Correlation of measurements of absorbance in the ultraviolet and

Dec 1, 1976 - ... liquid chromatographic measurements when the absolute number of moles of an analyte is measured. G. Torsi , G. Chiavari , C. Laghi ,...
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Correlation of Measurements of Absorbance in the Ultraviolet and Visible Regions at Different Spectral Slitwidths Frederick C. Strong 111 lnstituto Nacional de Tecnologia y Normalizacion,Asuncion, Paraguay, and Faculdade de Engenharia de Alimentos e Engenharia Agrhola, UniversidadeEstadual de Campinas, Campinas, S.P.,Brasil

Assuming particular shapes for spectrophotometer beam dispersion and true absorption bands, hypotheticalinstrumental spectra can be calculated by computer integration. These can then be matched with experimental spectra and the process reversed to calculate true spectra. This has been done in the infrared using various beam dispersion shapes and Cauchy or combination Cauchy-Gaussian absorption band shapes. In this paper, a triangular beam and a Gaussian absorption band are assumed for the ultraviolet-visible. Results calculated from the integrations Include: Tables for calculating true ratios of spectral slltwidth to absorption bandwidth from experimental values; equations for calculating true absorbances and true molar absorptivities; and error due to nonlinearityof a Beer’s law plot for a given ratlo. After demonstratinga Gaussian shape for chromate absorption at 372 nm, the above calculations are applied to absorbances of various solutions measured on an instrument with a relatively wide spectral slitwidth.

Theoretically, exact obedience to Beer’s law and calculation of true absorptivity (ab, tb) at an absorption maximum require monochromatic radiation (1,2) which no spectrophotometer, except one with a tunable laser source, can provide. Thus, every ordinary spectrophotometer has a finite spectral slitwidth, s 1 / 2 , variable in some instruments and fixed in others. Each absorption peak of a substance in a given physical state has a characteristic true absorption bandwidth, Ax412 (letting x = wavelength or wavenumber). Depending on whether the true bandwidth ratio,

Rt = S

l l 2 l 4 2

(1)

is relatively small or large, the experimental absorptivity ( a , e) will have small or large deviation when measured a t different spectral slitwidths, e.g., when measured on a uv-visible instrument where s 1 / 2 is in the range 0.2-2 nm and one where it is fixed at 20 or 35 nm by a grating-slit combination or at some similar value determined by absorption or interference filters. Furthermore, when Rt is relatively large, a Beer’s law plot of absorbance vs. concentration may deviate appreciably from linearity. Other factors can cause a and t to differ from u t and et, but, in a well-adjusted instrument and unless R is extremely small, finite slitwidth is the largest single cause of difference from true values and therefore the most important one to correct for (3). Mathematical Procedure. A method of correcting mathematically for slitwidth error was first published independently by Pirlot ( 4 ) and Ramsay ( 5 ) and subsequently modified and extended by a number of authors (6-9). The customary steps are as follows. (1) Assume a function for the shape of the beam dispersion (the slit function). (2) Assume a function for the shape of the true absorption curve. (3) Consider the beam to be centered on the absorption maximum, X O , and apply Beer’s law to the spectral range of

the beam, calculating the maximum instrumental absorbance reading, Ao, by numerical integration. (4) Calculate similarly a series of instrumental absorbances a t various values of wavelength/wavenumber until one is found that is half the maximum absorbance, from which the instrumental absorption bandwidth, Ax 112, is computed. Prepare tables or graphs of these calculations. (5) Utilize these to perform the reverse operation on experimental data to calculate true absorption bandwidth, true maximum absorbance, and true absorptivity. The Slit Function. Most spectrophotometer monochromators have entrance and exit slits of equal width, resulting in a slit function of triangular shape ( 1 0 , l I ) .The peak and ends may be slightly rounded because of diffraction, aberration, and optical misalignment ( 3 ) ,for which reason some authors have used Gaussian (6, 9, 12, 13) and Cauchy (6) shapes. However, Jones, Venkataraghavan, and Hopkins (12) concluded, after use of both triangular and Gaussian functions, that the real slit function probably lies between these and that “. . . the form of the slit function has only a minor effect . . A factor which seems tcj have been ignored by authors is the shape of the combined source emission-detector response curve. If the curve varies considerably when a relatively large spectral slitwidth is used, the triangular shape of the latter could be significantly distorted. This point will be considered further in the Experimental section. The Absorption Band Function. A number of equations have been proposed for the shape of an infrared absorption band ( 1 4 ) . A study of the relation of their derivatives to the curvature of experimental peaks led this author to recommend only the Gaussian equation, the Cauchy equation, and combinations of these (15). Theoretical considerations predict Gaussian and Cauchy contributions to the shape of absorptions in the infrared region ( 3 ) . I t is generally felt that electronic transitions in the uvvisible region are well represented by the Gaussian equation (16).Siano has applied the log-normal distribution function to an experimental uv spectrum, recommending it because it starts at zero, not minus infinity (17).The papers containing the most useful tables for converting experimental absorbances to true absorbances have used a triangular slit function and a Cauchy absorption band function ( 4 , 5 , 7,8). No tables have been prepared for the Gaussiar. function. Objectives of This Work. In the light of what others have done, the author set out to do the following: (1) Use a triangular slit function and a Gaussian absorption band function to prepare tables for converting R and A0 to Rt and Ab. (2) Deduce convenient equations for converting Ao, ao, and to to Ah, ab, and €6,respectively, and conversely, for predicting a0 and EO for a given instrument when ab and e; are known. (3) Deduce a method of calculating the deviation from linearity to be expected from an absorbance-concentration plot for a given analysis with a given instrument. (4) Test the results experimentally on various instruments with various solutions.

