An Exercise in Measurement, Calculations, and Graphical Analysis

Laboratory Experiment pubs.acs.org/jchemeduc

Hydration of Decorative Beads: An Exercise in Measurement, Calculations, and Graphical Analysis Rebecca A. Hill† and Christopher P. Nicholson*,‡ Department of Chemistry, University of West Florida, Pensacola, Florida 32514, United States S Supporting Information *

ABSTRACT: Throughout the general chemistry lab curriculum, a common shortcoming is the way in which students measure, record, and manipulate quantitative data. From initial measurements with different digital and analog instruments to proper conversions, calculations, and comparisons, students are often expected to be experts before they have been taught proper technique and scientific principles. While the start of any General Chemistry 1 course involves a period of familiarization with the scientific method, significant figures, and elements of atomic structure, these often do not correlate well with laboratory experimentation. We have developed an experiment to be conducted during the first weeks of a general chemistry lab that emphasizes measurement techniques, accuracy, average value calculations, and uncertainty of measurement calculations. The experiment is designed such that time versus mass change measurements are taken and used in an introduction to graphical analysis. This allows for the experiment to be done in a short period of time while also affording student-generated data for teaching spreadsheet use, data processing, and linear regression. Instructor feedback and student survey data following this experiment indicate significant improvement in students’ abilities to collect and properly analyze data. KEYWORDS: First-Year Undergraduate/General, Laboratory Instruction, Hands-On Learning/Manipulatives, Quantitative Analysis

F

early in one’s education allows for a greater focus on the chemistry of topics like titration and energy rather than devoting more time to the mathematics.9−11 Finally, students in the first weeks of the semester frequently have little to no knowledge of chemical properties that could be probed in a deeper, hands-on way in a laboratory exercise. Over the years, there have been many attempts to address this gap at all levels of chemistry through the development of “first-day experiments” in general chemistry.8,12 As a “first-day experiment” to bridge the gap between measurement experience and real applications of lecture material, an experiment utilizing decorative hydrating beads has been designed to engage students with the different measurement devices they will be expected to use throughout the laboratory course, and to reinforce many basic science and laboratory math concepts. Over the course of this experiment students measure mass, volume, and size by different instruments to compare accuracies and quantify physical change and conservation of mass.

undamental to the study of chemistry is the ability to obtain, manipulate, and interpret quantitative data. At the beginning of many general chemistry courses a great deal of time is devoted to the difference between quantitative and qualitative measurements as well as to concepts such as accuracy and precision.1−4 In the laboratory portion of the course, however, students are often expected to start experiments with an appreciation for different levels of accuracy in equipment which many of them have not handled previously. The differences in devices used to measure mass or volume are often not intuitive, and developing an appreciation for the various measurement tools is critical to instill in students an understanding of both what data are being collected and also why it is collected in a specific way. The laboratory is the ideal setting for developing and enhancing these applied skills that will stay with the student for a lifetime regardless of their course of study.5,6 Another skill with which students are frequently inexperienced is the proper use of spreadsheets for assessment of data requiring repetitious calculation or graphical analysis.7,8 A significant proportion of incoming general chemistry students report limited or no experience with Excel or similar spreadsheet products (Table 1). Developing these skills can begin to reap benefits as early as the study of gas laws if students have experience with the program and a basic understanding of its application. Addressing basic statistics © XXXX American Chemical Society and Division of Chemical Education, Inc.

Received: May 21, 2017 Revised: August 7, 2017

A

DOI: 10.1021/acs.jchemed.7b00349 J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

Laboratory Experiment

Table 1. Comparison of Students’ Self-Assessments of Skills Average Self-Assessment Scoresa Skill Areas Students Assess

Preassessmentb

Postassessmentc

Changed

Score Increase, %

Familiarity with measuring liquid volumes Familiarity with measuring masses Understanding which measurement technique or device is most accurate Ability to calculate the volume of a solid object using geometry Ability to take measurements by difference Ability to calculate an average of a group of numbers Ability to calculate the standard deviation of a group of numbers Using significant figures rules in calculations Understanding how to apply the law of conservation of mass Entering data into an Excel data table (spreadsheet) Generating a graph of data using Excel Adding a trend line to graphed data and making predictions with the graph

3.94 3.85 3.51 3.44 3.72 4.43 3.40 4.08 3.47 3.41 3.23 2.91

4.47 4.46 4.32 4.10 4.43 4.62 4.29 4.34 4.21 3.77 3.68 3.76

0.53 0.61 0.81 0.66 0.71 0.19 0.89 0.26 0.74 0.36 0.45 0.85

13 16 23 19 19 4 26 6 21 11 14 29

a The self-assessment scale ranges from 1 (no familiarity) to 5 (confident enough in the skill to teach someone else). bN = 290 students. cN = 258 students. dFor each skill students assessed, the calculated p-values were p < 0.001 (one-way ANOVA, two-tailed distribution); pre−post change is statistically significant at a 95% confidence interval.

