Laboratory Experiment pubs.acs.org/jchemeduc
The Method of Continuous Variation: A Laboratory Investigation of the Formula of a Precipitate William R. Furlong, Miles A. Rubinski, and Ramee Indralingam* Department of Chemistry, Stetson University, DeLand, Florida 32723, United States S Supporting Information *
ABSTRACT: The method of continuous variation is applied to the reaction between barium chloride and diammonium hydrogen phosphate in neutral, acidic, and basic conditions. Depending on the medium, barium dihydrogen phosphate, barium hydrogen phosphate, or barium phosphate is precipitated. The precipitates are washed, dried, and weighed. Construction of a continuous variation plot for each condition leads to the deduction of the molecular formula of the phosphate precipitated. This experiment demonstrates the concept of stoichiometric relationships between ions in the formation of compounds and serves to give students practice in calculations involving limiting reagents.
KEYWORDS: First-Year Undergraduate, Second-Year Undergraduate/General, Analytical Chemistry, Laboratory Instruction, Physical Chemistry, Hands-On Learning/Manipulatives, Gravimetric Analysis, Quantitative Analysis, Stoichiometry
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The second publication15 described similar experiments carried out by combining aqueous solutions of potassium iodide, sodium carbonate, and potassium chromate with aqueous lead(II) nitrate and barium chloride to form the precipitates of lead and barium, and compared the results obtained by measuring the mass of the precipitate with the results obtained by measuring the height of the precipitate in a graduated cylinder. The conclusion of the author was that “better” results were obtained when the mass of the precipitate was used to plot the graph. An Internet search revealed a commercially available laboratory experiment that is used in advanced placement chemistry classes.16 In this experiment, iron(III) hydroxide and copper(II) phosphate were precipitated by mixing aqueous solutions of iron(III) nitrate and sodium hydroxide, and copper(II) chloride and sodium phosphate, respectively. The method of continuous variation was used to determine the formula of the precipitates by plotting the volume of the precipitate as measured in a graduated cylinder versus the mole fraction of one of the reagents in each experiment. The accuracy of the results could be improved by using the mass of the precipitate rather than the volume, but, apparently, a tradeoff was made in favor of expediency over the more labor intensive technique of having high school students filter, wash, and dry each precipitate. The experiments described above do not pose any surprises for students. They are all given the same two aqueous solutions, and because they are aware of the identity of the two ions that
he method of continuous variation, or Job’s method as it is commonly called, has been commonly used in laboratory experiments in instrumental analysis classes to determine metal-to-ligand ratios in complex formation reactions.1−13 In the technique, the total amount of ligand and metal are held constant in a series of solutions of constant volume, whereas the individual amounts of ligand and metal are varied continuously. A physical property, such as the absorbance of the colored complex, is measured for every solution. A plot of absorbance versus mole fraction of the metal yields a curve with ascending, then descending branches whose extrapolated sides meet at a point of maximum absorbance. This point denotes the optimum mole fraction of the metal at which complete complex formation occurs. Hence the formula of the complex is deduced. This technique may be applied to the determination of the formula of any ionic compound, provided some characteristic of the compound may be measured. For instance, if the compound forms a precipitate when aqueous solutions of the component ions are mixed, the mass of the washed and dried precipitate may be plotted against the mole fraction of one of the ions. The optimum mole fraction as obtained in a Job’s plot would indicate the mole ratio of the ions and hence the formula of the precipitate may be deduced. Two papers have been published with details of application of the method of continuous variation to the determination of the stoichiometry of precipitates. One14 gave details of measuring the height in a graduated cylinder of barium chromate precipitate formed when various volumes of equimolar solutions of barium chloride and potassium chromate were mixed, keeping the total volume constant. © 2013 American Chemical Society and Division of Chemical Education, Inc.
