In the Laboratory
A Quantitative Examination of Multiple Methods for Standardizing a Dilute Hydrochloric Acid Solution in an Undergraduate Chemistry Laboratory
W
Nancy E. Meagher,*† Dana B. Bowens, and B. Shawn Clark Department of Chemistry and Physics, Texas Woman’s University, Denton, TX 76204; *
[email protected] The standardizing of dilute acid and base solutions are lab operations routinely performed by students in a quantitative analysis laboratory. Performing this procedure is useful because the students gain experience in preparing their own solutions, and it presents the opportunity for teaching about primary reference standards and the meaning of the term “standardized”. Many quantitative analysis textbooks present more than one base and indicator combination for the standardization of dilute hydrochloric acid. Students often asked “which is the best indicator?” for the standardization of dilute hydrochloric acid when presented with more than one option. The question could not be answered because data on accuracy and precision for the various base– indicator combinations could not be located. It was decided that this question deserved an answer based on an experimental assessment of the accuracy of the various options, rather than an answer based on the personal preference of the instructor for a particular base–indicator combination. Consequently, the study presented herein was undertaken. Indicator titrations are rapid, but they suffer from the inherent variability in individual color perception that comes into play when identifying the endpoint. Although potentiometric endpoint determination provides data that are not biased by an individual’s color perceptions, obtaining the concentration of the solution being standardized is a tedious process requiring the students to leave the laboratory to plot their data to determine the endpoint. Sodium hydroxide standardization has an excellent indicator, one that changes from colorless to pink. This indicator is not particularly susceptible to errors from poor color sensitivity in a student’s vision; even if a student cannot distinguish a color as “pink” they may have the ability to distinguish the presence or absence of color, with a faintly pink-colored solution appearing pale gray if the student is color blind. Unfortunately, this situation is not replicated for the methods of standardization of dilute HCl solutions using primary standards. A survey of textbooks (1– 17) turned up eight different base–indicator combinations for use in standardizing dilute hydrochloric acid solution. Experimental To answer the students’ questions on which is “the best” indicator–base combination, the following procedure was performed. Standardized dilute hydrochloric acid solution (0.1000 ± 0.0002 N) was obtained from GFS Chemicals
(GFS Chemicals, Inc. P.O. Box 245, Powell, OH 43065) and this solution was divided and relabeled for the students as “unknowns”. These unknowns were then provided to the students with an accompanying handout with instructions to determine the concentration of their “unknown” HCl solution with the eight indicator–base combinations and report their results in the manner instructed in the handout, including subjective opinions on their favorite and least favorite technique for standardization. The question of student preference was included owing to the many complaints of several classes of students for the indicator–base combination previously selected. Of particular interest in this experiment was determining the most accurate and precise base and indicator combination. Subjective information on student preference was sought in an attempt to ascertain whether there was any correlation between student preferences for a given base–indicator combination and either accuracy or precision of the results. The base and indicator combinations used are listed in Table 1. In the handout used in the laboratory, the students were told their unknown solutions were approximately 0.1 M. The students were required to perform four standardization titrations (with the first as a quick trial to ascertain the vicinity of the endpoint, if desired) against the base, which had been dissolved in boiled, distilled deionized water. Calculations were performed by the students to determine the appropriate quantity of base to use by assuming 0.1 M HCl and a desired titration volume of 25.00 mL. Students reported the HCl molarity (amount concentration) based on the actual volume of acid used for each titration (some students did four careful titrations, others performed one rapid “trial” titration and three precise titrations for use in their calculations, a few performed five titrations on some of the indicator–base combinations), the average molarity, the percent relative standard deviation (% RSD), and their preference for the base indicator used. The reaction of the acid with sodium carbonate is well known; its reaction with TRIS (tris-(hydroxymethyl)-aminomethane) is a 1:1 reaction, and the reaction with sodium tetraborate decahydrate is given below as reaction 2. Only half of the borate remains in the basic form upon dissolution, as shown in reaction 1, yielding an overall 2:1 stoichiometry for the HCl:Na2B4O7⭈10H2O calculations. Na2B4O7⭈10H2O(s) → 2Na+ + 2H3BO3 + 2H2BO3− + 5H2O (1) H2BO3− + H+ → H3BO3
†
Current address: Department of Chemistry, SUNY Cortland, Cortland, NY 13045.