.”.

ANALYTICAL CHEMISTRY, VOL. 48, NO. 14. DECEMBER 1976

2155

-1

0.5 &!

0

-0.5

1

1.5

y

Figure 2. Absorption maximum curves obtained with monochromatic radiation (At) and with radiation having finite spectral bandwidth ( A ) , Rt = 1

At = A6 exp,[-(x Figure 1. Triangular dispersion of spectrophotometer beam and Gaussian dispersion of absorption

At =: Ab expe[-4(ln 2)(x - X ~ ) ~ / ( A X ~ / ~ )(6) ~] With the monochromator set on x: 1,

DERIVATION OF THE BASIC EQUATIONS

P,”= P,o,1(x

= PP

(2)

The equation for the upper left boundary of the triangle is

- x1 -k S1/2)1S1/2

(5)

Replacing ut by Ax 112:

The ordinate of a beam dispersion (Figure 1) is aPolax or P! (I).At any instrumental monochromator setting, X I , P! is P!l and the area of the triangle (with center at X I ) is the radiant power of the beam:

PP = s1/2p;,

- xo)2/2(ut)2]

P,“ Sx’+s”z

explo(-At)dx

(7)

x1-s1/2

Separating the integration a t xl,

(3)

and for the upper right boundary is

P,”= P,O,(-x

+ x 1 + S1/2)/S1/2

(4)

Gauss’ equation in spectroscopic symbols is

and substituting from Equations 2 , 3 and 4,

Table I. Calculated Instrumental Absorbances for Various True Absorption Maxima and True Bandwidth Ratios A:

0.1000

0.2500

0.4343

0.6000

0.8000

1.000

1.200

1.500

2.000

1.000 1.000 1.000 0.999 0.997 0.995 0.981 0.958 0.883 0.751 0.614 0.521 0.416 0.306 0.240

1.200 1.200 1.200 1.199 1.197 1.194 1.178 1.149 1.055 0.887 0.713 0.598 0.471 0.342 0.267

1.500 1.500 1.499 1.498 1.496 1.493 1.472 1.435 1.311 1.082 0.849 0.700 0.541 0.386 0.299

2.000 2.000 1.999 1.998 1.995 1.991 1.962 1.910 1.728 1.382 1.043 0.838 0.632 0.442 0.338

A”

Rt ~

0.01 0.02 0.03 0.05 0.075 0.1 0.2 0.3 0.5 0.75 1.0 1.2 1.5 2.0 2.5

2156

0.1000 0.1000 0.1000 0.0999 0.0997 0.0995 0.0982 0.0960 0.0897 0.0798 0.0698 0.0626 0.0536 0.0426 0.0352

0.2500 0.2500 0.2499 0.2497 0.2494 0.2488 0.2454 0.2399 0.2238 0.1978 0.1712 0.1522 0.1287 0.1009 0.0826

0.4343 0.4342 0.4341 0.4338 0.4332 0.4323 0.4263 0.4166 0.3875 0.3396 0.2901 0.2550 0.21 24 0.1637 0.1324

0.6000 0.5999 0.5998 0.5993 0.5984 0.5972 0.5890 0.5754 0.5338 0.4640 0.3915 0.3406 0.2800 0.2126 0.1703

ANALYTICAL CHEMISTRY, VOL. 48, NO. 14, DECEMBER 1976

0.8000 0.7998 0.7997 0.7991 0.7979 0.7963 0.7852 0.7667 0.7091 0.6099 0.5066 0.4352 0.3524 0.2631 0.2089

