Laboratory Experiment pubs.acs.org/jchemeduc
Introduction to Validation of Analytical Methods: Potentiometric Determination of CO2 A. Ricardo Hipólito-Nájera,† M. Rosario Moya-Hernández,† Rodolfo Gómez-Balderas,*,† Alberto Rojas-Hernández,‡ and Mario Romero-Romo§ †
Laboratorio de Fisicoquímica Analítica, UIM, FES−Cuautitlán, UNAM, Campo 4. Km 2.5 Carretera Cuautitlán Teoloyucan, 54740 Estado de México, México ‡ Departamento de Química, Á rea de Química Analítica, Apdo, UAM−Iztapalapa, Apdo. Postal 55−534, 09340 Iztapalapa, Cd. México, México § Departamento de Materiales, Á rea Ingeniería de Materiales, UAM−Azcapotzalco, Av. San Pablo 180, Colonia Reynosa−Tamaulipas, 02200 Cd. México, México S Supporting Information *
ABSTRACT: Validation of analytical methods is a fundamental subject for chemical analysts working in chemical industries. These methods are also relevant for pharmaceutical enterprises, biotechnology firms, analytical service laboratories, government departments, and regulatory agencies. Therefore, for undergraduate students enrolled in majors in the field of chemistry, learning validation of methods and chemometrics is essential. The following article presents the development of a laboratory experiment to validate a method to determine CO2 by means of potentiometry. This experiment will allow students to approach a subject that may be part of their professional activities. The validated method was applied to determine CO2 in commercial carbonated beverages. A teaching activity on method validation was proposed and implemented for senior students. After its application, students were able to improve significantly their knowledge on the topic. The potentiometric technique, underlying the validated method, has the advantage of being easy to apply and accessible in almost any undergraduate laboratory. Furthermore, the required reagents are available practically in any chemistry department. The shown procedures might be executed as laboratory activities in analytical chemistry due to their overall simplicity and rapidity. KEYWORDS: Analytical Chemistry, Upper-Division Undergraduate, Ion Selective Electrode, Potentiometry, Chemometrics, Laboratory Instruction
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INTRODUCTION To fulfill more stringent local and international regulations, and to maintain worldwide competitiveness, global firms must ensure the highest quality control of their products. Validation of an analytical method is a documented process used to confirm that the procedure employed to conduct a specific test is adequate for the intended application and used to assess the quality, reliability, precision, and consistency of analytical determinations.1−3 Skills related to the validation of analytical methods are fundamental for good practices in chemistry. Although there are courses in chemometrics, method development, verification, and validation, they are rather intended to professional chemists. Thus, it is highly desirable for students of chemistry to develop these skills while enrolled in the university. There are numerous approaches to validate analytical methods; all of them are acceptable as long as they are scientifically supported.2 Guides and technical publications on method validation are abundant;4 however, the aim of those texts is different from direct application on undergraduate © XXXX American Chemical Society and Division of Chemical Education, Inc.