428
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(2)
The sodium carbonate was dried and stored in an oven at 110 ⬚C. The students removed some from the communal
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In the Laboratory Table 1. Base and Indicator Combinations Used in the Multiple Standardizations of a Solution of Dilute Hydrochloric Acid Method 1
Base
Indicator
Color Change
Reference
Na2CO3
bromocresol greena
pale blue to pale green
2, 8, 9, 11–5
b
2
Na2CO3
modified methyl orange (v1)
green to grey to purple
2, 3, 7, 17
3
Na2CO3
methyl redc
yellow to red
3, 7, 10, 11
canary yellow to orange yellow
3, 6, 10, 11, 16, 17
yellow to purple
1, 4, 5
4 5
Na2CO3
methyl orange
Na2CO3
e
methyl purple
d
f
6
Na2CO3
modified methyl orange (v2)
green to magenta
10, 11
7
TRIS (THAM)
bromocresol green
pale blue to pale green
3, 13
8
Na2B4O7⭈10H2O
methyl red
yellow to red
10, 11, 16
a
The color change interval of bromocresol green reported is pH 3.6–5.2 (10).
b
Modified methyl orange (v1) is methyl orange with xylene cyanol FF added and has a color change reported at approximately pH 3.8 (10).
c
The color change interval for methyl red is pH 4.2–6.3 (10).
d e f
The color change interval for methyl orange is pH 2.9–4.6 (10).
Methyl purple is a mixture of methyl red and an inert, blue dyestuff and has a color change range of pH 4.8 – 5.4 (6).
Modified methyl orange (v2) is methyl orange mixed with indigo carmine and undergoes color change at approximately pH 4 (10).
container and cooled their individual samples to ambient temperature in a desiccator. Students dried the TRIS (THAM) in an oven at 100–105 ⬚C for one hour and cooled it to ambient temperature in a desiccator; the Na2B4O7⭈10H2O was stored in a desiccator, but not dried in an oven. The bases were dissolved in previously boiled, distilled deionized water. Primary standard-grade sodium carbonate and TRIS were obtained from GFS Chemicals, as was ACS reagent-grade sodium tetraborate decahydrate, which was used as a primary standard since higher purity was not obtainable. The result from a potentiometric titration of primary standard sodium carbonate by dilute HCl is shown in Figure 1. This figure is included to present the actual pH data in a representative titration, as compared to the indicator color-change ranges, obtained from the literature.
Results and Discussion The students had ample experience with performing titrations and weighing solids, so overall technique should not have contributed excessively to errors in standardizations. One thing that was immediately noted in the experiment was that the sodium tetraborate decahydrate did not dissolve rapidly, increasing the time required to complete the experiment. That standard has the advantage of having the highest weight per equivalent of the three bases, so relative errors due to poor
12
Hazards
10
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8
methyl red
pH
Dilute HCl is mildly corrosive, and if spilled must be cleaned up immediately. If it gets on the skin, it should be washed off promptly. TRIS (THAM) is a mild irritant to eyes, skin, and respiratory system: do not inhale the dust. Wear gloves when handling TRIS. Sodium carbonate is an irritant and should not be inhaled. Sodium tetraborate decahydrate may cause eye, skin, and respiratory tract irritation: do not inhale the dust. Wear gloves when handling sodium tetraborate decahydrate. The indicator methyl purple is in an isopropyl alcohol solution, and hence is flammable. Keep away from open flame. Methyl purple solution may also cause eye irritation or respiratory tract irritation. Do not inhale the fumes. The other indicators are in water solutions and should be rinsed from skin if contact is made as they are irritants and will also stain the skin.