1

r

,mV.

~~~

(9)

~

~~

Table 11. True Maximum Absorbances at Various Bandwidth Ratios for Instrumental Maximum Absorbances of log e and 2 log e and Relative Deviation from Linearity of the Two Points A0

Simplifying, substituting

0.4343

0.8686

Let Yo = b o - X d / S 1 / 2 x

- xo = x

- X I

=W2(Y (X

+

X I

-xo

- Yo)

- xo)/Ax4/2 = ~ 1 / 2 -( ~Y O ) / A X !=/ ZRt(y - YO)

(12)

.(13) (14) (15)

Substituting in Equation 6 and changing to the base 10, At = Ab exp10{-4(log 2)[Rt(y -

0.01 0.02 0.03 0.05 0.075 0.1 0.2 0.3 0.5 0.75 1.0 1.2 1.5 1.75 2.0 2.25 2.5

0.4343 0.4344 0.4345 0.4348 0.4354 0.4363 0.4424 0.4527 0.4872 . 0.5601 0.6728 0.7979 1.0645 1.3993 1.923 2.816 4.448

... ... ...

0.8686 0.8688 0.8690 0.8696 0.8709 0.8726 0.8850 0.9065 0.9834 1.1722 1.5464 2.126

...

0.001 0.002 0.012 0.061 0.461 2.220 6.49

12.47

(16)

Thus, the spectrophotometer transmittance is Equation 11, with At given by Equation 16. For the special case of the beam centered on the absorption maximum, XI = XO, yo = 0, and A t = Ab exp10(-4(log Z)(RLY)~)

Non-linearity, re1 dev, %

4

Rt

Table 111. Calculated Instrumental Bandwidth Ratios for Various True Bandwidth Ratios a t Constant Instrumental Absorbances of log e

(17)

The two parts of the integral become symmetrical and

C O M P U T E R CALCULATIONS The functions just derived do not appear to be integrable, so use of a computer is indicated. Integration was performed on an IBM 1130 Computer at the Centro Nacional de Computaci6n of the Universidad Nacional de Asuncibn. The QATR subroutine was used, the integrating intervals being divided into 128 points. Tests indicated that this gave more than the desired accuracy. Equation 18 was integrated over selected ranges of Ab and Rt (Table I). Calculation of AQ from Ao. According to Equation 17, R t can be specified at will. However, this does not mean that R will not vary with Ah, and, in fact, this was found to be the case (shown later). This makes a total of two parameters that must be specified, R t and Ah (or R and Ao), requiring a two-dimensional array of data like Table I and other tables in some of the papers cited. T o simplify this situation and reduce the labor of computation, it was decided to hold A0 constant. Since most uv-visible spectrophotometers measure linearly in transmittance and it has been shown that the greatest accuracy of determination of T (18) and of the position of an absorbance maximum (15)occurs in the vicinity of To = l/e 1 0.3679, this value was used for calculations. Then, from Table I, values of AE, that would yield A0 = log e were estimated for each value of R t and the correct values calculated by computer (Table 11, column 2). For a test of the linearity of Beer's law, Ah was also calculated for A0 = 2 log e (Table 11, column 3). Calculation of a Complete Absorption Curve. T o be able to visualize the effect of finite slitwidth on the shape of an absorption maximum, Equation 11was integrated a t a series of points for the center of the beam, taking A0 = log e and Rt = 1.The results are plotted in Figure 2, curve A. Curve At was

Rt

Yo

R

0.02 0.03 0.05 0.075 0.1 0.2 0.3 0.5 0.75 1.0 1.2 1.5 1.75 2.0 2.25 2.5

0.5000 0.5001 0.5003 0.5006 0.5012 0.5047 0.5109 0.5322 0.5784 0.6460 0.7126 0.8262 0.9291 1.0376 1.1514 1.2694

0.82000 0.02999 0.04997 0.07490 0.09977 0.1983. 0.2936 0.4697 0.6483 0.7740 0.8420 0.9078 0.9418 0.9687 0.9771 0.9848

Table IV. Variation of R with A , when Rt is Constant Rt

0.3

1.0

To,% 34.00 36.79 40.00 36.79 10.00

A,

-4

0.4685 0.4343 0.3979 0.4343 1.0000

0.4884 0.4527 0.4148 0.6727 1.8812

R 0.2940 0.29363 0.2931 0.7740 0.8800

U I R ,%

0.15

... -0.16

*.. 13.69

plotted from values obtained from a table for the normal distribution curve, d(y) =

(1/dZd exp,[-(y - Y O ) ~ / ~ I

by multiplying the ordinate values by

6 Ab and

(19)

using

0.6728 for Ab when R t = 1 (Table 11).

Calculation of R. Consider the center of the beam passing through Ao/2 in Figure 2: A0

= 0.434312 = 0.21715

(20)

and

To = explo(-0.21715) = 60.65%

ANALYTICAL CHEMISTRY, VOL. 48, NO. 14, DECEMBER 1976

(21) 2157

IO-

Table V. Values of True Bandwidth Ratios at Round Number Values of Instrumental Bandwidth Ratios When Instrumental Absorbance Is log ea R 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 a