teaching. This might hinder students in learning the essentials of validation. Therefore, in this work, we provide students with a single appropriate validation method to analyze CO2 in carbonate drinks. The presented method takes parameters and recommendations from different guides. Here, such parameters and recommendations are unified with a pedagogical intention. Scholarly papers that include some aspects of validation have been recently published. For instance, Stitzel et al.5 worked on an internal standard calibration and then a validation of a high− performance liquid chromatography (HPLC) method by comparison to a certified reference material. Usher6 gave an introduction for students to some validation procedures on liquid−liquid extraction and HPLC methods comprising calibration curves and recovery evaluations. This work is an example of a partial validation with a small set of parameters. By working with cold vapor atomic absorption spectroscopy, Received: April 5, 2017 Revised: June 16, 2017
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DOI: 10.1021/acs.jchemed.7b00252 J. Chem. Educ. XXXX, XXX, XXX−XXX
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Kristian7 determined the linearity and limit of detection for analyzing referenced materials. Recommendations on recovery studies are given to students. Earlier, Donais8 had carried out studies of the limit of detection and precision for flame atomic absorption spectroscopy, and students studied the significance of precision in data evaluation. Homem9 reported how students validated a method to analyze amoxicillin in river waters by means of liquid chromatography−mass spectrometry. Validation of this particular analytical method included drawing a calibration curve, determining detection and quantification limits, as well as precision and accuracy of the method. Literature shows important aspects of method validation, but their implementation depends on advanced instrumental analytic techniques, which might be a shortcoming for average undergraduate laboratories. In contrast, the laboratory experiment presented here relies on the broadly accessible potentiometric technique. To accomplish the validation of a particular analytical method, several experimental procedures are usually required.3 For example, sample preparation, plotting calibration curves, and data analysis are core procedures of method validation. Depending on the analytic application of the method, a set of parameters is chosen to validate its performance1 such as precision, limit of quantification, limit of detection, etc. Teaching validation of analytical methods could be addressed by performing a narrow validation and calculating only one parameter such as accuracy (and its uncertainty) across several techniques, for example, spectroscopy, voltammetry, or potentiometry. Also, a partial validation is feasible by determining a selected set of parameters for only one technique. Certainly, this second approach requires less equipment and laboratory resources. Because full validations are beyond the teaching goals in a scholarly environment, partial validations are more appropriate due the amount of resources involved in their execution. Therefore, we have chosen a partial potentiometric validation, by means of a gas sensing electrode, taking into account that this is one of the most easy and accessible techniques in almost any laboratory. The beginning of the selective electrodes started with the development by Walter Nernst of the hydrogen H+(aq)/H2(g) electrode. One of the most important selective electrodes is the glass membrane electrode, also known as the pH electrode.10 Later, in 1953, Stow11,12 developed a gas sensing electrode for CO2. As can be seen in Figure 1, the CO2 sensing electrode has a gas permeable membrane and a standard NaHCO3 internal aqueous solution. The CO2 gas to be quantified diffuses to the internal solution across the membrane generating the ionic species H+, HCO3−, and CO32−. As concentration of these species change in the internal solution, pH variations are detected by an inner pH electrode 11−13 (Figure 1). Applications of this sensing electrode include CO2 measurements in blood,14 CO2 generated from metabolic processes in plants,15 and determination of urea16 and oxalate.17 Moreover, quantification of CO2 is a fundamental element of quality assurance in fields such as agricultural industry and food.18 For instance, CO2 detection and quantifications are carried out by practically any soft drinks, mineral water, and breweries producers.17,19 The aims of the present work are first, to present the performance of a series of parameters needed to validate a potentiometric method to quantify CO2 in carbonated drinks. Second, demonstrate the application of the validated method. Finally, propose, implement, and corroborate the achievements
Figure 1. Parts and schematic view of a gas sensing electrode responsive to CO2. This probe fundamentally works as a pH electrode.
of a laboratory experiment in team-working guided sessions. This experiment has been carried out with students enrolled in undergraduate programs, at the Facultad de Estudios Superiores Cuautitlán of the Universidad Nacional Autónoma de México, on chemistry but can be extended to related majors such as industrial chemistry, chemical engineering, pharmacy, food engineering, etc.
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MATERIALS, EQUIPMENT, AND REAGENTS Carbon dioxide sensing probe, supplied with membrane kit, sodium hydrogen carbonate internal electrolyte solution (Mettler Toledo), combined pH/conductivity meter (SevenMulti S47, Mettler Toledo), recirculating bath (FC 6, SEV), deionizer (Pure Lab Classic, ρ = 18.2 MΩ cm). Sodium hydrogen carbonate (analytical grade, JT Baker), dihydrate sodium citrate, (ACS grade, JT Baker), concentrated hydró chloric acid, (Quimica Meyer), sodium chloride (analytical ́ grade, Reactivos y Productos Quimicos Finos, México), sodium ́ hydroxide (analytical grade, Quimica Meyer), anhydrous dibasic sodium phosphate (ACS grade, Fermont).