6
methyl purple methyl orange
4
bromocresol green 2 0
5
10
15
20
25
30
Volume of Titrant / mL Figure 1. Data from a titration of sodium carbonate solution with dilute HCl with potentiometric endpoint detection. Color-change ranges of four indicators used in the study are shown.
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In the Laboratory
quantitative transfer technique are lowest, but the rather slow dissolution was problematic. Standardization against sodium carbonate is complicated by the formation of the carbonic acid–bicarbonate buffer system from supersaturation of the solution with carbon dioxide; boiling the solution and cooling to room temperature can be performed to obtain a sharp end point. Sodium carbonate also has the lowest equivalent weight (52.99 g兾equiv) of the bases studied. For standardization against sodium carbonate, the references recommended boiling the solution prior to the endpoint for use of methyl purple, bromocresol green, methyl red, and methyl orange. However, destruction of the buffer system by boiling can only serve to sharpen the endpoint of the titration by increasing the pH change as the equivalence point is approached, so the students were instructed to boil the sodium carbonate solutions for all indicators used. Boiling the solution is not an insurmountable problem; however, the students must understand the importance of rapidly cooling the solution to room temperature in order not to have temperature effects on the KIn invalidate the endpoint (18). Nine students performed the experiment. There was no clear consensus among the group for the base and indicator combinations as to which was the preferred method. Only one student selected the sodium tetraborate decahydrate with methyl red as the most desirable combination of base and indicator. Three selected sodium carbonate with bromocresol green (method 1) as most preferable, and one selected
sodium carbonate with methyl red (method 3). More unanimity was seen on the “least favorite” methodology. Four of the nine students reported that “modified methyl orange (v1)” (method 2) was the worst indicator, one reported “modified methyl orange (v2)” (method 6) was most disliked and two reported sodium carbonate with bromocresol green (method 1) was least favored. One student selected sodium tetraborate decahydrate with methyl red as the least liked method (method 8). Upon first analysis, the quantitative data reported by the students revealed that there was not any clearly superior base– indicator combination, although there did appear to be some difference between the options. The data for the entire class are presented in Table 2. Examining the average molarity for the class as a whole indicates that the much disliked “modified methyl orange (v1)” with sodium bicarbonate (method 2) produced the best accuracy. The individual student’s precision with that indicator was relatively poor in terms of percent relative standard deviation (% RSD), with the best precision (% RSD) of 0.29% and the worst at 2.68% on replicate titrations. For the purposes of preparing standardized dilute hydrochloric acid, the students are required to obtain 0.5% RSD or lower prior to moving on to the next determination. Obtaining results with good precision with that indicator was an issue generating a substantial number of student complaints during the semester. The modified methyl orange indicators do have optical properties that can only be
