necessary to correct IO and I for background 1,adiation whencver the extinction data were used for detcrmining absolute values of extinction coefficients, cell constants, cell thicknesses, ctc. The background Correction for IO was determined by using a very thin cell with highly polished windows filled with carbon tetrachloride, which has strong absorption bands near the wave lengths of interest but almost no absorption in the short wave length region. The residual intensity, measured a t a wave length for which the absorption is virtually complete and multiplied by a factor (about 1.1) to compensate for the reflcction losses in the cell, gives the correction which must be subtracted from the measured value of ZO. When expressed as a perccntage of lo,this correction can be applied to any later value of Io. The background correction for Z must be determined for the particular cell with which measurements are being made, and, strictly, for the cell filled with the liquid being studied. If the liquid has a band giving complete absorption near the desired wave length, the residual deflection a t this band is taken to be the correction. If there are intense bands near the wave length in question, the residual deflections a t these bands are determined, and the desired correction is found by interpolation. For very thin cells, where the absorption for no band is complete, more elaborate methods must be employed. The magnitude of the background correction is indicated by the following examples: The correction for I waa 5.4 per cent of (.5).
INDUSTRIAL AND ENGINEERING CHEMISTRY
614
I@a t 11.74~(slit width 0.60 mm.), 3.8 per cent of IO a t 10.06~ (slit 0.50 mm.), and 2.3 per cent of 10a t 8 . 1 5 ~(slit 0.25 mm.). The corrections for ZOwere slightly larger.
Determination of Cell Constant The constant, K , for a given cell a t a given wave length may be determined by filling the cell with a liquid which has negligible absorption a t this wave length and measuring 10 and I. For, when c = 0, the cell equation (9) becomes E = log (Io/Z)= K . If no liquid is available which is transparent a t the desired wave length, one or more liquids which are transparent a t other wave lengths may be used to determine K for these wave lengths, and the cell constant for the desired wave length may then be obtained by interpolation.
The thickness of a 10.0-mm. cell was measured with calipers to within 0.1 per cent. The cell wm then filled with standard solutions of pure n-hexane in pure carbon tetrachloride, and the extinction coefficient of n-hexane at 3 . 4 1 ~was determined. The thin cell to be measured was then filled with standard solutions of n-hexane in carbon tetrachloride of sufficient concentration to give accurately measurable E-values. The extinctions and the K was plotted cell constant were measured a t 3.41~,and E against the concentration of n-hexane. The cell thickness W&IJ then determined by dividing the slo e of the curve by the extinction coefficient of n-hexane. In t t i s manner the thickness of thin cells could be determined to within 1 per cent or better.
-
Determination of Extinction Coefficients Since the extinction coefficient of an absorbing compound is independent of the amount of sample used, and since it is of fundamental importance in the analysis of mixtures obeying Beer's law, its use for specifying absorption is to be preferred to the more widely used term of per cent transmission. Various methods of measuring extinction coefficients have been investigated. The cell equation for a cell filled with a pure compound is
E
CELL THICKNESS
log (lo/l)= c d + K
(9)
AT
Slit width 0.25 mm. Extinction coefficients. measured b y slopes of lines, us: 2-nitropropane 0.178, nitroethane 0.533,l-nitropropane 3.30 cm. - 1 X (per cent by volume) -1
If a liquid is available whose extinction coefficient is known for the given wave length, and if the cell thickness is known, the cell constant may be determined by measuring E and applying Equation 9. The liquid or liquids used for determining K should strictly have the same index of refraction a t the desired wave length as the liquid under investigation. However, the variation in refraction index is rarely large enough to require consideration.
Measurement of Cell Thickness For thick cells the thickness with vernier calipers before the must be measured after they method was found satisfactory measured before assembly.
=
Hence, if the thickness of the cell is accurately known, measurement of E and K enables one to determine e. However, since high and low values of E cannot be measured accurately, the data obtained with a single cell do not give accurate values of c over the entire wave-length range but only for those regions where the absorption gives intermediate values of E for the particular cell. To obtain accurate values over a wide wave-length range, a set of cells of varying thickness is required. All intensity measurements must be corrected for background, and the values of K and 1 must be accurately determined. For the wave lengths selected for analytical work increased accuracy was obtained by averaging the extinction coefficient values obtained with cells of different thickness. E - K was plotted against I and c was determined by measuring the slope of the straight line and dividing it by the concentration. Figure 6 shows the curves obtained for nitroethane, I-nitropropane, and 2-nitropropane a t 8.15~(slit 0.25 mm.). Only for the thickest cell could the background correction be determined directly by filling the cell with I-nitropropane, which has a strong absorption band at 8.15~. The background corrections for t h e thinner cells were estimated by comparing their transmissions with that of the thickest cell at some wave length where the liquid does not absorb. For 1-nitropropane the absorption at 8 . 1 5 ~was so strong that only with the thinnest cell was the extinction small enough to be measurable.
IN CM.
OF EXTINCTION COEFFICIENTS FIGURE 6. DETERMINATION 8 . 1 5 ~WITH CONSTANT-THICKNESS CELLS
Vol. 15, No. 10
of the spacer can be measured cell is assembled. Thinner cells are assembled. The following for all cells which could not be
TABLE IV. EXTINCTION COEFFICIENTS Wave Length
Slit Width
Microm
Mm.