Rt 0.1001 0.1508 0.2019 0.2540 0.3070 0.3614 0.4175 0.4761 0.5380 0.6043 0.6757

R < 0.1. Use: log ( R t

R 0.65 0.7 0.75 0.8 0.85 0.9 0.92 0.94 0.96 0.97 0.98

- R)

= 3.028 log

,9’

Rt 0.780 0.839 0.945 1.027 1.230 1.450 1.594 1.734 1.953 2.113 2.345

06I I I I

I I I

I I I I

, 0

04

I

I

I,

N

M

10

14

L

A:

R - 0.6057.

Figure 3. Method of measuring deviation of Beer’s law plot from linearity Data for Rt = 1, R = 0.7740. Relative deviation from linearity is dlOM

Table VI. Relative Beer’s Law Deviations of Points for Instrumental Absorbances of log e and 2 log e at Round Instrumental Bandwidth Ratios R

Re1 dev, %

R

Re1 dev, %

0.1 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0.002 0.013 0.033 0.067 0.127 0.228 0.380 0.601

0.55 0.6 0.65 0.7 0.75 0.8 0.85

0.96 1.48 2.51 3.35 5.3 7.3 13.3

Equation

0.4619

0.02 0.03 0.05 0.075 0.1 0.3 0.4 0.5 0.75 1.0 1.2

A! - A ,

AORp

0.0001 0.0002 0.0005 0.0011 0.0020 0.0081 0.0184 0.0529 0.1258 0.2385 0.3636

0.0001 0.0002 0.0005 0.0011 0.0020 0.0081 0.0184 0.0534 0.1305 0.2592 0.4117

0.4670

A,(R;/R)’/’

0.0001 0.0002 0.0005 0.0012 0.0020 0.0082 0.0185 0.0529 0.1257 0.2406 0.3871

Let this position for X I (Figure 1) be X I ’ , which corresponds to y = 0 in Figure 2. Using Equation 12, Yo’ =

(X1’

- Xo)/S1/2

(22)

I t is desired to find a value of yo’ such that, when substituted in Equation 16, and Equation 16 substituted in Equation 11, and Equation 11 integrated, 60.65% T is obtained. From Figure 2, yo’ is estimated as 0.65. Computer iteration gives 0.6460. Then R = 1/2yo’ = 0.774

Max. error, PPt

0.004 0.018 3

APPLICATIONS OF COMPUTER CALCULATIONS Calculation of Rt from R.In the laboratory, A0 and R are measured, not Ab and Rt. Therefore, we need to be able to calculate R t from R , not vice versa as done in Table 111. I t is apparent from this table and theoretical considerations that R approaches 1as Rt continues to increase. A plot of log R vs. log (Rt - R ) from the data in Table I11 resulted in a very good straight line up through R t = 0.1, considering the uncertainty of small values of Rt - R . A straight line through Rt = 0.15 and 0.2 was used to calculate R t for R = 0.15 and 0.2. The remaining values of R t for round number values of R in Table V were obtained from a large scale, log-log plot of a smooth curve. Beer’s Law Linearity. For correct application of Beer’s law, AI, is proportional to concentration. Hence, the validity of assuming a linear relation between an instrumental value of Ao and c can be tested by plotting Ao vs. Ab for a series of bandwidth ratios. Such plots appear quite linear up to a value of r of about 0.3 and are similar to experimental curves of Wentworth (2). A quantitative measure is given by the ratio dlOL (Figure 3) which is the relative deviation of the curve from a straight line:

- OL - 2 ON d/OL = OM - ON OL 2 OL

(23)

as compared with Rt = 1.Values of R obtained for a range of values of Rt from 0.02 to 2.5 are shown in Table 111. Variation of R w i t h Ao. As stated earlier, R is found to vary with A0 when R t is kept constant (Table IV), which is the reason why a constant value of A0 was chosen for calculating Rt. However, it is apparent that, for a relatively small value for R , some variation in Ao is permissible. 2158

Range

Af, = A o [ l + 0.4619 R ; / R ] 0 < R < 0.3 A! = A o [ l + 0.4670 ( R : / R ) * / 3 ] 0.3 < R < 0.65 0.65 < R < 0.77

Table VII. Relation betyeen Difference of True Absorbance from Instrumental Absorbance of log e and Bandwidth Ratios Rt

Table VIII. Equations for Calculating True Absorbance from Instrumental Values and Bandwidth Ratios at A , = Log e

Results are shown in Table 11, column 4. By plotting log relative deviation vs. log Rt and using Table I11 to provide the Rt values to read from the graph, the relative deviations at round number values of R in Table VI were obtained. The points from R t = 0.2 to 1.2 lie on a fairly good straight line. For the classical limit of accuracy of 0.1%, cal-

ANALYTICAL CHEMISTRY, VOL. 48, NO. 14, DECEMBER 1976

