LABORATORY EXPERIMENT pubs.acs.org/jchemeduc
Gibbs Energy Changes during Cobalt Complexation: A Thermodynamics Experiment for the General Chemistry Laboratory Michael J. DeGrand, M. Leigh Abrams, Judith L. Jenkins, and Lawrence E. Welch* Department of Chemistry, Knox College, Galesburg, Illinois 61401, United States
bS Supporting Information ABSTRACT: By adding a large quantity of Cl- to an aqueous solution of CoCl2 3 6H2O, a mixture containing a red octahedral cobalt complex and a blue tetrahedral complex is produced. When the solution temperature is modified, the equilibrium constant, Keq, of the complexation reaction is shifted and the proportion of the two colored forms altered correspondingly. Absorbance spectrophotometry is utilized to determine the concentration of each cobalt species, allowing Keq and the change in Gibbs energy, ΔG°, values to be found at each temperature tested. By plotting ΔG° versus temperature, the changes in entropy and enthalpy for the reaction can be determined. KEYWORDS: First-Year Undergraduate / General, Laboratory Instruction, Physical Chemistry, Hands-On Learning / Manipulatives, Thermodynamics, Equilibrium, Transition Elements, UV-vis Spectroscopy
E
nthalpy changes are a crucial topic within any general chemistry course, and they are almost universally probed via experiments in the laboratory. Gibbs energy and entropy are also crucial portions of these courses, but they have proven more elusive to pursue in the introductory laboratory. Reviewing 16 general chemistry laboratory manuals, most were found to be bereft of experiments treating Gibbs energy or entropy. Two flavors of Gibbs energy or entropy treatment were found. Kildahl and Varco-Shea1 described mixing of soluble ions looking for exchange reactions and precipitates, comparing experimental results with theoretical ΔG° values. Szafran et al.2 recorded galvanic cell potential as a function of temperature to determine the entropy change for the reaction. A similar approach has been described in the chemical education literature.3 Elsewhere in the chemical education literature, two introductory experiments4,5 pursue the endothermic dissolution of urea in water, measuring the urea concentration and using calorimetry for enthalpy information, allowing Keq, ΔG°, and ΔS° determination. Two other articles describe finding the Ksp for KNO36 and Ca(OH)27 as a function of temperature, using visual detection of a precipitate and titrations, respectively, for quantitative analysis, allowing ΔG° and ΔS° calculation. This article also features a reaction whereby Keq variation with temperature is used to pursue the calculation of ΔG° and ΔS° for a reaction. It differs in that visible spectrophotometry is used for the quantitative analysis, and a different type of reaction system is studied. Chemical demonstration enthusiasts will recognize the reaction system as one from the classic Shakhashiri chemical demonstration, “Chloro and Thiocyanato Complexes of Cobalt(II)”.8 Chloride is added to aqueous Co2þ, and the chloride Copyright r 2011 American Chemical Society and Division of Chemical Education, Inc.
displaces the coordinated waters, going through a series of stepwise additions: ½CoðH2 OÞ6 2þ þ Cl- h ½CoClðH2 OÞ5 þ þ H2 O
ð1aÞ
½CoClðH2 OÞ5 þ þ Cl- h CoCl2 ðH2 OÞ2 þ 3H2 O
ð1bÞ
CoCl2 ðH2 OÞ2 þ Cl- h ½CoCl3 ðH2 OÞ- þ H2 O
ð1cÞ
½CoCl3 ðH2 OÞ- þ Cl- h ½CoCl4 2- þ H2 O
ð1dÞ
A dramatic shift in d orbital energies causes the octahedral cobalt species to be red and the tetrahedral species to be blue. This produces a vivid shift in the cobalt d-d transition being monitored in the visible region. Bjerrum et al.9 determined that the concentrations of the dichloro and trichloro complex forms are negligible. By prudent selection of reaction conditions, we were able to treat the reactions, eqs 1a-1d, as a single reaction, which results by summing eqs 1a-1d and ignoring the contribution of the monochloro complex: ½CoðH2 OÞ6 2þ þ 4Cl- h ½CoCl4 2- þ 6H2 O
ð2Þ
The striking color change allows the concentration of both cobalt species in eq 2 to be determined selectively via spectrophotometry and for Keq to be calculated. The Keq values measured at varying temperatures can be converted into ΔG° Published: March 03, 2011 634
dx.doi.org/10.1021/ed100833x | J. Chem. Educ. 2011, 88, 634–636
Journal of Chemical Education
LABORATORY EXPERIMENT
Table 1. Beer-Lambert Law Constants for [Co(H2O)6]2þ and [CoCl4]2Compound
Wavelength/nm
[Co(H2O)6]2þ
500
[CoCl4]2-
690
Absorptivity/(L mol-1 cm-1) 4.613 577.2
Figure 2. ΔG° vs T plots derived from the authors’ data. All linear fits have R2 values of greater than 0.97. The total cobalt concentration for all plots is 0.04822 M and the total chloride concentration is 6.15 M. Solid and hollow square symbols represent method A and method B, respectively, using uncorrected data collected by the authors. Triangle symbols and diamond symbols represent method A and method B, respectively, using the previous raw data and applying activity corrections.