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HAZARDS Concentrated HCl and NaOH are corrosive, toxic, and irritants; work under a fume hood. Sodium citrate and sodium phosphate are harmful if swallowed and eye irritants. Wear laboratory coat, safety glasses, and gloves.
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VALIDATION OF A POTENTIOMETRIC METHOD FOR DETERMINATION OF CO2 As mentioned before, validation relies on evaluating a set of suitable chosen parameters that gives the performance of a particular method.1 Thus, to accomplish the validation of the potentiometric determination of CO2 in a solution, we have chosen the following parameters, regarded as the most important for validating analytical procedures:1 linearity range, limit of quantification (LOQ) and limit of detection (LOD), precision, robustness, sensitivity, accuracy, and specificity. Parameter definitions, as well as experimental protocols for their determination, are provided in detail in the Supporting Information. It is important to mention that a diligent experimental design must be applied in the whole validation procedure. B
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Linearity Range, Limit of Quantification, and Limit of Detection
It is interesting to analyze the origin of nonlinearity at the extremes of the calibration curve. The lowest section in Figure 2 is horizontal because of the low concentrations of CO2. In this region, a small amount of CO2 diffuses across the membrane, having no effect on the pH of the internal solution. Then the upper section of the curve is again horizontal due to the limited range of response of the CO2 saturated internal solution and the glass electrode.17 Once the linearity range has been determined, the LOQ17 and LOD13 can be obtained being 8.98 ± 1.1 mg L−1 and 1.48 ± 0.04 mg L−1, respectively. See details in Supporting Information, sections 1.3 and 1.4. Performance parameters of the calibration curve are shown in Figure 2 and compiled in Table 1.
Linearity defines the ability of the method to obtain test results proportional to the concentration of analyte. In case of a CO2 sensing electrode, the LOQ is defined as the beginning of the linear range where the Nernstian response starts. For some authors,17 this is the lowest point for making useful determinations (Figure 2). The standards should be prepared
Table 1. Results of Parameters of the Method Parameter
Figure 2. Variation of the potential E as a function of log [CO2]TOTAL for the three sets of determinations. Linearity range, LOQ, and LOD are indicated. [CO2]TOTAL is given in mg L−1.
carefully to observe the point where the calibration line becomes curved. Thus, the LOQ becomes independent of the chosen concentrations to prepare the standards. On the basis of the IUPAC recommendation,13 the practical lower LOD may be taken as the concentration of CO2 at the intersection point of the extrapolated linear midrange and final low concentration level segments of the calibration curve (Figure 2). To establish our interval of linear analytical response and to set up the LOQ and LOD, an experimental calibration curve was plotted (three times) by measuring the potential (E) of standards of CO2 with concentrations ranging from 8.88 × 10−5 to 2.81 × 104 mg L−1. NaHCO3 was used as primary standard to prepare standard solutions, and to adjust the pH value to 4.5 a 1.73 M citrate/citric acid buffer solution was used (see Supporting Information, section 1.1). Visually we can establish that the calibration curve, presented in Figure 2, tends to be linear in a defined interval of concentrations. To define the linearity range, a search within different data sets must be conducted by choosing the set that gives the best R2 and closely follows the Nernst law. Linearity range is established from Figure 217,20 by applying least-squares fitting to the experimental potentials; thus,
a
Acceptability Criteria
Linearity
R2 ≥ 0.98a,b
LOQ LOD Precision
r&R < 10%c
Robustness
|di| ≤ 3%d
Sensitivity Accuracy
Slope ≈ 59.16 mVe CV ≤ 5%d
Specificity
100% must be included in PRec
Experimental Results R2 = 0.9994 Slope = 54.02 ± 0.34 mV Range: 8.89−280.92 mg L−1 8.98 ± 1.1 mg L−1 1.48 ± 0.04 mg L−1 r = 5.94 mV R = 2.38 mV r&R = 3.00% Temperature: |di| = 2.8% Buffer solution: |di| = 3.4% Open beaker: |di| = 6.5% 54.02 ± 0.34 mV CV = 2.73% and 2.00% PRec = 99.7% and 99.6% PRec = 96.7 ± 6.2%
See ref 1. bSee ref 17. cSee ref 25. dSee ref 21. eSee ref 13.
