LABORATORY EXPERIMENT pubs.acs.org/jchemeduc
A Multicomponent UV Analysis of α- and β-Acids in Hops Haley Egts, Dan J. Durben, John A. Dixson, and Micheal H. Zehfus* Department of Natural Sciences, Black Hills State University, Spearfish, South Dakota 57799, United States
bS Supporting Information ABSTRACT: A method is presented for the determination of α- and β-acids (humulones and lupulones) in a hops sample using a multicomponent UV spectroscopic analysis of a methanolic hop extract. When compared with standard methods, this lab can be considered “greener” because it uses smaller volumes of safer solvents (methanol instead of toluene). The data analysis for this lab is interesting because it relies on a three-component analysis, instead of the more common two-component analysis. This lab is educationally useful because it can be employed at any level, from a general introductory class up to an advanced instrumental class. The Supporting Information includes a lab procedure with instructor notes and an extensive math review that uses the hop system to introduce the student to Gaussian elimination, GaussJordan elimination, matrix inversion, and matrix manipulation on TI calculators and in Excel. KEYWORDS: First-Year Undergraduate/General, Upper-Division Undergraduate, Analytical Chemistry, Laboratory Instruction, Calculator-Based Learning, Hands-On Learning/Manipulatives, Agricultural Chemistry, Food Science, Quantitative Analysis, UVVis Spectroscopy
T
Most analytical chemistry texts dealing with spectroscopy discuss the BeerLambert law,
his lab uses humulones (α-acids) and lupulones (β-acids) present in hops, a component of beer, to explore and explain several different chemical and mathematical concepts. The hop system is educationally engaging because it can be integrated into the curriculum at many different levels. In the nonmajors chemistry lab this experiment can be used to introduce the concept of an absolute method that does not require calibration versus a relative method that does. If a minor interfering species is ignored, the hop analysis can also be used at the general chemistry level to introduce the standard two-component analysis using high school algebra. At the chemistry major’s analytical chemistry level the same lab can be used as a multicomponent analysis that includes an interfering species, and the mathematics behind the multicomponent analysis can be used as a bridge to the method of Gaussian elimination and matrix algebra to explain how systems of several equations and unknowns can be solved. At all levels a comparison of this method with the original, industry standard analysis method1 can be used to illustrate a more “green” methodology in analytical methods development. This lab also can be used to expose students to units of specific absorptivity as well as the more often used unit of molar absorptivity. Finally, as a lab with a direct practical application to a real-world problem, a problem that will allow a student to interact with a brewer on a professional level, we predict that this exercise is one that the students will remember for years. Copyright r 2011 American Chemical Society and Division of Chemical Education, Inc.
A ¼ εlc where A is the absorbance at a particular wavelength, ε is the absorption coefficient, l is the path length, and c is the concentration for a single absorbing species. In a two-component system the absorptions of the individual components add, so A ¼ εcomp1 lccomp1 þ εcomp2 lccomp2 To find the concentration of both components, the absorbance of the solution at two wavelengths must be obtained, and a system of two equations and two unknowns set up. Initially, the mixture of α- and β-acids present in a hop sample appears to be a simple two-component system that can be analyzed by standard techniques presented in most texts on UVvisible spectroscopic analysis. However, more careful analysis reveals that this system is a complex system containing at least two analytes and an additional interfering species. Hops, the inflorescence (cone) of the Humulus lupulus plant, contain both α-acids (humulones) and β-acids (lupulones), the major chemical components of which are shown in Figure 1. The quantity of α- and β-acids varies with the type of hop used,2,3 how the hop was processed,4 how it was stored, and how long it has Published: October 17, 2011 117
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The one nonstandard piece of equipment required for this lab is a grinder for grinding the hop sample. A simple household coffee grinder such as a low-end Mr. Coffee model IDS 55 gives satisfactory results for ∼$20. Procedure
Roughly 3 g of dried hop is ground to a fine powder using a household coffee grinder. About 2.5 g of this material is accurately weighed to the nearest milligram and placed in a 100 mL beaker with 50.0 mL of methanol and stirred for 30 min at room temperature. The mixture is then allowed to stand for 10 min to let the particulate matter settle, and the extract is gravity filtered to remove the particulate matter. A 50 μL aliquot of the filtrate is then placed in a 25 mL volumetric flask, and the flask is filled with methanolic NaOH (0.5 mL of 6 M NaOH in 250 mL of methanol). An aliquot of this solution is then placed in a 1 cm quartz cell, and its UVvisible spectrum is obtained using of blank of 50 μL of methanol in 25 mL of methanolic NaOH. Depending on equipment and time constraints, either a complete spectrum between 520 and 210 nm can be used or just absorbance values for the three key wavelengths of 275, 325, and 355 nm can be obtained. Because some methanol may evaporate during the extraction process, the extraction should be performed in a closed container. For higher accuracy, the extract mixture can be weighed before and after the extraction, and additional methanol added before filtration to replace any solvent lost to evaporation.