culations indicate that a value of 0.33 for R should not be exceeded. Calculation of Ah a n d E;. Table VI1 shows convenient relations found between A0 (= log e), Ab, R , and Rt that are surprisingly accurate up to certain limits for R and Rt. From these, the equations shown in Table VI11 are obtained. Maximum R for EO to Equal e.; A useful calculation is the maximum value R can have for the experimental value of EO tobe equal to E; within the accuracy limits of a high quality spectrophotometer. The limit of a uv-visible instrument is generally of the order of 0.001 absorbance unit when measured vs. a blank. If the absorbance is close t o log e , AAolAo = Aco/eo = 0.001/0.4343 = 0.2%

(26)

From Table VII, Ah - Ao = 0.0011 for Rt = 0.075 and, for this value of Rt, R = 0.07490 (Table 111), so

Rt

1R

< 0.07

(27) Overlapping Absorptions. Up to this point, an isolated, single absorption has been assumed, a situation which seldom occurs in practice. When absorptions overlap, the calculated, graphed summations of component curves by Vandenbelt and Henrich (19) are helpful. By comparing these with the experimental spectrum, it should be possible to estimate the point a t which contribution from the interfering absorption begins to be appreciable. If this point is outside x o f Ax1/2/2, there will be no interference with the measurement of R. If there is only one interfering absorbance and it does not affect Ao, the measurement can be made on the other side and the assumption made that the absorption is symmetrical. An approach that is feasible when there is interference a t A012 but not a t 3/4Ao is to use the latter point: exp10[-4(log ~ ) ( A X ~ / ~ ~ ) ~ I=A314 X ? , ~ ] (28) from which A ~ 1 / 2=

1.552Ax,/4

(29)

Cabana and Sandorfy (7) have used Ax3/4 to fit the upper part of peaks. if two or more absorptions contribute to Ao, the problem is too complex to be solved by the simple treatment given here. Bell and Biggers (16) used a computer and Gaussian curves to resolve the uv-visible absorption spectrum of uranyl ion into 16 bands. Pitha and Jones (20) corrected the infrared spectrum of a steroid for slitwidth error and then resolved the true spectrum into 16 bands of combination Gaussian-Cauchy shape by computer techniques. Schwartz (21) prepared a FORTRAN program for calculating up to four Gaussian component peaks of a complex spectrum from good initial estimates of XO, AAl/2, and A0 for each. It is an iteration procedure based on minimizing least square deviations. EXPERIMENTAL Test of Gaussian Shape for an Absorption Curve. Alkaline

potassium chromate is the substance that has probably been used most as a standard for absorbance in the uv-visible region (10,22), though acidic K2Cr207 has recently been recommended (23),even though it does not obey Beer's law. C.P potassium chromate was dissolved in 0.05 M KOH and diluted with the same solvent until it gave an absorption maximum just less than 1.0 in a cell 1.000 cm thick. An Instrument with a Relatively Large Spectral Slitwidth.

The spectrophotometer used in the previous experiment was operated with a spectral slitwidth of 0.5 nm. The Spectronic 20 Spectrophotometer, manufactured by Bausch & Lomb, is a popular, low-priced instrument with a considerably larger spectral slitwidth (20 nm) that is known to give quite satisfactory quantitative results. It is an appropriate instrument on which to test the calculations given in this paper. Source Emission-Spectral Response Curve. It was suggested earlier that attention should be paid to the possible effect of variation

of source emissiondetector response on the assumed triangular shape of the spectral beam dispersion when the spectral slitwidth is relatively large. Therefore, this curve was measured first. Maximum response was found to occur at 510 nm, so the beam attenuator was set to provide a reading of 100%at this wavelength and left unchanged. Readings were then made every 5 nm. Only the blue-sensitive phototube was used. The Spectronic 20 square cell, filled with water, was used to depress the lever that opened the shutter. Absorption of Potassium Chromate Solution. Though the absorption maximum for chromate is just within the region arbitrarily defined as near ultraviolet (200-380 nm), it is still above the lower limit of the Spectronic 