Precision
Precision is described by two components: the smallest expected precision and the largest encountered measured precision, known as repeatability (r) and reproducibility (R), respectively.22,23 These components were evaluated via a standard study of two-way analysis of variance (ANOVA) without interactions. It has been recommended to prepare ten different concentrations (c = 10), in duplicate (m = 2), and perform readings by three different analysts (a = 3).24−26 For this purpose, concentration ranged from 5.02−891.69 mg L−1. Notice that concentrations values outside the linearity range have been used to challenge the validation beyond its linearity limits: r = 5.15 MSE R = 5.15
E = −(210.55 ± 0.61) + (54.02 ± 0.34) log[CO2 ]TOTAL
MSA − MSE cm
(2)
(3)
In eqs 2 and 3, MSE and MSA stand for mean square error and mean square of the analyst, respectively.24−27 For normally distributed data, the value 5.15 defines 99% of the space under the normal curve.28 The raw data, the explanation for the use of ANOVA without interaction and the evaluation of r and R through ANOVA analysis are found in Table 5−8 of Supporting Information, section 1.5. The r and R are calculated by means of eqs 2 and 3.24,26 Results for r and R are shown in Table 1; please notice that
(1)
where E is obtained in mV. Linearity is observed from 8.89−280.92 mg L−1 (Figure 2), and the obtained potentials display a high determination coefficient of R2 ≥ 0.99, denoting also a Nernstian behavior.21 Furthermore, at 97.5% significance level the plot exhibits a slope value with a confidence interval (CI) of 54.02 ± 0.34 mV (eq 1). Refer to Supporting Information, section 1.2. C
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(or activity) of the active species (aA) with charge zA, which is expected to have a slope of 59.16/zA mV per unit change of log(aA) at 298.15 K. Both recommendations point out that the slope of the potential versus logarithm of the concentration curve gives the method sensitivity. Thus, this parameter is already established from the linearity range fitting equation (eq 1), its value is 54.02 ± 0.34 mV. See Supporting Information, section 1.7.
these parameters have the same units of measurement as the original observation. Thus, r = 5.94 mV > R = 2.38 mV, and this result might indicate that the equipment needs adjustments or that the measurement processes should be improved.25 Finally, to evaluate the inherent precision of the method r&R, eq 4 is applied:29,30 r 2 + R2
r &R =
(4)
Accuracy
The value of r&R = 6.40 mV, to obtain the percentage is necessary to make a relation with the total variation obtained with ANOVA as 100%; the percentage of r&R is 3.00%. Because the percentage of r&R < 10%, the measurement system is acceptable.24−26
Accuracy is the quantity resulting from the differences between the average of a series of measurements, or an individual measure, and the accepted value as the true or correct value for a measurement.1,21,23 The accuracy is determined by means of the percentage of recovery, with an experimental calibration curve obtained in the linear interval of E versus log[CO2]TOTAL. To do so, the potential of two solutions of two known concentration, 88.61 and 132.91 ppm, was measured in sextuplicate.1,21,22 Results of experimental determinations, the average of PRec, and the coefficients of variation, are compiled in Table 1, see Supporting Information, section 1.8. The average recovery for two different concentration levels 88.61 mg L−1 and 132.91 mg L−1, are 99.7% and 99.6% with coefficients of variation of 2.7% and 2.0%, respectively. Consequently, the accuracy of the method is acceptable.1
Robustness
