Determination of Calcium in Powdered Milk via X-ray Fluorescence

Laboratory Experiment pubs.acs.org/jchemeduc

Determination of Calcium in Powdered Milk via X‑ray Fluorescence Using External Standard and Standard Addition Based Methods Jason C. Chan and Peter T. Palmer* Department of Chemistry & Biochemistry, San Francisco State University, San Francisco, California 94132, United States S Supporting Information *

ABSTRACT: A handheld energy-dispersive X-ray fluorescence (XRF) analyzer was used to determine calcium in powdered milk. Quantification was performed using two different methods (external standards and the method of standard additions) to illustrate a matrix effect as well as a means for compensating for it. Both methods require calibration of the XRF analyzer using authentic standards prepared by mixing known masses of calcium carbonate into known masses of cellulose or dry milk. The use of XRF for this application requires analysis times on the order of 1 min per sample, provides linear calibration curves, and gives good precision with %RSDs of 4% or less. External standard based calibration gave erroneously low results due to the attenuation of calcium fluorescence by potassium in the sample, whereas the method of standard additions gave 1.29% calcium, which is very close to the manufacturer’s equivalent concentration of 1.3%. This experiment is well suited for an analytical chemistry course and provides an excellent example of the advantages and limitations of these two calibration methods for addressing matrix effects and deriving accurate quantitative results. KEYWORDS: Upper-Division Undergraduate, Analytical Chemistry, Laboratory Instruction, Hands-On Learning/Manipulatives, Food Science, Fluorescence Spectroscopy, Quantitative Analysis

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poor (R2 = 0.9757) and XRF results showed negative bias for Ca in 29 validation samples.8 Pashkova used certified reference materials and Compton normalization to calibrate instrument response and compensate for different sample matrices and densities and obtained −4% error in the analysis of an SRM.9 The article describes a simpler and faster XRF method for this application that involves the preparation of authentic standards to calibrate instrument response, does not require the use of a pellet press, and is based on the use of a hand-held energy dispersive XRF analyzer. Calibration was performed via two different methods: the first using standards prepared by mixing known masses of CaCO3 into a cellulose matrix (which was intended to “approximate” the primarily organic matrix of the sample) and the second using the method of standard additions in which known masses of CaCO3 were mixed into known masses of a powdered milk sample. This method is well suited for an analytical chemistry lab experiment. The use of XRF offers a number of advantages for a lab class including minimal sample preparation, simplicity in setup and operation, and fast analysis times on the order of a minute or less.10 More importantly, this experiment provides students with experience in preparing and homogenizing solid samples, a firsthand look at matrix effects and the inability of external standards to provide accurate results when they are present, and how to achieve accurate quantification in complex matrices via the method of standard additions.

etermination of calcium (Ca) in water, milk, and biological samples is a popular experiment in many chemistry laboratory classes and can be achieved using a number of methods including EDTA titration, ion selective electrodes (ISEs), or flame atomic absorption spectrophotometry (FAAS). EDTA titration is perhaps the most commonly used method, requiring basic laboratory equipment (i.e., balances and burets), but is nonselective and typically requires several lab periods for preparation, standardization, and analysis of the different solutions.1,2 A potentiometric method based on use of an ISE is faster, more sensitive and selective, and is unaffected by color or turbidity.3,4 FAAS requires more expensive instrumentation and is even more sensitive and selective.5,6 Energy-dispersive X-ray fluorescence (hereinafter referred to as XRF unless otherwise noted) is a selective and rapid means for quantifying Ca but ideally requires a set of standards that closely approximate the sample matrix to achieve accurate quantification. A number of references document the use of XRF for determination of Ca in milk,7−9 each of which used a pellet press to prepare samples and different methods to calibrate instrument response. An early reference describes the use of fundamental parameters based on quantification and gives relative errors of 12 and 20% for two milk standard reference materials (SRMs).7 Perring and Andrey calibrated XRF response using inductively coupled plasma-atomic emission spectrometry (ICP-AES) data on the same samples, but the correlation between the two methods was relatively © XXXX American Chemical Society and Division of Chemical Education, Inc.

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dx.doi.org/10.1021/ed4001975 | J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

Laboratory Experiment

a fume hood to minimize exposure to particulates from the grinding process. More information on radiation safety as it pertains to the use of XRF analyzers is provided elsewhere.10 Use of the XRF analyzer in a test stand in “closed beam” mode is recommended for use in instructional lab classes to ensure radiation exposure is well below background sources.

This experiment is currently implemented in a quantitative chemical analysis lab class. Each lab section has a maximum of 20 students, which are then divided into four different groups of up to 5 students each, with different groups focusing on the use of a different XRF method for quantification of Ca in milk. Students are given an appropriate introduction, background, and demonstration of XRF in a prelab lecture. The experiment uses three 3-h lab periods that focus on preparing and analyzing the samples, generating calibration curves and computing relevant analytical figures of merit (linearity, precision, and accuracy), and a discussion and comparison of results from different methods and different groups. With XRF results available in minutes, the “bottlenecks” in this experiment are the sample preparation and data analysis. Students gain a sense of appreciation for modern XRF technology, analysis of spectroscopic data and derivation of quantitative results, and the relative pros and cons of XRF versus alternate methods based on EDTA titration, ISEs, and FAAS.