Table 2. Student Data for the Different Standardization Options Student
Method from Table 1
Parameter
1 a
1 2 3 4
2
3
4
5
6
7
8
Ave Mean
0.1014
0.1002
0.1017
0.09958
0.1004
0.1000
0.1006
0.09893
%RSD
1.06
0.39
0.34
0.26
0.51
0.27
0.80
0.14
Ave Mean
0.1012
0.09981
0.1002
0.09824
0.1007
0.09907
0.09958
0.09828
%RSD
0.86
0.60
0.36
1.88
0.35
0.27
0.58
0.52
Ave Mean
0.1013
0.09998
0.1040
0.1009
0.1037
0.1005
0.1000
0.09971
%RSD
0.40
1.43
1.65
0.57
1.45
0.17
0.64
0.56
Ave Mean
0.1037
0.1028
0.1057
0.1026
0.1028
0.1024
0.1011
0.09998
%RSD
1.58
0.80
1.90
0.59
0.55
0.73
0.12
0.04
Ave Mean
0.09347b
0.09886
0.1012
0.1023
0.1054
0.09622
0.1004
0.09913
%RSD
2.00
1.29
1.96
0.73
1.81
5.01
1.55
0.41
Ave Mean
0.1027
0.09942
0.1043
0.1016
0.1022
0.1026
0.1016
0.1025
%RSD
0.29
2.68
0.54
1.44
0.43
2.16
0.15
2.30
Ave Mean
0.1009
0.09941
0.1006
0.1016
0.1010
0.1011
0.09832
0.09929
%RSD
0.14
0.75
0.26
0.15
0.54
1.78
2.82
1.00
Ave Mean
0.1006
0.1001
0.1068
0.1002
0.1027
0.1005
0.1006
0.09963
%RSD
0.68
0.29
2.32
0.41
1.91
0.17
0.97
0.02
Ave Mean
0.1005
0.09986
0.1012
0.1002
0.1010
0.09995
0.09972
0.09882
%RSD
0.35
0.48
0.37
0.13
0.30
0.55
1.26
0.04
Ave Mean
0.1015
0.0997
0.1029
0.1008
0.1022
0.1003
0.1002
0.09922
sx
0.0011
0.0004
0.0023
0.0014
0.0016
0.0019
0.001
0.0006
Number of High Values
8
3
9
7
9
5
6
1
Number of Low Values
1
6
0
2
0
3
2
8
5 6 7 8 9 Class
a
Units are mol/L.
430
b
Data eliminated from further consideration are bolded in the table.
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In the Laboratory
described as “odd”; the solutions are nearly iridescent, appearing to have different colors depending on viewing angle. Molarity presented is the average value of replicate titrations with the percent relative standard deviation (% RSD) of the data for the individual students. The students applied the Q test to eliminate outlying data points on their individual titrations for a given indicator–base combination. The average molarity of the dilute HCl and standard deviation of the data for the class is calculated after application of the
Q test at 95% (19). Data eliminated from further consideration are bolded in the table. The number of high and low values shown indicates the number of data points above and below the true concentration of the HCl solution for the class as a whole. A possible manifestation of systematic error in the methodology is the number of reported results that are above or below the true molarity of the solution, regardless of the calculated class average molarity. These are shown in the last
Table 3. Student’s t-Test Results Comparing Average Measured to Known Molarity of Solution Student
1
2
3
4
5
6
7
8
9
Parameters
Method from Table 1 1
2
3
4
5
6
7
8
Ave Mean
0.1014
0.1002
0.1017
0.09958
0.1004
0.1000
0.1006
0.09893
sx
1.07 x 10᎑3 3.90 x 10᎑4 3.50 x 10᎑4 2.62 x 10᎑4 5.11 x 10᎑4 2.66 x 10᎑4 8.02 x 10᎑4 1.42 x 10᎑4
n
5
5
4
4
4
4
5
Diff.
Yes
No
Yes
Yes
No
No
No
4 Yes
Ave Mean
0.1012
0.09981
0.1002
0.09824
0.1007
0.09907
0.09958
0.09828
sx
8.71 x 10᎑4 6.04 x 10᎑4 3.59 x 10᎑4 1.85 x 10᎑3 3.50E-04
2.65E-04
5.78 x 10᎑4 5.10 x 10᎑4
n
4
4
4
6
4
3
4
4
Diff.
No
No
No
No
Yes
Yes
No
Yes
Ave Mean
0.1013
0.09998
0.1040
0.1009
0.1037
0.1005
0.1
0.09971
sx
4.03 x 10᎑4 1.43 x 10᎑3 1.72 x 10᎑3 5.72 x 10᎑4 1.50 x 10᎑3 1.73 x 10᎑3 6.40 x 10᎑4 5.60 x 10᎑5
n
4
4
4
4
4
3
4
Diff.