The robustness of an analytical procedure is a measure of its capacity to remain unaffected by small, but deliberate variations in method parameters. Robustness provides an indication of the method reliability during normal usage.1 For determining robustness, one deliberate modification at the time in the experimental conditions must be carried out.1 We modified temperature, nature of the buffer, and beaker either closed (with lid) or open (without lid). For the regular conditions of the experiment, T = 25 °C, citrates buffer in a closed system, a calibration curve in the linearity range was built reading three standards. Then this curve is employed to estimate, again in triplicated, a standard analyte of a known concentration of [CO2]TOTAL = 50 mg L−1, under regular and altered conditions: T = 38 °C or buffer of phosphates (pH = 4.5) or open system. After the average percentage of recovery (PRec) was obtained, by means of eq 5, for the regular and altered conditions, PReco and PReci, respectively, the absolute difference |di| = |PReci − PReco| was determined to evaluated the robustness of the method: the smaller the |di|, the more robust the method. It has been established18 that, after altering a factor, a |di| ≥ 3% indicates the robustness of the method is compromised. Table 1 compiles the results obtained for the described challenges to the method; see Supporting Information, section 1.6. PRec =
[CO2 ]TOTAL exp × 100 [CO2 ]TOTAL Standard
Specificity
Specificity is the capacity of the analytical method to determine exactly and specifically the analyte of interest, in the presence of other components, in a sample matrix under the established test conditions.1 To know the specificity of the method for the objective it is intended for, it is necessary to execute determinations in the presence of the matrix. In this particular case, carbonated drinks were degassed to eliminate the CO2 as much as possible by heating and ultrasound−bath agitation; this matrix was then employed to prepare NaHCO3 standard solutions. The specificity parameter determined in such a way shows the viability of using a calibration curve in water to quantify the CO2 in carbonated drink samples. Table 1 displays the experimental results for evaluating the specificity of the method, Supporting Information, section 1.9. As it can be observed in Table 1, the average value of the recovery is 96.7% with a coefficient of variation of 6.2%. Such a low value for the recovery might indicate that the treatment of the matrix introduces unexpected variability on the results.
(5)
Thus, the factor that has more impact on the recovery is opening the beaker (6.5%), followed by switching the buffer solution from citrates to phosphates (3.4%) and the change in temperature (2.8%). Therefore, because the |di| of the temperature and the buffer solution did not go over 3%, these factors can be modified under regular working conditions and would have a minimum effect on the overall performance of the method. In contrast, CO2 determination is revealed to depend strongly on the open/closed condition of the system. Consequently, it is not recommended to modify this parameter for routine application of the method.21
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APPLICATION OF THE VALIDATED METHOD: DETERMINATION OF CO2 IN CARBONATED DRINKS
CO2 Calibration Curve
As it has been discussed, a central element for analyte determinations is the calibration curve. Unknown samples are read in the calibration curve to find the corresponding concentrations. Calibration curve validity is based on an accurate and precise recovery for known samples, which are independent of the standards, prepared in the same manner as the unknown. In this particular case, we prepared a series of solutions by dissolving NaHCO3 in deionized water. The covered range of concentrations went from 24.98 to 149.91 mg L−1, which lies in the linearity interval. The E was then measured for each solution, three times, and the average plot was used for the
Sensitivity
Following the EURACHEM Guide,1 the analytical sensitivity is the change in instrument responses, which corresponds to a change in the measured quantity (for example an analyte concentration), that is, the gradient of the response curve. When the potentiometric method sensitivity needs to be estimated, IUPAC13 recommends to observe the Nernstian response in the plot of the potential difference of the ISE (ionselective electrodes) against the logarithm of the concentration D
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acquired knowledge. At the end of the last session, a final quiz was applied to evaluate the global learning. Results of the grades on these quizzes showed that the scored average substantially increased from 2.3, 3.8 to 6.5 on a scale of zero to ten. Finally, Table 2 compiles all the results obtained by the students for determining CO2 content in carbonated drinks;