Figure 1. Structure of major α- and β-acids found in hops.
been stored.5 It is important for a brewer to know the quantity of α-acids in the hop used because the α-acids isomerize to form iso-α-acids during the brewing process, adding bitterness to balance the flavor of the finished beer. In this lab students undertake a simple extraction of a hop sample followed by spectrophotometric analysis at three wavelengths to quantify the quantities of α- and β-acids as well as a third component linked to hop degradation. Upon completion of the lab the students know the percent of α- and β-acids present in their hop sample, a key number that a brewer needs to know before the brewing process has begun. The lab is closely modeled after brewing industry standards,6 but the volume of the extract has been scaled down and an alternative extraction solvent used to make the lab more environmentally friendly. The lab is relatively short, can be easily performed in a two- or three-hour lab period, and is simple enough to be done in a nonmajors introductory class. However, depending on the mathematical sophistication of the analysis, the same data can be used in any chemistry lab from the introductory level up through instrumental analysis.
’ EXPERIMENTAL PROCEDURE
’ HAZARDS Methanol is highly flammable and toxic by inhalation, ingestion, or skin absorption. Waste methanol should be placed in a labeled nonhalogenated waste container for disposal by burning. Sodium hydroxide (NaOH) is corrosive and can cause severe burns. ’ RESULTS AND DISCUSSION
Materials
Extraction Rational
Owing to a wide interest in home brewing, a variety of hop samples can be obtained either at local breweries or on the Web, often with an estimate of the percent of α-acids the sample contains. Results obtained with two hop varieties are presented: Millennium, which typically has a high α-acid content, and Glacier, which has a low α-acid content. Commercial hop samples are already dried and can be used directly in pellet, plug, or leaf form. Fresh hop samples contain large quantities of water and must be dried before analysis; otherwise, the sample will mold quickly, even when stored at 4 °C. Drying the fresh hop sample also makes the results more consistent with dry commercial products. Hops should be stored in either a refrigerator or a freezer and be kept out of direct sunlight. Chemicals used in this exercise include reagent grade NaOH and spectrophotometric grade methanol. Although the results shown here display spectra obtained between 510 and 210 nm, the analysis only requires data at three key wavelengths: 355 and 325 nm, where lupulones (β-acids) and humulones (α-acids) have their maximum, and 275 nm, where both species have low absorbance. Thus, the spectroscopy can be performed on most UVvisible spectrophotometers, and the instructor has the option of having students obtain either complete spectra or data at limited wavelengths if their access to the spectrometer is limited.
Petroleum ether was used for the extraction solvent in the original method describing this procedure.1 The high volatility and flammability of this solvent precludes its use in an undergraduate lab. The industrial method presently endorsed by the American Society of Brewing Chemists6 uses toluene instead of petroleum ether for the extraction solvent. Toluene, however, is also not a good choice for an undergraduate laboratory because it has a strong absorbance at 269 nm and slight errors in the volume of toluene used, in either the sample or the blank, can significantly affect the absorbance value at 275 nm, a key analysis wavelength. Methanol, ethanol, hexane, and ether were tried as other possible extraction solvents (data not shown). For an undergraduate lab methanol works almost as well as toluene as an extraction solvent; it has the added advantages of having negligible absorbance at 275 nm so it does not interfere with spectroscopic measurements, and it is less toxic than toluene. If this procedure is going to be used to evaluate a hop sample for brewing, however, the toluene extract should be used, because that is the industry standard. In the standard procedure6 5 g of hop is extracted into 100 mL of toluene. In the procedure given here, the size of the sample and the volume of solvent were cut back to minimize expense and to make this a more “green” procedure. The lab can be made even more environmentally friendly by further reducing sample size to 118
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0.625 g of hops extracted into 12.5 mL of methanol, having several groups use a single extract, and by using a 20 μL aliquot of extract diluted into 10 mL of methanolic NaOH.