20 (350 nm) and can serve as a useful test of the calculations of this paper at a wavelength well away from the peak of the instrument source-emission response curve. Potassium dichromate from G. Frederick Smith Co., purity factor 100.00, was dried at 105 "C for 2 h as recommended. Since the NaOH available was of higher purity than the KOH, it was used to convert the dichromate to chromate and provide a 0.050 M OH- solution. (Though technically this did not yield potassium chromate, we will speak of it as such.) One liter of 9.98 X M K2Cr04 in 0.050 M OH- was prepared and 9.00 ml of this were diluted to 11. to give an absorbance of approximately log e in a 1.000-cm cell. To study the effect of the wide spectral slitwidth of the Spectronic 20, it was necessary to make measurements on the same solution in the same cell with both the Spectronic 20 and another spectrophotometer with a much narrower spectral slitwidth. The square cell provided with the Spectronic 20 is thicker (nominally 1.175 cm) and taller than the conventional 1.000-cmcells of other instruments, the increased thickness presumably intended to compensate for the lower absorbance caused by the wider spectral slitwidth. Some experiments were done initially by wedging a 1.000-cm cell into the holder of the Spectronic 20, but this was awkward and inconvenient. Then it was discovered that the Perkin-Elmer Model 356 Two-Wavelength Spectrophotometer would accommodate the extra large diameter and height of the Spectronic 20 cell in its standard holder. Consequently this spectrophotometer was used for comparison. Read-out was obtained on the chart of the recorder (Model 56). The absorbance of the K2Cr04solution above was measured on the Model 356 at 372.4 nm using the transmittance mode and a spectral slitwidth of 1.0 nm. The absorbance was then measured with the Spectronic 20. Both measurements were made against a water blank. The cells were then compared with both containing water. Readings on the Spectronic 20 were made on the linear transmittance scale to facilitate estimation of fractions of a division. Absorption of Rhodamine B Solution. It was desired to find a second substance to study that would have an absorption nearer the peak of the emission-response curve and narrow enough to give a reduced absorbance, to which the calculations proposed in this paper could be applied. Rhodamine B was found to give such an absorption at 556.0 nm. A solution was prepared from a spray can used for chromatography (Riedel de Haen A.G.) to give an absorbance just less than 1.0 and its spectrum recorded on a Perkin-Elmer Model 402 Spectrophotometer. It was then diluted so as to give an absorbance of approximately log e in a 1.000-cmcell, and absorbances of this solution were measured in the 1.175-cm cell in the two spectrophotometers as described for K2Cr04. Tests for Stray Light. To be able to explain a decrease in absorption with increase in spectral slitwidth by means of the calculations presented in the paper, it was necessary to be sure that stray light was not affecting the measurements. The manufacturer of the Spectronic 20 states that stray light is less than 0.5%for a full-scaletransmittance reading. One way to measure stray light in a spectrophotometer is to insert a solution or filter that absorbs strongly over the range of the beam dispersion, but transmits well beside it, and see if there is any measureable transmittance. The cut-off wavelengths and transmittance ranges of several filters that were available and of suitable size were determined in a Zeiss M4 QIII Spectrophotometer and then inserted in the Spectronic 20 for a test measurement. RESULTS AND DISCUSSION The chromate spectrum obtained has a fairly symmetrical peak centered at 372.4 nm (determined by symmetry and after wavelength calibration correction) with Ao = 0.971 (Figure 4) and slightly overlapped by an adjacent peak. Superposition of an inverted copy of the peak a t 372.4 nm showed good symmetry above A = 0.60, but slight dissymmetry below. Hence, it was preferred to measure AX3/4 and calculate from Equation 29 (Table IX), giving

ANALYTICAL CHEMISTRY, VOL. 48, NO. 14, DECEMBER 1976

2159

ljo

l0tCy)

500

550

I

600