■

EXPERIMENTAL PROCEDURE

Mass and volume change of the bead, and heating time of the bead, are reported to the instructor, and the class set of data is distributed for graphical analysis which can be conducted in the same laboratory session or a future session or assigned as a take-home exercise. Representative student data from two laboratory sections is shown in Figure 1.

Data Collection

Student handouts (see the Supporting Information) were distributed to all students, instructors, and student teaching assistants using class management software (eLearning). Students were provided with a variety of volume measuring devices of different levels of accuracy. Initially, a 50.0 mL buret was filled near the 0.0 mL mark with water. Students assessed the initial buret reading and then transferred the water to successively less accurate measurement devices recording the measured volume according to the level of accuracy allowed by the device. Finally, the water was transferred to a tared beaker, and the mass of the beaker with water is measured to determine the mass of the water by difference. This process provides four distinct measurements of the water volume: three direct volume measurements and one calculated from mass and density. Students are asked to think about the accuracy of the four measurements and to rank them from most to least accurate. The beaker of water is then used in the hydration bead with the mass being used for subsequent conservation of mass analysis. Students are then issued a small, decorative hydration bead and asked to color the bead with a small dot of permanent marker. The mass of the bead is recorded on four different analytical balances, and the average mass of the bead and standard deviation are calculated. The diameter is also measured with a micrometer, and the volume of the sphere is calculated. The beaker with the water previously measured is placed in a boiling water bath, and the bead is placed in the measured water. The bead is heated for a preassigned time from 30 to 60 min. After the assigned heating time, the smaller beaker is removed from the water bath, and the exterior is dried. The hydration bead is carefully removed, and the mass of the bead is measured on four different analytical balances. Again, the average mass of the bead is calculated as well as the standard deviation of the mass and mass change. The diameter of the hydrated bead is also measured and the new sphere volume calculated along with the change in volume. The beaker with the measured water is also weighed on the pan balance to determine the mass of water remaining in the beaker for conservation of mass analysis.

Figure 1. Results of student-collected mass and volume changes for two sections of the General Chemistry 1 course. The red and blue circles in each graph represent data from two different student groups, both enrolled in the Fall 2014 semester, but with different instructors.

Data Analysis

The first analysis conducted on the data involves the law of conservation of mass. Students are asked to consider the total mass of materials before the hydration and compare that to the mass of materials after hydration. The principle of measurement by difference is reinforced through both water mass B




Table 2. Comparative Student Demonstration of Skills and Concepts Correct Responses, % Questions and Statements for Student Response

Preassessmenta

Which of the following laboratory volume measuring devices is the most accurate? Which of the following is a measurement by difference? Calculate the average of the following mass measurements. The law of conservation of mass states that... Which of the following volume measurements has the most significant figures? Which of the following statements best defines precise data? Based on the following graph, what would you expect a bead mass to be after 75 min? (The initial mass of the bead was 0.0176 g.)

42 93 84 63 81 56 56

Postassessmentb Increase, %c 74 95 86 71 89 63 67

76 2d 2e 13 10 13f 20

a N = 290 students. bN = 258 students. cExcept as noted, for each skill or concept tested, the calculated p-values were p < 0.001 (one-way ANOVA, two-tailed distribution), indicating statistical significance at a 95% confidence interval. dp = 0.252. ep = 0.493. fp = 0.017.

prior to the experiments on a scale from 1−5, with 1 being no familiarity with the skill or concept and 5 being confident enough to teach it to someone else. To validate self-assessment data, a series of multiple-choice question were asked prior to the experiment to quantify understanding of concepts and skills. Upon completion of the graphical analysis portion of the experiment, students were asked to repeat the set of assessments. The results of these assessments are presented in Tables 1 and 2. A score of 5 is the maximum value for each assessment item. A score of 3 is equivalent to an ability to use a concept but not necessarily explain it to others. Throughout the semester, as the concepts of this experiment recurred in other experiments, student assessment was conducted on individual rubric-graded items to assess retention and application of skills. The specific concepts assessed in future experiments were appropriate performance of calculations, specifically averaging of data and determination of standard deviation, and the use of spreadsheets to manipulate and graph data as well as incorporation of a trend line to make predictions. The scores on the specific graded items are presented in Table 3.

measurements, and the concept of conservation of mass is tested by the differences in mass before and after the reaction. Students are challenged to think critically about sources of mass loss or gain not accounted for in the simple measurement of water and bead masses. Using the class set of heating time and bead change data, students are instructed on the use of Excel or other spreadsheet programs and asked to generate separate graphs of the mass change versus heating time and volume change versus heating time. A linear regression is performed on each graph, and the trend lines are used to predict both the change and final value of either property after any proposed heating time. This experiment can be incorporated into a more comprehensive introduction to the use of spreadsheets for calculations and graphical analysis.