275 nm but has significant absorptions at 325 and 355 nm where it augments the absorption of α- and β-acids and interferes with a standard two-component analysis. To a first approximation this very complex system can be studied as a three-component system if the focus is placed on the major component families, rather than on trying to analyze each individual chemical. Instead of using a molar absorptivity (units of L/(mol cm)), which relates the absorbance measurement to the molar concentration of a single compound at a given path length, this system is more easily examined using specific absorptivity (units of L/(g cm)), which, in this case, relates the absorbance measurement to that of a mixture of compounds with a total concentration of 1 g/L at a given path length. Alderton et al.1 found that the α-acids have specific absorptivities of 31.8, 38.1, and 9.0 L/(g cm) at 355, 325, and 275 nm, respectively. The β-acids have absorptivities of 46.0, 33.1, and 3.7 L/(g cm) at the same wavelengths, whereas the third degradation component has absorptivities of 1.0, 1.5, and 3.1 L/(g cm) at these wavelengths. Because absorbance of the solution can be found by summing the absorptivities of the individual components, and assuming a 1 cm path length so the path length term can be removed to simplify the equation, the following three equations with three unknowns can be used to describe this system
Typical Results
Typical results are shown in Figure 2 for three samples: a Glacier hop that is low in α-acids, a Millennium hop that is high in α-acids, and the same Millennium hop sample that has been degraded by storing at room temperature for one week. Three key wavelengths are used in this analysis: 325 nm where the α-acids have their maximum absorbance, 355 nm where β-acids have their maximum absorbance, and 275 nm where both the α- and β-acids have low absorptivity, but a degradation product has increased absorptivity. Ideally standards of pure α-acids, β-acids, and the degradation product would be helpful to identify the absorbance maxima and confirm the proper choice of wavelengths; however, these materials are not readily available. Reference spectra can be found in the literature and used for this purpose if needed.1 Analysis
Because there are two major components in the hop extract, the mixture of α- and β-acids appears to be an ideal system for a classic two-component analysis as is covered in most quantitative analysis texts. All that is needed is molar absorptivity coefficients at two different wavelengths for each component, so a system of two equations can be solved for two unknowns. This natural product extract is, however, more complex. For starters neither the α-acids nor the β-acids are a single compound. Instead they are each a family of related compounds with similar absorption characteristics. Additionally there is a third component that appears over time as the α- and β-acids are degraded. This third component has not been purified and is thought to be some other breakdown component of the hop.1,7 It absorbs most strongly at
A355 ¼ 31:8Cα þ 46:0Cβ þ 1:0Ccomp3
ð1Þ
A325 ¼ 38:1Cα þ 33:1Cβ þ 1:5Ccomp3
ð2Þ
A275 ¼ 9:0Cα þ 3:7Cβ þ 3:1Ccomp3
ð3Þ
where A355, A325, and A275 are the absorbancies at the three analysis wavlengths and Cα, Cβ, and Ccomp3 are the concentrations (in g/L) of the α-acids, β-acids, and the third component, respectively. Although generating the equations is easy, solving them, for many undergraduates, is not. If there were simply two equations with two unknowns, either substitution or determinants could be used to solve the system. With three or more equations the situation becomes more complicated. One method to solve the system of three equations and three unknowns is to use programs on graphing calculators such as the SIMULT function on TI-85 calculators or a the Simultaneous Equation Solver Application that can be downloaded for free for TI-83 or TI-840 s from the Texas Instruments Web site.8 Although this method finds an answer, it is not educationally satisfying because the student uses the calculator as a “black box” to find the solution without understanding the method used to obtain the answer. A better procedure is to use this system as an introduction to the method of Gaussian elimination. Once the students understand the Gaussian elimination method, they know how their calculators actually work, and they have a tool that they can use to solve virtually any system containing an equal
Figure 2. The UVvisible spectrum of three hop samples: Glacier hops (low in humulones), Millenium hops (high in humulones), and the same Millenium hop sample that has been degraded by storing at room temperature for one week. Key wavelengths used in this analysis are 275, 325, and 355 nm.