determinations. More details of the calibration curve are found in Supporting Information section 2. Sample Preparation and Determinations
Several different samples were prepared from the four commercial cola carbonated drinks retailed in Mexico City, labeled as X, X Light, Y, and Y Light. The drinks used in this experimentation were from 600 mL of polyethyene terephtalate (PET) bottles. As soon as the drinks are opened, due to the change of pressure, they start to effervesce, and CO2 escapes. Thus, the pH must be promptly adjusted to a value greater than 10 for the CO2 to be transformed in CO32− and stay in the solution during manipulations. Determination of CO2 concentration was successfully achieved using the validated method; it produces acceptable results because the values are in good agreement to those reported for CO2 in carbonated drinks (4−8 g L−1).31,32 Table 15 in Supporting Information section 2 compiles these results. An evident advantage of this potentiometric method is its inherent rapidity for the determination of a large series of samples. Once the method has been validated, it is possible to carry out several measurements of the problem samples, with only one calibration curve, in minutes for routine use.
Table 2. Students Experimental Results and CO2 Content in Carbonated Drinks Working Group
[CO2] in the Bottle (g L−1)a
1 2 3 4 5 6 a
6.36 6.17 6.31 6.72 6.01 6.80
± ± ± ± ± ±
0.11 0.08 0.08 0.25 0.19 0.36
Average on triplicated measurements.
notice that treatment of the samples implies dilution to adjust the concentration to the linearity range of the method. Their results are consistent with our previous results showing that students were able to apply a validated method to quantify the analyte in commercial samples.
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LEARNING EXPERIENCE Bearing in mind that method validation is a subject scarcely treated in regular courses of chemistry, a didactical approach was designed for teaching validation to students on this field by employing the same set of validation parameters already discussed. We employed the CO2 gas sensing potentiometric determination previously discussed for introducing the topic on method validation as well as the application of the validated method for CO2 quantification in carbonated drinks. Initially, to develop the laboratory experiment, we invited 19 students enrolled in the B.Sc. on either chemistry or industrial chemistry, in the Facultad de Estudios Superiores Cuautitlán (Universidad Nacional Autónoma de México); this group was subdivided in six smaller working groups. The experiment was divided in three laboratory sessions. Working with potentiometry is rather simple; therefore, skills of the students were not evaluated prior to experimentation, but a series of good laboratory practices were recapped. Each laboratory session proceeded with a short lecturing on the principles of method validation and the parameters to be evaluated during the session, followed by hands-on guided sessions for data collection. After the potentiometric readings were performed, the students input the collected data in Excel worksheets previously prepared for statistical data processing (raw data as well as processed data are included in Supporting Information, section 3). The instructor assisted students on the analysis and interpretation of results for each evaluated parameter by focusing on how the results could impact the validation of the whole method. Lecturing (approximate 15 min) and total data collection took about 12 h, divided on three laboratory sessions (from 3 to 4 h), preparation of standard solutions is not considered in this time. To explore the pedagogical effectiveness of the laboratory experiment, we compared the results of a series of the applied quizzes. These quizzes are available in Supporting Information, section 4. Before the experimental sessions, students took individual quizzes on validation of analytical methods to assess their previous knowledge on the subject. After lecturing and experimental session, a final quiz was applied to assess the
