In the Laboratory
Variable Path-Length Cells for Discovery-Based Investigation of the Beer–Lambert Law Sarah A. Stewart and André J. Sommer* Molecular Microspectroscopy Laboratory, Department of Chemistry and Biochemistry, Miami University, Oxford, OH 45056
Background For several years there has been great interest in using discovery-based learning to explore the principles associated with the Beer–Lambert law. An account of this approach has been given by Ricci et al. (1). Students are taught the fundamental skills required to obtain a spectrum with a visible spectrophotometer, after which they are free to explore the variables inherent in the Beer–Lambert law. While the concentration and analyte can be varied easily, changes in the path length are problematic for two reasons. First, most entrylevel spectrometers are built to accommodate only cuvettes of 1-cm path length, and any cuvette with greater path length requires an additional holder or modification of the instrument. Second, although cuvettes with reduced path lengths are available, their cost and the numbers required to give a reasonable data set make them prohibitively expensive in classes with large enrollments. We have investigated an approach employed in the late 1950s and early 1960s, which to our knowledge was commonly employed but never reported (private communique, Bill Fateley, Kansas State University). It involves placing a quartz or glass spacer within the cavity of a 1-cm path-length cuvette to reduce the path length. These inserts can be obtained in various sizes, but the more common ones reduce the path length by an order of magnitude. Although glass spacers are relatively inexpensive, quartz spacers cost upwards of $225.00. One benefit of quartz spacers is that the path length is usually controlled to a tolerance of ± 5 µm, making them ideal for quantitative analysis. Keeping in mind that this level of accuracy is not required for analysis of general relationships and that cost and *Corresponding author. Email:
[email protected].
durability are factors, we have constructed spacers out of polycarbonate (LEXAN) and acrylic (Plexiglas). These spacers are used in conjunction with common 1-cm disposable polystyrene or acrylic cuvettes. The primary focus of the investigation was to determine if such spacers could be employed to vary the path length and to what extent they affect the quantitative capacity of measurements made with them. Experimental Procedures Visible absorption spectra were collected using a Hewlett Packard Model 8452A diode array spectrophotometer. A standard solution of holmium oxide (4% w/w) dissolved in 1.4 M perchloric acid was employed as the analyte, using the 536-nm absorption for quantitative purposes (2). Cuvette spacers were cut from polycarbonate sheets 0.063-, 0.125-, and 0.250-in. thick (nominal) and machined to alternate dimensions of 1 cm by 6 cm. The actual thickness measured for each spacer with a digital caliper was 0.156, 0.298, and 0.544 ± 0.001 cm, respectively. These spacers were used in conjunction with a Fisher disposable acrylic cuvette of 1-cm path length (catalog #14-385-996). Single-beam measurements were made using distilled water for the background measurement. Because of the ready availability of polycarbonate, this material was employed for the entire investigation. An acrylic spacer was constructed, but only for comparison with the polycarbonate. Results and Discussion Figure 1 illustrates absorption spectra of thick (0.544 cm) polycarbonate and acrylic spacers. Comparison of the spectra shows that the acrylic spacer has a lower cutoff than the polycarbonate spacer, making it useful over a slightly larger 0.6
3.0
Polycarbonate (upper trace) 0.5
Acrylic (lower trace) Peak Absorbance
Absorbance
2.5
2.0
1.5
1.0
0.3
0.2
0.1
0.5
0.0 350
0.4
400
450
500
550
600
650
700
750
800
Nanometers
Figure 1. Absorption spectra of polycarbonate and acrylic spacers 0.544 cm thick.
0.0 0.0
0.2
0.4
0.6
0.8
1.0
Path length / cm
Figure 2. Plot of peak absorbance of the solution vs path length, using the spacers.