Table 1. Analysis of Spectra Shown in Figure 2 concn/ (g L1)
absorbance data 355 nm
325 nm
275 nm
α-acids
β-acids
third component
Glacier (fresh) Millennium (fresh)
0.55 1.17
0.51 1.27
0.29 0.66
0.0037 0.0208
0.0078 0.0079
0.073 0.143
Millennium (degraded)
0.91
1.01
0.87
0.011
0.0069
0.24
hop sample
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number of unknowns and equations. An introduction to Gaussian elimination is found in the Supporting Information. Because many of the manipulations used in Gaussian elimination are more easily handled using matrix manipulations, this system can be further extended to introduce the advanced students to the basics of linear algebra. Table 1 gives the experimental absorptivities of the samples shown in Figure 1 at the analysis wavelengths of 275, 325, and 355 nm, and the amounts of α- and β-acids (humulones and lupulones) and third component found using the above three-component analysis. Yet a third solution to this educational problem, and one that could be used in a nonmajors chemistry lab with no algebra, is to use the following equations: Cα ¼ 0:05156A355 þ 0:07379A325 0:01907A275
ð4Þ
Cβ ¼ 0:0555A355 0:04759A325 þ 0:00510A275
ð5Þ
Ccomp3 ¼ 0:08336A355 0:1574A325 þ 0:3719A275
ð6Þ
Equations 4 and 5 are similar to those given in Alderton et al.,1 but the coefficients are 1000 times smaller because Alderton’s equations yield concentrations in mg/L. Even this simple, nonmathematical approach has its use in the more advanced lab. First, it can be used to check the answer obtained using more advanced algebra. Second, as shown in the Supporting Information, the above equations can be obtained by taking the inverse of the matrix formed from eqs 13. This is another calculation that the students can do easily on their calculators or in Excel, but requires a background in linear algebra to do rigorously. If the instructor wishes to take the more rigorous approach, the inversion matrix can be found by extending the Gaussian elimination to a complete GaussJordan diagonalization followed by normalizing the diagonal matrix. In the end, the brewer is not interested in knowing the concentration of α- and β-acids in an extract, but rather, wants to know the percentge of α- and β-acids in the actual dried hop. Thus, the final task for the student is to work back through the dilutions to find this number. The way the procedure is designed, if exactly 2.5 g of hops is extracted with 50 mL of methanol, the number for concentration of α- or β-acid found in the final extract expressed in mg/L is exactly the same as the percentage of α- or β-acid in the hop material. It should be noted that results for the third component occasionally yield negative values, indicating that this component is not yet completely understood. For additional usefulness, this lab can be performed in conjunction with a laboratory that uses HPLC to analyze hops for α- and β-acids9 so the same material can be analyzed by two different instrumental methods and the strengths and weakness of the two methods compared.
’ ASSOCIATED CONTENT
bS
Supporting Information A lab procedure with instructor notes; an extensive math review. This material is available via the Internet at http://pubs. acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT We would like to thank Steve Polley, a local hops grower, for bringing the hop analysis problem to our attention. We would also like to thank Steve Polley and the Crow Peak Brewery for donating several different hop varieties for our students to analyze. Finally, the authors would like to thank Chris Yushta for the opening photograph. ’ REFERENCES (1) Alderton, G.; Bailey, G. R.; Lewis, J. C.; Stitt, F. Anal. Chem. 1954, 26, 983–992. (2) Henning, J. A.; Steiner, J. J.; Hummer, K. E. Crop Sci. 2004, 44, 441–417. (3) Lemmens, G. W. C. Brew. Dig. 1998, 73, 16–26. (4) Virant, M.; Majer, D. Hop Storage Index—Indicator of a Brewing Quality. http://www.czhops.cz/tc/pdf/hop.pdf (accessed Sep 2011). (5) Weber, K. A.; Norman, O. J.; Foster, R. T., II. Am. Soc. Brew Chem. 1979, 37, 58–60. (6) American Society of Brewing Chemists. Methods of Analysis, 8th ed.; Hops-6A α- and β-Acids by Spectrophotometry, Hops-12 Hops storage index; The Society: St. Paul, MN, 1992. (7) Likens, S. T.; Nickerson, G. B.; Zimmermann, C. E. Am. Soc. Brew. Chem. Proc. 1970, 68–74. (8) Polynomial Root Finder and Simultaneous Equation Solver Version 2.0. http://education.ti.com/educationportal/sites/US/productDetail/us_poly_83_84.html (accessed Sep 2011). (9) Danenhower, T. M.; Force, L. J.; Petersen, K. J.; Betts, T. A.; Baker, G. A. J. Chem. Educ. 2008, 85, 965–956.
’ CONCLUSIONS Laboratories dealing with hops or brewing spark instant interest in most students. This lab is particularly useful because it can be performed with different levels of sophistication from a nonmajors class up to an instrumental class with an involved discussion of the mathematical methods used to solve a system of multiple equations and unknowns. In our locale where we have both microbreweries and hop growers, the techniques introduced in this lab will be used in student research projects for the next several years. 120
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