Yes
No
Yes
No
Yes
Yes
No
4 No
Ave Mean
0.1037
0.1028
0.1057
0.1026
0.1028
0.1024
0.1011
0.09998
sx
1.64 x 10᎑3 8.22 x 10᎑4 2.01 x 10᎑3 6.08 x 10᎑4 5.68 x 10᎑4 7.50 x 10᎑4 1.26 x 10᎑4 3.50 x 10᎑5
n
4
4
4
4
4
4
4
4
Diff.
Yes
Yes
Yes
Yes
Yes
Yes
No
No
Ave Mean
0.09347
0.09886
0.1012
0.1023
0.1054
0.09622
0.1004
0.09913
sx
1.87 x 10᎑3 1.27 x 10᎑3 1.99 x 10᎑3 7.50 x 10᎑4 1.90 x 10᎑3 4.88 x 10᎑3 1.56 x 10᎑3 4.02 x 10᎑4
n
4
4
4
4
4
4
4
4
Diff.
Yes
No
No
Yes
Yes
No
No
Yes
Ave Mean
0.1027
0.09942
0.1043
0.1016
0.1022
0.1026
0.1016
0.1025
sx
2.99 x 10᎑4 2.67 x 10᎑3 5.68 x 10᎑4 1.46 x 10᎑3 4.43 x 10᎑4 2.22 x 10᎑3 1.50 x 10᎑4 2.36 x 10᎑4
n
4
4
4
4
4
4
4
4
Diff.
Yes
No
Yes
No
Yes
No
Yes
Yes
Ave Mean
0.1009
0.1001
0.1006
0.1016
0.1010
0.1011
0.09832
0.09929
sx
1.41 x 10᎑4 7.44 x 10᎑4 2.65 x 10᎑4 1.53 x 10᎑4 5.50 x 10᎑4 1.80 x 10᎑3 2.77 x 10᎑3 9.98 x 10᎑4
n
4
4
3
3
4
4
4
Diff.
Yes
No
Yes
Yes
Yes
No
No
No
Ave Mean
0.1006
0.1001
0.1068
0.1002
0.1027
0.1005
0.1006
0.09963
sx
6.88 x 10᎑4 2.96 x 10᎑4 2.48 x 10᎑3 4.14 x 10᎑4 1.96 x 10᎑3 1.71 x 10᎑4 9.81 x 10᎑4 2.00 x 10᎑5
n
4
4
4
4
4
4
4
4
Diff.
No
No
Yes
No
No
Yes
No
Yes
Ave Mean
0.1005
0.09986
0.1012
0.1002
0.1010
0.09995
0.09972
0.09882
sx
3.50 x 10᎑4 4.75 x 10᎑4 3.74 x 10᎑4 1.29 x 10᎑4 2.99 x 10᎑4 5.53 x 10᎑3 1.26 x 10᎑3 3.61 x 10᎑5
n
4
Diff. Number Diff.
4
4
4
4
4
4
4
4
No
No
Yes
No
Yes
No
No
Yes
6
1
7
4
7
4
1
6
NOTE: Average molarity in units of mol/L, standard deviation, sx, and number of replicate titrations, n, reported by student is presented, and results of the student’s t test when the true value is known. The bottom row indicates the number of student results that were statistically significantly different for the given method.