8.15 10.06 10.90
0.25 0.50 0.55 0.60
11.74
Nitromethane
Nitro2-NitroI-Nitroethane propane .propane (Cm. X % bu aolume)-l 0.486 0.177 3.38 0.252 0.061 1.85 0.063 0.097 0.782 0.114 0.135 2.09 (5.26) 0.194 0,035 0.328
The results show that it is possible to determine extinction coefficients fairly accurately with cells of k e d thickness. The procedures worked out for measuring the cell thickness, the cell constant, and the background correction are satisfactory. However, the use of a set of several cells to obtain accurate extinction coefficients for analytical work is laborious and cumbersome, and high accuracy is not easily obtained for large extinction coefficients. For these reasons another method which employs a variable-thickness cell was developed.
ANALTYICAL EDITION
October 15, 1943
615
The precision variable-thickness cell constructed will be described elsewhere. It is essentially an all-metal Baly-type cell with rock-salt windows and a screw drive. With this cell, curves similar to those of Figure 6 can be easily and quickly obtained. I n addition, several simplifications occur. Since the cell constant does not change with the thickness setting, its value need not be determined. Similarly, since no appreciable time is required to change the setting of the cell, the intensity, l o , of the incident radiation can easily be held constant while several measuremenb are taken and, hence, its value need not be determined. The cell equation may be written -log
z
= ec2
+ H - log lo
(10)
and, hence, the extinction coefficient can be determined from a plot of log Z us. 1. Such plots are shown in Figure 7. For this purpose the absolute thickness of the cell is of no importance; only the thickness increments between successive cell settings are required, and these can be determined with higher accuracy than the absolute thickness values. I n Table IV are listed the extinction coefficients for the four nitroparaffins for each of the four wave lengths chosen for analytical work. These values were used to obtain the correction factors used in the ternary analyses reported. The coefficients a r e defined by the convention used here of expressing the concentrations in per cent by volume. The molecular extinction coefficients, obtained by multiplying these values by the molecular weight divided by ten times the density, are listed in Table V.
TABLE V. MOLECULAR EXTINCTION COEFFICIENTS W a v e Length MicrmJ 8.15 10.06 10.90 11.74
Slit Width
Nitromethane
Nitroethane
2-Nitropropane
1-Nitropropane
1.35 0.52 1.12 0.19
3.47 13.2 0.82 2.34
1.59 0.57 1.21 (47.2)
30.0 0.54 6.95 1.72
Mm. 0.25 0.50 0.55 0.60
CELL THICKNESS IN CM.
FIQURE 7. DETERMINATION OF EXTINCTION COEFFICIENTS AT 10.90p WITH
The extinction coefficient for 2-nitropropane at 1 1 . 7 4 ~w a so ~ large that it could not be determined directly. The following procedure was therefore used. The difference between the extinction coefficients for 2-nitropropane and nitromethane was first determined by using known binary mixtures, and the extinction coefficient for nitromethane was then added to this difference. The accuracy obtained with the variable-thickness ccll depends upon three factors: the precision with which the thickness increments are determined, the accuracy of the intensity measurements, and the accuracy of the background correction. The 6rst two quantities were measured with less than 1 per cent error. It is not easy to estimate the accuracy with which the background correction was made. However, the fact that the plots of log I UB. 1 are all very nearly linear indicates that the background correction applied to the intensity values was not much in error. The values, 0.178 and 0.177, for the extinction coefficient of 2-nitropropane a t 8 . 1 5 ~ measured with iixed-thickness cells and t h e variable-thickness cell, respectively, are in excellent agreement. For nitromethane and I-nitropropane the agreement is not so close. The values obtained by the variable-thickness cell should be the more accurate. Extinction coefficient data enable one to predict accurately t h e sensitivity which will be obtained when a given wave length lis used in a binary analysis and, hence, to choose the optimum wave length and the optimum cell thickness for any particular analysis without additional experimental’work; as a matter of fact, since the slope of the working curve is determined by the diEerences between the extinction Coefficients, and since the
THE
VARIABLE-THICKNESS CELL
Slit width 0.55 mm. Extinction coe5cients, measured by negative d o p a . are nitromethane 2.09, I-nitropane 0.782 om.-] X-(per cent by volume)-s
intercept of the cuwe is given by the extinction of the cell filled with the pure solvent, the working curve can be drawn without recourse to standard solutions, if Beer’s law is known to hold. The correction factors used in the simplified method of analysis of ternary and multicomponent mixtures are also determined by extinction coefficients. Hence, the use of a variable-thicknesa cell, with which extinction coefficients can so easily be measured, represents an important advance in analytical work with mixtures obeying Beer’s law.
Acknowledgments The writers wish to express their gratitude to the ReynolQ Manufacturing Company for the gift of the infrared specgraph, and to the Commercial Solvents Corporation and the University of Oklahoma Faculty Research Fund for financial assist ance. Thanks are due also to E. B. Dale for assistance with some of the measurements.
Literature Cited (1) Barnes, R. B., Liddel, U., and Williams, V. Z., IND.ENQ.CHSM., ANAL.ED.,15,83(1943). (2) Brattain, R. R.,Petroleum World, 50,46 (1943). (3) Brattain, R.R.,and Beeck, 0..J . Applied Phys.,13,699 (1942). (4) Coblentz, W. W., “Investigations of Infrared Spectra”, Carnegis Inst. Washington, Publidation 35, 1905. (6) Gabriel, C. L., Chem. Id., 45, 664 (1939);IND.ENO.CEEY.. 32, 887 (1940). (6) Mueller, R.,Ann. Physik, 1,613(1929). (7) Strong, J., “Procedures in Experimental Physics”, p. 444, New York, Prentice-Hall, 1938. (8) Wells, A. J., and Wilson, E. B., J . Chem. Phy8., 9,314 (1941). (9) Wright, N., IND.ENQ. Cam&, ANAL.ED.. 13, 1 (1941).