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CONCLUSIONS An analytical method aimed to quantify the amount of CO2 in carbonated drinks has been successfully proposed and validated, following the recommendations of international regulatory agencies. As the validation procedure relies totally on potentiometry, it is easily affordable to almost any chemistryteaching laboratory, which allows the teachers to include method validations as an important subject to be taught. More sophisticated and costly techniques could be validated by evaluating basically the same set of validation parameters presented here. A learning experience of method validation was proposed and implemented in a team-working guided teaching activity to introduce the topic in undergraduate level. Evaluation of the learning experience shows that students improved their knowledge on method validation. The present work showed that once students have validated the method, they are capable to satisfactorily quantify CO2 in real commercial samples.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.7b00252. Comprehensive information on solution preparation and data treatment, usable by teacher assistants or professors, to conduct the experiment (PDF, DOCX)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Rodolfo Gómez-Balderas: 0000-0002-3293-1841 Notes
The authors declare no competing financial interest. E
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(20) Guidelines for Collaborative Study−Procedures to Validate Characteristics of Methods of Analysis, Appendix D. In Official Methods of Analysis of AOAC INTERNATIONAL; AOAC International: Rockville, MD, 2015; pp 1−11. ́ (21) Colegio Nacional de Quimicos Farmacéuticos Biólogos México, ́ A.C. Guiá de Validación de Métodos Analiticos, 2nd ed.; Colegio ́ Nacional de Quimicos Farmacéuticos Biólogos México: México City, México, 2002. (22) Compendium of Chemical Terminology; Gold, V., Loening, K. L., McNaught, A. D., Shemi, P., Eds.; Blackwell Scientific: Melbourne, 1987. (23) ISO 3534−1:2006. Statistics−Vocabulary and Symbols−art 1: Probability and General Statistical Terms; International Organization for Standardization: Geneva, Switzerland, 2006. (24) Engineered Software, Inc. Repeatability and Reproducibility; Engineered Software, Inc.: Belleville, MI, 1999. http://www. engineeredsoftware.com/papers/msa_rr.pdf (accessed May 28, 2017). (25) Llamosa, L. R.; Meza, L. G.; Botero, M. Estudio de Repetibilidad y Reproducibilidad Utilizando el Método de Promedios y Rangos para el Aseguramiento de la Calidad de los Resultados de Calibración de Acuerdo con la Norma Técnica NTC-ISO/IEC 17025. Scientia Et Technica. 2007, 13 (35), 455−460. (26) Montgomery, D. C. Introduction to Statistical Quality Control; Wiley: New York, 2009; Vol. 7, pp 368−378. (27) Duncan, A. J. Quality Control and Industrial Statistics, 5th ed.; Richard D. Irwin: Homewood, IL, 1986. (28) Dell Inc. Statistics: Methods and Applications; Dell: Tulsa, OK, 2007. https://support.quest.com/technical-documents/statistics/ current/textbook/16#TOPIC-322268 (accessed May 28, 2017). (29) Burdick, R. K.; Larsen, G. A. Confidence Intervals on Measures of Variability in R&R Studies. J. Qual. Technol. 1997, 29 (3), 261−273. (30) Dolezal, K. K.; Burdick, R. K.; Birch, N. J. Analysis of a twofactor R & R study with fixed operators. J. Qual. Technol. 1998, 30 (2), 163−170. (31) Baur, J. E.; Baur, M. B.; Franz, D. A. The Ultrasonic Soda Fountain: A Dramatic Demonstration of Gas Solubility in Aqueous Solutions. J. Chem. Educ. 2006, 83 (4), 577−580. (32) Levy, J. B.; Hornack, F. M.; Levy, M. A. Simple Determination of Henry’s Law Constant for Carbon Dioxide. J. Chem. Educ. 1987, 64, 260−261.
ACKNOWLEDGMENTS The authors are grateful to PAPIME(UNAM) Grant No. 203911 and PIAPI (FESC-UNAM) Grant No. 1629 for partially financing this work. A.R. H.-N. thanks the PAPIME program scholarship to pursue his major on chemistry. We are in debt with all the students that generously worked in the project.
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DOI: 10.1021/acs.jchemed.7b00252 J. Chem. Educ. XXXX, XXX, XXX−XXX