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In the Laboratory
two rows of the table. Ideally, the number above and below the true value would be equal, or close to it, indicating only random error. The titration against sodium carbonate using modified methyl orange (v2) (method 6) as the indicator had the closest to an even division of high and low values. Methods 2 and 7 had similar results. All the others revealed some skewing of the data either above or below the true value. The method with the best precision when performed by an individual student, based upon student reported %RSD values, is the technique using sodium tetraborate decahydrate with methyl red as the indicator (method 8). It appears that as a group the students had good reproducibility in identifying the endpoint of the titration. Averages of the reported %RSD for the different methods (not presented in the table) were fairly constant, varying from 0.68 to 1.23%, with the exception of method 8, where the average of the reported %RSD for the class was 0.56%, with several extremely low %RSD values from data obtained by individual students. The student’s t test on the average molarity results (omitting outliers removed at 95% confidence) reveals a statistically significant difference from the true concentration of the unknown for methods 1, 3, 5, and 8, using the t test when an accepted value is known (2). Methods 1, 3, and 5 appear to be the most flawed, at least in the hands of the undergraduate students who performed the experiment, if the data are examined in terms of the class averages for resulting mo-
larity of the HCl solution. Those three indicators with sodium carbonate all produced unacceptably high values for the molarity of the test solution. The remaining methods appear to be roughly equivalent to each other in terms of the class accuracy as a whole when judged on this basis, with the exception of method 8, which is discussed in more detail below. An alternative manner of examining the data is to determine whether or not an individual student’s average molarity for a given method was statistically significantly different from the true value of their unknown. This can be accomplished by utilizing the student’s t test under the conditions when an accepted value is known (2). Examining the class data in this manner may, in fact, prove of more value in assessing whether or not a given method is an appropriate method of standardization of dilute strong acid for a class of undergraduate students. The results of this analysis reveal that only two of the methods (method 2 and 7) yield data in which the vast majority of the students have standardized their solution in such a manner that there is no statistically significant difference between the results of their standardization and the true value for the concentration of the solution. However, it must be acknowledged that a large standard deviation on replicate titrations could mask inaccuracy in the method. The results of this manner of examining the data are shown in Table 3.
Table 4. ANOVA Results for Tests of Within-Subjects Effects Type III Sum of Squares
Source
Method
Error (Method)
Replicate
Error (Replicate)
Method*Replicate
Error (Method*Replicate)
432
df
Mean Square
F
Sig.
Partial Eta Squared
Sphericity Assumed
0.000
7
0.000
4.684
0.000
0.369
Greenhouse-–Geisser
0.000
2.149
0.000
4.684
0.022
0.369
Huynh–Feldt
0.000
2.963
0.000
4.684
0.011
0.369
Lower-bound
0.000
1.000
0.000
4.684
0.062
0.369
Sphericity Assumed
0.001
56
0.000
Greenhouse–Geisser
0.001
17.188
0.000
Huynh–Feldt
0.001
23.703
0.000
Lower-bound
0.001
8.000
0.000
Sphericity Assumed
0.000
3
0.000
5.328
0.006
0.4000
Greenhouse–Geisser
0.000
2.325
0.000
5.328
0.012
0.4000
Huynh–Feldt
0.000
3.000
0.000
5.328
0.006
0.4000
Lower-bound
0.000
1.000
0.000
5.328
0.05
0.4000
Sphericity Assumed
0.000
24
0.000
Greenhouse–Geisser
0.000
18.603
0.000
Huynh–Feldt
0.000
24.000
0.000
Lower-bound
0.000
8.000
0.000
Sphericity Assumed
0.000
21
0.000
0.896
0.597
0.101
Greenhouse–Geisser
0.000
3.641
0.000
0.896
0.471
0.101
Huynh–Feldt
0.000
7.058
0.000
0.896
0.517
0.101
Lower-bound
0.000
1.000
0.000
0.896
0.372
0.101
Sphericity Assumed
0.000
168
0.000
Greenhouse–Geisser
0.000
29.126
0.000
Huynh–Feldt
0.000
56.461
0.000
Lower-bound
0.000
8.000
0.000
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In the Laboratory
When examining the data in the manner presented in Table 3, it is clear that methods 2, 4, 6, and 7 result in the fewest number of students obtaining a value from standardization that is statistically significantly different from the true value, particularly methods 2 and 7, which had only one student of nine obtaining an average molarity from the replicate titrations (after Q testing at 95%) that statistically significantly differed from the true value. Method 2 appeared to be one of the more accurate methods when the class data as a whole were examined in Table 2. In fact the one student who did end up with a statistically significant difference from the true value for the concentration using method 2 was dropped from the calculation of the class average result (presented in Table 2) with the Q test at 95% confidence. The average of molarities reported by the students for method 7 in Table 2 was not statistically significantly different from the true value, and the number of reported molarity values above and below the true was fairly even, given the sample size. Method 7 also benefits by not being a sodium carbonate based