Figure 6. Absorption spectrum of Rhodamine B solution (Perkin-Elmer 402 Spectrophotometer,spectral bandwidth 1.O nm at maximum, slow

scan)

Figure 4. Absorption peak for alkaline K2Cr04 solution at 372.4nm and points for Gaussian curve calculated from (Coleman 124D Spectrophotometer, spectral bandwidth 0.5 nm, slow scan, fast response, recorder speed 60 mm/min)

R = 0.50/50.0 = 0.0100

(30)

For such a small value, R = Rt (Table V), Ah112 = Axil2, and = Ah (Table VII) to the accuracy of the measurements. Therefore the spectrum can be taken as that of At. Figure 4 is marked with points for a Gaussian curve calculated from Equation 6 and the above numerical value. Obviously, a Gaussian curve fits the peak very well. Cauchy curves based on experimental values for both Ah112 and AX314 gave a very poor fit to the peak. The source emission-spectral response curve is shown in Figure 5, its maximum occurring a t approximately 510 nm. Obviously, a triangular beam dispersion with total width of 40 nm will have considerable distortion across its width when it is on the side of the curve. However, for a moderately straight slope, one might expect that the decreased contriA0

Table IX. Data and Calculations from Recorded Spectra (Figures 4 and 5) 0'

3%

430

L50

Nnrrl

500

556

Solution

A0

K,CrO, Rhodamine B

0.971 0.886

6OC

Figure 5. Source emission-detector response curve for the Spectronic 20 Spectrophotometer

A,

Ah,/,

Ah/z

372.4 556.0

32.2 20.9

50.0 32.4,

Table X. Absorption Measurements in the Same Cell with Two Spectrophotometers Solution

K,CrO,

HZ0

K,CrO, H2

0

Rhodamine B

H2O

Rhodamine B

Instrument

Perkin-Elmer 356

s l x Y

1.0

T, %

A,

374.2

32.05 100.0

Spectronic 20 Perkin-Elmer 356

20 1.0

556.0

35.0 100.3 31.70 100.0

Spectronic 20

20

38.0 100.70

HZ 0

A

0.494a 0.000a 0.4560 -0. O O l U

0.499 0.000a 0.4200 -0.003

a Calculated.

Table XI. Comparison of Experimental and Calculated Absorbances for Two Solutions in Two Spectrophotometers Solution

Instrument

Rt

Ra

A , (expt1)b

0.0100 0.0100 0.494 Perkin-Elmer 356 Spectronic 20 0.400 0.384 0.457 0.031 0.031 0.499 Rhodamine B Perkin-Elmer 356 Spectronic 20 0.617 0.559 0.423 a Calculated from Table V by interpolation. b Corrected for cell absorbance. C Calculated from Table VIII, first d Calculated from Table VIII, second equation.

K,CrO,

2160

ANALYTICAL CHEMISTRY, VOL. 48, NO. 14, DECEMBER 1976

A , (calcd)

0.494C 0.492C 0.499C 0.503d equation.

Table XII. Stray Light Test of Spectronic 20 with Filters Coleman Violet Filter 12-222 Zeiss

A, nm

M 4 QIII, T, %

420 425 430 440 450 47 0 480 485 49 0 49 5 500 505 510 513 520 530 540 550 570 57 5 580 600 625 650

1.6 15.4 29.1 32.2 27.9 10.6 3.05

Spec. 20,

T, %

Coleman Yellow Filter 14-21 2 Zeiss

M 4 QIII,

Spec. 20,

T, %

T, %

Spectronic 20 Red Filter Zeiss

M 4 QIII,

T, %

Spec. 20,

T, %

0.05 0.05

0.5

0.1

0.07 0.05 0.05

0.1 0.00

0.4 12.1 58.4 77.4 82.1 86.3

1.2 3.6 9.0 17.0

0.00

LITERATURE CITED

4.0 74.5 87.3

bution to absorbance along the low side of would be compensated by the increased contribution along the high side. The data on K2Cr04 and Rhodamine B obtained from their recorded peaks (Figures 4 and 6) and the calculations from them are shown in Table IX. Because of the second absorption on the side of the principal Rhodamine B peak, A X ~ Nwas used to calculate AX112 instead of measuring it directly. Data for solutions in the same cell in the two spectrophotometers are shown in Table X, together with calculations of absorbance and transmittance where necessary. Values of Rt were calculated from AX1/2 and sl/2 (Tables IX and X) and are given in Table XI. R values were then calculated from Table V by interpolation and the appropriate equations in Table VI11 used to calculate Ah (Table XI, last column). The agreement for both solutions appears quite good, indicating the feasibility of using the tables in this paper to calculate the absorbances to be expected with a relatively wide spectral slitwidth from true molar absorbances. Apparently, the distortion of the triangular beam dispersion is compensated as expected. If present, stray light would cause absorbance to be smaller. Using the manufacturer's maximum of 0.5% of full scale for stray light and 38.0% T as an example, 38.0% T