■

HAZARDS The primary hazard of this experiment is the presence of hot water baths and hot plates. Standard safety equipment, including appropriate laboratory attire, closed-toe shoes, and safety glasses, should be employed. The beads are commercial decorative products and have no special hazard information or cautions, and no additional reagents are used in the course of the reaction.

Table 3. Student Scores on Subsequent Experiments

■

STUDENT EXPERIMENTAL DATA Student data from two different laboratory sections is presented in Figure 1. The data collected through this experimental process has resulted in a wide variety of changes in both mass and volume that can be attributed to drops of water not removed from the bead prior to weighing, as well as variation in the temperature of the water baths and close adherence to the assigned heating time. Additionally, while most beads are spherical when hydrated, some beads are asymmetric, resulting in a less accurate volume calculation. The variation in student data makes for a useful example in the graphical analysis portion of the experiment where R2 values for linear fits to graphical data can be discussed in the context of how accurately a trend line represents measured data.

Assessment Items Volumetric determination of % acid: Calculated values associated with measurements Gas laws: Boyle’s law graph Gas laws: Pressure versus temperature graph Gas laws: Absolute zero graph Heat of vaporization: Calculations of heat of vaporization of liquid nitrogen

Student Reports, N

Possible Rubric Points

Average Student Score

173

7

5.19

161 161

4 2

2.74 1.66

161 159

2 5

1.44 4.00

■

STATISTICAL ANALYSIS Analysis of student pre- and postassessment averages was conducted using one-way ANOVA to assess the significance of the change in student self-assessment and demonstration of skills and concepts. For all self-assessment data presented in Table 1, the calculated p-values indicate that the change from pre- to postlaboratory is statistically significant at a 95% confidence interval. One-way ANOVA analysis of the pre- and postlaboratory assessment of concepts and skills, presented in Table 2, was more varied in the significance of the change. Questions 2 and

■

STUDENT OUTCOME DATA This experiment was conducted in the Fall 2014 semester across 14 separate sections of General Chemistry I Lab (CHM2045L) at the University of West Florida. Students conducting this experiment during the Fall 2014 semester were evaluated multiple times to assess their ability to collect, manipulate, and interpret quantitative data. Students were asked to rate their strength in a variety of skills and concepts C




pressure versus temperature as well as create a graph trending back to determine absolute zero. On these graphs and trend line applications students averaged 83.0% and 72.2%, respectively. Comparison of rubric item scores from prior semesters was, unfortunately, not possible as aggregation of that data in prior semesters was not performed. Without the hindsight of retrospective analysis, it is impossible to say exactly what the impact of the experiment is on future laboratories; however, anecdotal observation from long-time faculty, both full time and adjunct, indicates a substantial improvement over past student performance. In conclusion, we have developed a safe, simple, and inexpensive study in scientific measurement, calculations, and data analysis. All relevant measurement calculations are practiced in a real context with repetition to reinforce the process of measurement by difference, averaging, and standard deviation calculation. The use of laboratory-generated data is also valuable as it shows students what real (as opposed to “cooked”) data looks like and affords a brief discussion of the use of a trend line and R2 value. Finally, it teaches a way to address an initial chemical concept, conservation of mass, and asks students both to assess whether mass was conserved and to assess errors in the experimental analysis of conservation of mass.

3, which assessed rudimentary aspects of laboratory measurement involving difference and averages, showed no statistical significance, with p-values of 0.252 and 0.493, respectively. All other questions in Table 2 showed a statistically significant improvement from pre- to postlaboratory at a 95% confidence interval.