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RESULTS AND DISCUSSION Figure 1 shows a calibration curve generated by plotting the Ca Kα intensity versus the concentration of a blank and five Ca

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METHODS Powdered milk samples were obtained from a local grocery store. These typically contain 30% of the U.S. Recommended Daily Allowance (RDA) of Ca per 23 g serving. Given that the RDA of Ca is 1000 mg/day for adults,11 this corresponds to 1.3% Ca (mass Ca/mass sample). For the external standard method, standards containing ∼0.2, 0.4, 1, 2, and 4% Ca were prepared by mixing known masses of high purity CaCO3 into known masses of high purity cellulose (Premier Lab Supply). For the standard addition method, samples were prepared by adding ∼0.2, 0.4, 1, and 2% Ca to known masses of powdered milk. Although these standards can be prepared by grinding and hand mixing the solids in a mortar and pestle, the use of a relatively inexpensive coffee grinder ensures a more homogeneous sample for analysis. Standards should be prepared from low to high concentrations and the equipment used for mixing should be thoroughly cleaned between each prep to avoid carryover and contamination. The blank, standards, and samples were placed in single, open-ended, 32-mm o.d. XRF sample cups and covered with 3.5 μm Mylar film and a sealing ring (Premier Lab Supply). Analysis was performed using an Olympus-Innov-X Delta model hand-held XRF analyzer equipped with a Rh X-ray tube source, several different filters, and a silicon drift detector (SDD). The analyzer was set up in soil beam 3 (light element) mode and spectra were acquired over a 1-min acquisition period. Raw spectral data was exported into Excel for subsequent analysis. The data were converted from counts versus channel number to a more useful format of intensity (counts per second or cps) versus energy (keV). Excel was also used to create plots of spectra, compute Ca response (maximum intensity of the Ca Kα peak at 3.69 ± 0.05 keV), generate calibration curves, and compute results. Although the data analysis can be made easier by “recalibrating” XRF response (i.e., plotting instrument-reported Ca concentration vs true concentration), there is obvious merit in having students work directly with raw spectral data and derive quantitative results using first principles.

Figure 1. External standard based calibration curve.

standards in a cellulose matrix. The high R2 value (0.9999) demonstrated the viability of the method used to prepare and homogenize the standards and showed linear response for Ca levels varying from ∼0.2−4%. Precision was assessed by performing three replicate analyses of each standard and RSDs of the standards were in the range of 0.5−2%. Accuracy was evaluated by comparing the 0.97% %Ca found in the sample to the 1.3% “true” value. This corresponds to a relative error of −25% and indicates a significant negative bias. This can be attributed to a matrix effect due to differences in the composition of the sample and standards. High levels of potassium in the sample absorb Ca fluorescence emitted from the sample, resulting in a decrease in its intensity. This matrix effect can be corrected for using a fundamental parametersbased model (that requires detailed information on the sample including levels of organic elements not detected via XRF), dilution of the sample to levels where the matrix effects are negligible, or use of the method of standard additions. The standard additions method used here did not involve diluting the samples to a constant volume or mass and hence required the use of more complicated calculations to linearize the calibration curve and correctly compute the sample concentration. A popular quantitative analysis text12 provides this equation as ⎡ ⎛ V ⎞⎤ ⎛V⎞ I ⎢Is + x ⎜ ⎟⎥ = I x + x [S]i ⎜ s ⎟ ⎢⎣ ⎝ V0 ⎠⎥⎦ [X ]i ⎝ V0 ⎠n n

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where in this case n refers the number of samples analyzed (n = 1 corresponds to analysis of the original sample, n = 2 corresponds to sample plus standard addition 1, etc.), Ix is the Ca Kα intensity in the original sample, Is+x is the Ca Kα intensity in the standard addition sample, [X]i is the %Ca in the original

HAZARDS The standards and samples are nontoxic and pose minimal risks. When using a sample grinder, students should be wary of the blade when cleaning this device and perform the grinding in B




concludes with each group giving a 10-min presentation of their results. This allows them to get feedback from other groups and the instructor, and compare their various figures of merit. This experiment also gives students experience with the “analytical process” from start to finish. They play a role in defining the problem (analyte, matrix, expected concentration, desired results), developing a suitable method (XRF excitation conditions, measurement time), acquiring and processing data, and computing results. From a broader perspective, integration of XRF into a quantitative analysis lab class can be used as an opportunity to compare it to alternate methods to better illustrate the relative merits and drawbacks of each for determination of a specific analyte.13

sample, [S]i is the %Ca in CaCO3 reagent used for the standard additions, V0 is the initial volume of the sample, Vs is the volume of the standard addition, and V is the final volume (V0 + Vs). In this study, the standard additions were prepared gravimetrically, and hence, masses can be used in place of the volumes to derive the following equation, where m0 is the initial mass of the sample, ms is the mass of standard addition, m is the final mass (m0 + ms), [%Ca]i has been substituted for [X]i, and %Ca in CaCO3 has been substituted for [S]i: ⎡ ⎛ m ⎞⎤ ⎛m ⎞ Ix ⎢Is + x ⎜ ⎟⎥ = I x + [%Ca in CaCO3]⎜ s ⎟ ⎢⎣ ⎝ m0 ⎠⎥⎦ [%Ca]i ⎝ m 0 ⎠n n