Published: May 10, 2013 937
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that formulas of ionic compounds depend on the mole ratios of their constituent ions. A secondary objective is to give students practice in the calculation of limiting reagents. The main objective is met when the students calculate the mole fraction of barium in the precipitate that they obtained and hence deduce the formula of the compound. The concept of limiting reagent is also reinforced when students carry out a calculation for experimental points in each branch of the graph.
form the precipitate, they all know what optimum mole ratio they should obtain from a graph. A new experiment that applies the method of continuous variation to the determination of the formula of an ionic compound is described here. The experiment is unusual in that, although the same two reagents are used as the starting materials, conditions are controlled so that one of three different molecular formulas is obtained. This allows an instructor to assign an unknown to each student or pair of students. Barium phosphate, Ba3(PO4)2, barium hydrogen phosphate, BaHPO4, and barium dihydrogen phosphate, Ba(H2PO4)2, are all sparingly soluble salts that are precipitated when aqueous barium chloride is mixed with a solution of the corresponding ammonium salt of phosphoric acid as given below:
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EXPERIMENTAL PROCEDURE Students are provided with an unknown that consists of two vials, one containing an aqueous solution of 0.3 M barium chloride and the other containing 0.3 M diammonium hydrogen phosphate in 0.3 M HCl, deionized water, or 0.3 M NH3. Students are also provided with six 13 × 100 mm test tubes, which they number 1−6 and weigh. Using a combination of volumetric pipets, 1, 2, 3, 4, 5, or 6 mL of the BaCl2 solution is placed in the appropriately numbered test tube. Using a different set of volumetric pipets, the phosphate solution is placed in the test tubes in reverse order of volumes so that the total volume in each test tube is 7 mL. A precipitate appears immediately in each of the test tubes. The mixture is stirred with a glass rod and the test tubes are placed in a hot water bath for 15 min to digest the precipitates. The test tubes are then centrifuged and the supernatant is discarded. The precipitate is washed first with water and then with 95% ethanol, and centrifuged each time; supernatants are discarded. The test tubes are set in a beaker and placed in an oven to dry at 120 °C. The dry, cool test tubes containing precipitate are weighed again. The experimental procedure can be completed in a 3 h laboratory period. Additional experimental details are described in the Supporting Information. A graph is constructed by plotting mass of precipitate versus mole fraction of barium in the test tube, and by determining the mole fraction at which the mass of precipitate would be a maximum, the formula of the precipitate in the unknown is deduced. The limiting reactant in each branch of the graph is also determined by calculation.
3BaCl 2(aq) + 2(NH4)3 PO4 (aq) → Ba3(PO4 )2 (s) + 6NH4Cl(aq) barium phosphate
(1)
BaCl 2(aq) + (NH4)2 HPO4 (aq) →
BaHPO4 (s) barium hydrogen phosphate
+ 2NH4Cl(aq)
(2)
BaCl 2(aq) + 2(NH4)H 2PO4 (aq) →
Ba(H 2PO4 )2 (s) barium dihydrogen phosphate
+ 2NH4Cl(aq)
(3)
The formula of each precipitated compound consists of a different stoichiometric ratio of the barium ion to the phosphate group. The mole fraction of barium, calculated as a fraction of the total amount of barium and phosphatecontaining ions, is different in each precipitate, as shown below: Ba3(PO4)2: ΧBa =
3 mol Ba 2 + = 0.600 3 mol Ba 2 + + 2 mol PO4 3 −
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BaHPO4: XBa
HAZARDS Barium chloride dihydrate and diammonium hydrogen phosphate are hazardous in case of skin contact, eye contact, ingestion, or inhalation. Care must be taken when handling concentrated hydrochloric acid and ammonia in order to dilute them. Hazards of 95% ethanol are due to ingestion, eye contact, and inhalation of high vapor concentrations. Use gloves and prepare all solutions in the fume hood. The phosphates of barium are not classified as hazardous to human health. However, clean up of the waste must be done scrupulously because phosphate compounds are hazardous to aquatic environments. A detailed procedure for efficient cleanup is given in the Supporting Information.