JChemEd.chem.wisc.edu • Vol. 76 No. 3 March 1999 • Journal of Chemical Education
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In the Laboratory
portion of the visible spectrum. However, each material provides sufficient transmission over the classical visible (400– 700 nm) spectral region. A plot of peak absorbance of the solution vs path length using the spacers is given in Figure 2. The plot demonstrates extremely good linearity and possesses an R 2 value from a least squares fit of .998. Moreover, the spacers can be paired to yield a combination of path lengths not obtainable with a single spacer. Path lengths of 0.158 and 0.300 cm were obtained by combining the thickest spacer with the two thinner ones. The only precaution that must be taken during the collection of spectra is to ensure that the spacer orientation employed for collection of the background spectrum is identical to that employed for collection of the sample spectrum. Spacers can be oriented either normal to the light beam by butting them up against the side of the cuvette, or tilted, as shown in Figure 3. A maximum angle of 11° tilt occurs with the thinnest spacer, effectively increasing its thickness, which will decrease the optical path length by 11 µ m. However, the associated decrease in absorbance is below the uncertainty of 1 milli-absorbance unit in the absorbance measurement. No difference in absorbances was measured experimentally by having the spacer normal to the light beam or tilted, provided that the tilt direction (orientation) was the same for the background and sample scans. Spacer orientations (tilt direction) that are different from background and sample scans will show a variation in the measured absorbances for the larger path lengths, as shown by the data in Table 1. A final point concerning the use of the spacers is the associated cuvette path length. The path length of the cuvettes was calculated by comparison of absorbance values obtained on a standard solution in the reduced-path-length cuvettes and the cuvette of 1-cm path length. Table 1 shows that the measured values and calculated values agree to within 10% with a general increase in percent difference as the path length is decreased (spacer thickness increased). We do not know the cause of this error, but it appears to be instrumental. The point to be made, however, is that using this method with a standard solution, students can easily obtain semiquantitative values for the absorption coefficient of a given material. In addition, the determination of the cuvette path lengths will expose the students to calibration procedures not necessarily addressed in this type of experiment. Conclusion We have shown that the inserts can be used successfully to vary the path length of an absorption cell for visible measurements. Both acrylic and polycarbonate are available in most university model shops or hardware stores and cost about $3.00 per square foot. One square foot can easily produce 100 spacers, which should suffice for most classes with large enrollments. Although both materials are suitable from a spectroscopic standpoint, the acrylic has slightly better
400
Normal
Tilted
Figure 3. The two orientations of the spacers in the cuvette: normal to the light beam and tilted.
Table 1. Selected Absorbance Data Using Polycarbonate Spacers Cell Path Length/cm Measured
a
Calculated
b
Absorbance
∆ Path Length (%)
Similar
Spacer Orientation Different
0.158
0.168
6.33
0.088
0.087
0.300
0.325
8.33
0.170
0.168
0.456
0.489
7.24
0.256
0.254
0.702
0.736
4.84
0.385
0.381
0.844
0.869
2.96
0.455
0.450
1.000
–
–
0.523 c
0.523 c
aMeasured
with digital calipers. by comparing absorbance values for a standard solution in the reduced-path-length cuvette and the cuvette of 1-cm path length. cNo spacer employed. bCalculated
chemical resistance to strong bases (3). Finally, the method is easily implemented with disposable plastic cuvettes and no instrument modification is required. The method can also be used on the more common Spectronic 20 with an optional cuvette holder and sample compartment (parts #33-31-76 and 33-31-78). Acknowledgments We would like to acknowledge Douglas A. Skoog of Stanford University, F. James Holler of the University of Kentucky, Sy Schoenfeld of NSG Precision Cells, and Thomas E. McNeel of Buckman Laboratories International for their many helpful discussions. Literature Cited 1. Ricci, R. W.; Ditzler, M. A.; Nestor, L. P. J. Chem. Educ. 1994, 71, 983–985. 2. Manual on Practices in Molecular Spectroscopy, 4th ed.; American Society for Testing Materials: Philadelphia, 1979; pp 7–21. 3. Rodriguez, F. Principles of Polymer Systems; McGraw-Hill: New York, 1982; pp 535–537.
Journal of Chemical Education • Vol. 76 No. 3 March 1999 • JChemEd.chem.wisc.edu