Figure 2 shows the resulting standard addition plot of y [Is+x(m/m0)] versus x [%Ca in CaCO3 (ms/m0)]. When y

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ASSOCIATED CONTENT

* Supporting Information S

Supporting Information for this lab experiment includes a writeup of the lab procedures for both students and instructors, an SOP for operation of the Olympus Innov-X delta model XRF analyzer, and an Excel template to facilitate processing of XRF data. This material is available via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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Figure 2. Standard addition based calibration curve.

REFERENCES

(1) Harris, D. C. EDTA Titration of Ca2+ and Mg2+ in Natural Waters. Experiments to Accompany Quantitative Chemical Analysis; Freeman: New York, 2010. (2) EPA Method 130.2. http://www.epa.gov/region6/6lab/ methods/130_2.pdf (accessed Jul 2013). (3) Birch, B. J.; Craggs, A.; Moody, G. J.; Thomas, J. D. R. Experiments with the PVC Matrix Membrane Calcium Ion-Selective Electrode. J. Chem. Educ. 1978, 55, 740−741. (4) Saurina, J.; López-Aviles, E.; Moal, A. L.; Hernández-Cassou, S. Determination of Calcium and Total Hardness in Natural Waters using a Potentiometric Sensor Array. Anal. Chim. Acta 2002, 464, 89− 98. (5) Fernandes, S.; Rangel, A.; Lima, J. Flow Injection Determination of Sodium, Potassium, Calcium, and Magnesium in Beer by Flame Emission and Atomic Absorption Spectrometry. J. Agric. Food Chem. 1997, 45, 1269−1272. (6) Bazzi, A.; Kreuz, B.; Fischer, J. Determination of Calcium in Cereal with Flame Atomic Absorption Spectroscopy. A Experiment for a Quantitative Methods of Analysis Course. J. Chem. Educ. 2004, 81, 1042−1044. (7) Alvarez, M.; Mazo-Gray, V. Determination of Trace Elements in Organic Specimens by Energy-Dispersive X-Ray Fluorescence Using a Fundamental Parameters Method. X-Ray Spectrom. 1991, 20, 67−71. (8) Perring, L.; Andrey, D. ED-XRF as a Tool for Rapid Minerals Control in Milk-Based Products. J. Agric. Food Chem. 2003, 51, 4207− 4212. (9) Pashkova, G. V. X-ray Fluorescence Determination of Element Contents in Milk and Dairy Products. Food Anal. Methods 2009, 2, 303−310. (10) Palmer, P. T. Energy-Dispersive X-ray Fluorescence Spectrometry: A Long Overdue Addition to the Chemistry Curriculum. J. Chem. Educ. 2011, 88, 868−872. (11) The National Academies Press. Dietary Reference Intakes: Recommended Intakes for Individuals. http://www.iom.edu/

equals zero, the %Ca in the original sample is equivalent to the absolute value of the x intercept. This plot gave a slightly lower R2 value versus external standard based calibration curve (0.9962 vs 0.9999). Precision was slightly better with RSDs of the standards ranging from 0.2−0.6%. Accuracy was much improved with a computed concentration of 1.29% Ca that is very close to the manufacturer’s equivalent value of 1.3%. This corresponds to a relative error of −0.01%, and clearly demonstrates the superiority of the method of standard additions versus external standard based calibration to correct for matrix effects. This XRF experiment is appropriate for a quantitative analysis or instrumental analysis laboratory course. It is far simpler and faster compared to EDTA, ISE, FAAS, and ICPAES methods for determination of Ca. It exposes students to a number of important learning concepts including preparing homogeneous samples, data analysis, matrix effects, and different calibration methods. Surprisingly, an informal review of “Quant” lab classes at several universities indicated that few use experiments that make use of solid samples or the method of standard additions. Through this XRF experiment, students gain practical experience on these concepts, observe an interference due to a matrix effect, and are able to see the utility of the method of standard additions for providing more accurate results. To facilitate this understanding, a review and discussion of the results in the lab is critical to allow students in the different groups to understand what did not work, what did work, and why. Our implementation of this experiment C




Activities/Nutrition/SummaryDRIs/∼/media/Files/ Activity%20Files/ Nutrition/DRIs/5_ Summary%20Table%20Tables%201-4.pdf (accessed Jul 2013). (12) Harris, D. C. Quantitative Chemical Analysis; Freeman: New York, 2010; pp 106−108. (13) Fitch, A.; Wang, Y.; Mellican, S.; Macha, S. Lead Lab: Teaching Instrumentation with One Analyte. Anal. Chem. 1996, 68, 727A− 731A.

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Determination of Calcium in Powdered Milk via X-ray Fluorescence

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