1 mol Ba 2 + = = 0.500 1 mol Ba 2 + + 1 mol HPO4 2 −
Ba(H2PO4)2: XBa =
1 mol Ba 2 + = 0.333 1 mol Ba 2 + + 2 mol H 2PO4 −
The method of continuous variation can be employed, and by plotting the mass of the precipitate obtained in each case versus the mole fraction of barium, the formula of the compound can be determined. However, although diammonium hydrogen phosphate, (NH4)2HPO4, and ammonium dihydrogen phosphate, (NH4)H2PO4, can be purchased, ammonium phosphate, (NH4)3PO4, is not available from a chemical supplier. Hence, pH conditions have to be controlled to generate (NH4)3PO4 from either (NH4)2HPO4 or (NH4)H2PO4 The details of the conditions are given in the Supporting Information. This laboratory experiment is suitable for inclusion in the general chemistry class typically taken by students in the first year of the undergraduate chemistry curriculum. The main goal of this experiment is to use a practical method to teach students
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RESULTS AND CONCLUSION This experiment was tested over three years by a total of 31 second-year undergraduates in three quantitative analysis chemistry classes, and the final version was carried out by students in one general chemistry class, comprising 50 first-year undergraduates. The analytical chemistry students carried out the experiment individually. General chemistry students worked in pairs. Of a total of 25 pairs of students, one pair was not able to obtain the correct formula of the precipitate. The error was 938
dx.doi.org/10.1021/ed3004337 | J. Chem. Educ. 2013, 90, 937−940
Journal of Chemical Education
Laboratory Experiment
on the pan of the analytical balance, necessitating a waiting period before the mass stabilized. The error in the mass of the filter paper led to lack of reproducibility in the final results. Also, the logistics of keeping track of each set of six small filter papers and their contents without contaminating them proved to be formidable. Hence, the method described here of drying the precipitates in the test tubes was adopted.
found to be due to not allowing the precipitate to digest long enough so that the discarded supernatant was cloudy and contained some of the precipitate. Instructors should be aware of this error that students are liable to make. All the students obtained a narrow range of values for mole fraction of barium of their precipitates, which, when rounded using appropriate rules of significant figures, yielded the correct formula. Representative student results taken from both, general chemistry and analytical chemistry classes are given in Figure 1.
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ASSOCIATED CONTENT
S Supporting Information *
Student handout; notes for the instructor including instructions on the preparation of solutions and unknowns, and clean up procedures. 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. Figure 1. Continuous variation plots of barium chloride and diammonium hydrogen phosphate: (A) acidic conditions, (B) neutral conditions, and (C) basic conditions.
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ACKNOWLEDGMENTS
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REFERENCES
The authors are grateful to Eric W. Hoffman for invaluable help with the graphics.
General chemistry and analytical chemistry students obtained similar results, showing that this experiment can be carried out successfully by students of varying caliber and experience. The point of intersection of the two branches of each graph, A, B, and C give the optimum mole fraction of barium in each precipitate under acidic, neutral, and basic conditions, respectively. The point of intersection is obtained by setting equal to each other the equations of the best-fit lines of the two branches of each graph. The points (0,0) and (1,0) are included in the graphs although they are not experimentally determined. These points aid in calculating the equations of the straight lines so that the optimum mole fraction of barium in each precipitate may be accurately determined. In addition to the concept of stoichiometric relationships between ions that form compounds, this lab experiment gave students practice in calculations involving limiting reagents and the use of a spreadsheet for the manipulation of data. The main goal of this experiment was met when students were successful in deducing the formula of an ionic compound by determining the mole ratios of its constituent ions. The secondary objective was also met when students successfully determined the limiting reagent in each branch of the graph. It was found that general chemistry students became more confident at carrying out limiting reagent calculations because this laboratory experiment reinforced the chemical principles that they were learning in class during the same week. In the case of the analytical chemistry students, who had not carried out this experiment during the previous year, the calculations served to reinforce previously learned concepts. Both groups needed help with the steps involved in the spreadsheet manipulations. To shorten the time in which the precipitates are brought to constant mass, a modification was tried by filtering the precipitate under vacuum, washing with water and ethanol, and placing the filter papers and precipitates in an oven heated to about 80 °C. However, it was found that the filter papers themselves then lost moisture, which they gained while placed
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