+ 0.5% = 38.5%

ACKNOWLEDGMENT I am grateful to Job de Jesfis Phrez Aguilar of the Centro de ComputaciBn of the Universidad de El Salvador for some preliminary computer calculations, to Josi. Luis Benza of the Centro Nacional de ComputaciBn of the Universidad Nacional de Asunci6n for all computer calculations given, to Gilvhn Wosiacki, Edgard L. Caielli, and Milton Barros de Oliveira for assistance with experimental measurements, and to Euripides Assurnp@o for help with some figures. I also thank Jod Martino, Director of the Instituto Nacional de Tecnoloba y Normalizaci6n for financial support of computer calculations, and Ian S. Hunt, Director of the United Nations Project at the Institute, for permission to devote the necessary time.

0.00

0.1

87.3 88.6

tronic 20 and more expensive spectrophotometers (0.7% deviation from the Cary 17)". However, correspondence with the author revealed that he used 1.000-cm cells with the Cary 17 Spectrophotometer and round, 13-mm 0.d. tubes with the Spectronic 20, and was referring to relative precision after multiplying measurements by an empirical factor.

(31)

which only decreases absorbance from 0.420 to 0.415. The experimental measurements of stray light (Table XII) do not indicate it to be significant. When this work was nearly completed, a publication by Williams (24) appeared which seemed to disagree with the author's experimental results. It states: "Close agreement was obtained between absorbance values found with the Spec-

(1) F. C. Strong 111, Anal. Chem., 24, 338-42, 2013 (1952). (2) W. E. Wentworth, J. Chem. Educ., 43, 262-4 (1961). (3) K. S. Seshadri and R. N. Jones, Spectrochim. Acta, 19, 1013-85 (1963). (4) G. Pirlot, Bull. SOC.Chim. Belges, 59, 352-64 (1950). (5) D. A. Ramsay, J. Am. Chem. SOC.,74, 72-80 (1952). (6) H. J. Kostkowski and A. M. Bass, J. Opt. SOC. Am., 46, 1060-64 (1956). (7) A. Cabana and C. Sandorfy, Specfrochim. Acta, 16, 335-51 (1960). (8) P. Montigny, Spectrochim. Acta, 20, 1373-86 (1964). (9) A. Roseler, lnfraredphys., 5, 51-6 (1965). 110) . . T. R. Hoaness. F. P. Zscheile, Jr., and A. E. Sidwell, Jr., J. Chem. Phys., 41, 379:415 (1937). (1 1) W. West, "Technique of Organic chemistry", A. Weissberger, Ed.. Wiley-lnterscience, New York, 1960, VoI. I, Part 111, Chapter 27, pp 1895-7. .

(12) R. N. Jones, R. Venkataraghavan, and J. W. Hopkins, Spectrochim. Acta, PartA, 23,925-39. 941-58(1967). (13) G. G. Petrash and S. G. Rautian, lnzh.-Fiz. Zh., I (7), 61-71 (1958); Natl Res. Counc. Can., Tech. Trans/., No. 902. (14) R. N. Jones and C. Sandorfy, "Technique of Organic Chemistry", A. Weissberger, Ed., Wiley-interscience, New York, 1956, Vol IX, Chap. 4, p 280. (15) F. C. Strong 111, Appl. Spectrosc., 23, 593-6 (1969). (16) J. T. Bell and R. E. Biggers, J. Mol. Specfmsc., 18, 247-75 (1956). (17) D. B. Siano, J. Chem. Educ., 49, 755-7 (1972). (18) R. H. Hamilton, Anal. Chem., 16, 123-6 (1944). (19) J. M. Vandenbelt and C. Henrich, Appl. Spectrosc., 7, 171-6 (1952). (20) J. Pitha and R. N. Jones, Can. J, Chem., 44, 3031-50 (1966). (21) L. M. Schwartz, Anal. Chem., 43, 1336-8 (1971). (22) R. Davis and K. S. Gibson, Naf. Bur. Stand. ( U S . ) Misc. Pub/., 114, 1931. (23) R. W. Burke, E. R. Deardorff, andD. S.Bright, Nat. Bur. Stand. (U.S.) Tech. Note 584, Anal. Coord. Chem. Sect., National Bureau of Standards, Washington, D.C., 27-45 (1971). (24) H. P. Williams, J. Chem. Educ., 52, 659 (1975).

RECEIVEDfor review February 1,1973. R e d m i t t e d August 28,1974. Accepted May 5,1976. Presented at the 28th Annual Meeting of the Sociedade Brasileira para o Progress0 d a Cisncia, Brasilia, July 1976, and at the Third Annual Meeting of the Federation of Analytical Chemistry and Spectroscopy Societies, Philadelphia,, Pa., November 1976. The Instituto Nacional de Tecnologia y NormalizaciBn is a cooperative project of the Government of Paraguay and the United Nations Development Programme. Work was completed a t the present address of the author, t)le Faculdade de Engenharia de Alimentos e Engenharia Agricola, Universidade Estadual de Campinas.

ANALYTICAL CHEMISTRY, VOL. 48, NO. 14, DECEMBER 1976

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