■

CONCLUSIONS Prior to this course, many students had never participated in a chemistry lab and were unfamiliar with any laboratory measurement equipment. Students participating in the experiment anecdotally reported increased knowledge of the equipment in the laboratory, and instructors reported far less need to remind and reteach students about the use of different pieces of equipment in subsequent experiments. Certain concepts, such as calculating an average or using significant figures, received high pre-experiment values of 4.43 and 4.08, respectively, out of a possible 5. Accordingly, these skills experienced only a slight increase in student selfassessment over the course of the experiment. Less familiar skills such as understanding device accuracy rated a lower initial level of understanding (3.51 out of 5), but upon completion of the experiment students reported a 23% increase in understanding of device accuracy. This was demonstrated in the multiple-choice assessment where only 42% of students chose the proper order of accuracy prior to the experiment but 74% could identify the correct order after completion of the experiment. Students also rated their initial understanding of trend line construction and application to be very low, 2.91 out of 5, along with relatively poor understanding of adding data to a spreadsheet and graphing that data, 3.41 and 3.23, respectively. These skills improved on self-assessment after the experiment with trend line analysis rating a score of 3.76 out of 5 after the experiment, a 29% increase in student understanding. As with accuracy analyses, the ability to use graphical data and trend line analysis showed an 11% increase in the postlaboratory assessment questions. In addition to initial assessment, data from experiments performed downstream in the curriculum were also collected to assess the ability of students to perform relevant chemical calculations and graphical analysis during more complex chemical experiments. On a future experiment with numerous calculations related to the averaging of data and standard deviation calculation, students scored 74% on the graded element for the calculations. In a later experiment students were asked to measure temperature change in the vaporization of liquid nitrogen and to perform a series of calculation related to the enthalpy of vaporization. Students scored 80% on these calculations including averaging data and standard deviation first taught in the hydration bead experiment. Finally, student scores on several different graphical analyses related to gas laws were collected with a focus on spreadsheet use, understanding of graphical data, and trend line analysis. In one gas laws experiment students are asked to measure Boyle’s law data using the MeasureNet data acquisition system and generate both raw data and linear graphs using Excel. Students scored an average of 68.4% on the construction of the graphs, indicating some trouble typically owing to the use of the spreadsheet to calculate the inverse of the pressure and properly graph calculated data. Students were then asked to measure pressure versus temperature data and both graph the

■

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.7b00349. Student handout (PDF, DOCX) Instructor notes (PDF, DOCX) Surveys (PDF, DOC)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Christopher P. Nicholson: 0000-0003-2659-5404 Present Addresses †

Department of Chemistry, Mississippi State University, Mississippi State, Mississippi 39762, United States. ‡ Department of Chemistry and Biochemistry, Rose-Hulman Institute of Technology, Terre Haute, Indiana 47803, United States. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Special thanks to Pamela Tanner and the instructional faculty at the University of West Florida General Chemistry laboratories for implementing and refining the experiment and for general feedback.

■

REFERENCES

(1) O’Reilly, J. E. The Length of a Pestle. J. Chem. Educ. 1986, 63 (10), 894−896. (2) Zipp, A. P. A Simple but Effective Demonstration for Illustrating Significant Figure Rules When Making Measurements and Doing Calculations. J. Chem. Educ. 1992, 69 (4), 291.

D




(3) Bularzik, J. The Penny Experiment Revisited: An Illustration of Significant Figures, Accuracy, Precision, and Data Accuracy. J. Chem. Educ. 2007, 84 (9), 1456−1458. (4) Prilliman, S. G. An Inquiry-Based Density Laboratory for Teaching Experimental Error. J. Chem. Educ. 2012, 89 (10), 1305− 1307. (5) Bopegedera, A. M. R. P. Putting the Laboratory at the Center of Teaching Chemistry. J. Chem. Educ. 2011, 88 (4), 443−448. (6) Atkinson, G. F. Measurement or Interpretation? J. Chem. Educ. 1972, 49 (4), 226−227. (7) Davis, W. H., Jr.; Pryor, W. A. Measures of Goodness of Fit in Linear Free Energy Relationships. J. Chem. Educ. 1976, 53 (5), 285− 287. (8) Padgett, L. W.; MacGowan, C. E. Thermochemistry as a Teaching Tool for Graphing: A First-Day Introductory Chemistry Laboratory Experiment. J. Chem. Educ. 2013, 90 (7), 910−913. (9) Nelson, L. S. The Experimental Determination of an Error Distribution. J. Chem. Educ. 1956, 33 (3), 126−131. (10) Cunningham, C. C.; Brown, G. R.; St. Pierre, L. E. Evaluation of Experimental Data. J. Chem. Educ. 1981, 58 (6), 509−511. (11) Salzsieder, J. C. Statistical Analysis Experiment for Freshman Chemistry Lab. J. Chem. Educ. 1995, 72 (7), 623. (12) Bent, H. A. A Burner and a Beaker. J. Chem. Educ. 1986, 63 (10), 890−893.

E


An Exercise in Measurement, Calculations, and Graphical Analysis

Recommend Documents