method, so the solution does not require boiling during the process. Combining the assessments of the eight methods presented in these two tables does lead to one conclusion, which is that method 2 (sodium carbonate with methyl orange–xylene cyanole FF as the indicator) and method 7 (TRIS with bromocresol green) prove to be the superior methods for standardization of a dilute solution of hydrochloric acid in a typical class of undergraduate quantitative analysis students. These numerical results are rather surprising, considering the seemingly strong student dislike of the modified methyl orange indicators and the bromocresol green endpoint, which is a mix of the acid and base forms of the indicator. An ANOVA (using SPSS for Windows, SPSS 12.0) was also performed on the data submitted by the students. The results of the ANOVA are presented in Table 4. Although ANOVA does not provide a method for comparison of the results of an analysis when the true value is known, as the Student’s t test does, it does give some insight for comparison of the methods against each other. The ANOVA was performed for method, student, and replicate interactions. The main effects for method and replicate were both highly statistically significant. The outcome varies significantly among both methods and replicates. The interaction between method and replicate was not statistically significant. A learning effect was seen on the analysis of the replicate titrations. Methods 3 and 5 proved to yield rather different results from method 8. The learning effect on peforming replicate titrations shows up in the fact that the average value was increasing over replicates for all methods. The effect of replicate titration on outcome does not depend on which method was used. Method 8 stood out from the other methods in the statistical analysis performed. What was noted was that the class had rather low values of the molarity when standardizing the solution by this indicator and base combination. Two main possibilities exist for the rather low average molarity for the standardization with sodium tetraborate decahydrate. The results could indicate that the base was not completely hydrated under the storage conditions, resulting in the small deviation of the results from the true value. Alternatively, the re-
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sults could indicate a tendency on the part of the students to exceed the equivalence point to obtain a consistent endpoint. This could be a facet of the color change of the indicator or a slight mismatch between the pH of the equivalence point and the indicator selected. A literature value for the pKIn of methyl red is 5.0, and the reported pKa for boric acid is 9.24 (10). The students were instructed to use 1.25 mmol of the sodium tetraborate decahydrate, and the final volume was approximately 75 mL. A quick calculation using the pKa for boric acid produced an equivalence point pH of 5.2 under the conditions of the experiment. The pH at the equivalence point should be slightly lower due to some carbon dioxide contamination of the solution during the titration. However, the calculated equivalence point pH is slightly higher than the pKIn for the indicator, which would imply the distinct possibility of a systematic tendency to pass the equivalence point to obtain the color change for the indicator. Sodium tetraborate decahydrate does have the desirable properties of being non-hygroscopic, not requiring boiling of the solution to obtain a sharp endpoint, and having a large equivalent weight (190.7 g兾equiv). Conclusions There are clearly some differences in results using the different methods of standardizing dilute HCl solutions presented in multiple quantitative analysis textbooks. Students show a distinct dislike for the modified methyl orange indicators for titration against sodium carbonate, mainly owing to difficulties in obtaining sufficiently precise results. However, the two versions of modified methyl orange proved to give some of the more accurate results obtained from the class as a whole. Modified methyl orange (v1) for titration against sodium carbonate and bromocresol green with TRIS appear to give the best results when looked at from the perspective of number of students with statistically significantly different results from the known value, and when examining the class performance as a whole. TRIS and Na2B4O7⭈10H2O have the benefit of not requiring boiling and cooling of the solution to obtain a sharp endpoint. There is little difference in price for the three standards, although the sodium carbonate is slightly less expensive. More scatter in the data might be observed with a different sample of students; all of the students in the class performing this experiment were women. There are some gender-based differences in sensitivity to color changes and color matching, although any effect in laboratory results due to gender-based differences may be negligible (20). This experiment lends itself very well to providing a data set for a statistical analysis experiment, particularly error analysis if the students are given the true value of the concentration of their solution (after the data have been collected). ANOVA could also be performed on the data collected from a class of students, at the instructor’s discretion. Acknowledgments This work was support in part by the Welch Foundation (Grant # M-0020) and ANOVA was performed by Steve Creech, Statistically Significant Consulting, LLC.
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In the Laboratory W
Supplemental Material
Instructions for the students and notes for the instructor are available in this issue of JCE Online.
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Literature Cited
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1. Ayres, Gilbert H. Quantitative Chemical Analysis, 2nd ed.; Harper & Row: New York, 1968; p 605. 2. Christian, Gary D. Analytical Chemistry, 5th ed.; John Wiley & Sons: New York, 1994; pp 676, 693. 3. Day, R. A., Jr.; Underwood, A. L. Quantitative Analysis, 6th ed.; Prentice Hall: Upper Saddle River, NJ, 1991; p 614. 4. Fischer, Robert B. Quantitative Chemical Analysis; W. B. Saunders: Philadelphia, PA, 1956; p 193. 5. Fischer, Robert B. A Basic Course in the Theory and Practice of Quantitative Chemical Analysis, 2nd ed.; W. B. Saunders: Philadelphia, PA, 1961; pp 225–226. 6. Fischer, Robert B.; Peters, Dennis G. Basic Theory and Practice of Quantitative Chemical Analysis, 3rd ed.; W. B. Saunders: Philadelphia, PA, 1968; p 314. 7. Fritz, James S.; Schenk, George H. Quantitative Analytical Chemistry, 5th ed.; Allyn and Bacon: Boston, MA, 1987; p 579. 8. Harris, Daniel C. Exploring Chemical Analysis, 2nd ed.; W. H. Freeman and Company: New York, 2000; p 501. 9. Harris, Daniel C. Quantitative Chemical Analysis, 5th ed.; W. H. Freeman and Company: New York, 1998; p 849. 10. Jeffery, G. H.; Bassett, J.; Mendham, J.; Denney, R. C. Vogel’s
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Textbook of Quantitative Chemical Analysis, 5th ed.; John Wiley & Sons: New York, 1989; pp 286–289. Kolthoff, I. M.; Sandell, E. B.; Meehan, E. J.; Bruckenstein, Stanley. Quantitative Chemical Analysis, 4th ed.; The Macmillan Company: London, 1969; p 778. Skoog, Douglas A.; West, Donald M. Fundamentals of Analytical Chemistry, 4th ed.; Saunders College Publishing: New York, 1982; p 742. Skoog, Douglas A.; West, Donald M.; Holler, F. James. Fundamentals of Analytical Chemistry, 7th ed.; Saunders College Publishing: New York, 1996; p 822. Skoog, Douglas A.; West, Donald M.; Holler, F. James; Crouch, Stanley R. Analytical Chemistry, An Introduction, 7th ed.; Saunders College Publishing: New York, 2000; p 735. Olson, Alex R.; Koch, Charles W.; Pimental, George C. Introductory Quantitative Chemistry; W. H. Freeman and Company: San Francisco, CA, 1956; p 283. Swift, Ernest H.; Butler, Eliot A. Quantitative Measurements and Chemical Equilibria; W. H. Freeman and Company: San Francisco, CA, 1972; pp 553, 558. Willard, Howard H.; Furman, N. Howell; Bricker, Clark E. Elements of Quantitative Analysis Theory and Practice, 4th ed.; D. Van Nostrand Company, Inc.: Princeton, NJ, 1956; pp 145– 148. Walton, H. F. Principles and Methods of Chemical Analysis; Prentice Hall: Englewood Cliffs, NJ, 1952; p 258. Rorabacher, D. B. Anal. Chem. 1991, 63, 139–146. Perez-Carpinell, J.; Baldovi, R.; de Fez, M. D.; Castro, J. Color Res. Applic. 1998, 23, 234–247.
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