Figure 1. Visible spectra for the cobalt species at 25 °C: absorption of 0.09645 M [Co(H2O)6]2þ in an aqueous solution containing 0.193 M Cl- (solid trace) and 0.003102 M [CoCl4]2- in an aqueous solution containing 11.7 M Cl- (dashed trace).
their calculated concentrations of the two cobalt species, they could determine the quantity of unaccounted-for chlorine and were told to assume that this was all in the form of free chloride ion. With concentration values determined for all species taking part in eq 2, a Keq value could be calculated at each of the five temperature values. Equation 3 was used to find a ΔG° value for each of the calculated Keq’s. Students plotted their values of ΔG° versus absolute temperature, yielding a straight line with a slope of -ΔS° and an intercept of ΔH°.
values via eq 3: ΔGo ¼ - RT ln Keq ð3Þ Using the standard assumption that ΔG° changes with temperature but ΔH° and ΔS° do not change to a significant degree for a small temperature range,3,6,7 a graph of ΔG° versus T can be made, and eq 4 can be used to solve for ΔH° and ΔS°. ΔGo ¼ ΔH o - TΔSo
ð4Þ
Method B
Because the blue tetrahedral product absorbed much more intensely than the red octahedral reactant, the students were asked to repeat their calculations in an alternative manner for the sake of comparison. The [CoCl4]2- was still found from their spectrophotometric data, but [Co(H2O)6]2þ was found by subtracting [CoCl4]2- from the total cobalt concentration in the stock solution, rather than using the Beer-Lambert law directly.
’ MATERIALS AND METHODS The spectrophotometers were V-spec models from Vernier Software and Technology (Beaverton, OR) and the cuvettes were the methacrylate models from Perfector Scientific (Atascadero, CA). Spectrophotometric data were collected and processed with Logger Pro software from Vernier. ’ RESULTS AND DISCUSSION Procedure, Method A
Working in pairs, students prepared a 50 mL stock solution containing approximately 0.085-0.095 M CoCl2 3 6H2O, known with precision, by weighing the solid reagent on a milligram balance and then diluting to volume in a volumetric flask with deionized water. After mixing and dilution, a 25.00 mL aliquot of this solution was pipetted into a 50 mL volumetric flask, and the solution diluted to volume with concentrated (12.1 M) HCl. Absorbance spectra of this solution were collected in duplicate along with a solvent blank at 5 different temperatures: 10, 20, 30, 40, and 50 °C. Preset community water baths were used for temperature control, and 5 minutes of equilibration time allotted prior to data collection. Absorptivity constants for each of the two prevalent cobalt species were provided (Table 1). These constants were determined experimentally in advance by diluting a stock solution of CoCl2 3 6H2O with either water or concentrated HCl (Figure 1). The students used the Beer-Lambert law to determine the concentration of each cobalt species. From their solution recipe, the students knew the total chloride concentration in the prepared cobalt solution. Given
’ HAZARDS Concentrated HCl is a highly corrosive substance. The students should wear goggles and gloves, and try to minimize inhalation of the vapors it produces. Cobalt chloride is an irritant to the skin, eyes, and respiratory tract; in addition, it has been shown to cause cancer when ingested by laboratory animals. ’ DISCUSSION ΔG° versus T plots derived from the authors’ data utilizing both methods A and B are included in Figure 2. Table 2 shows the ΔH° and ΔS° values taken from the plots, plus the ΔG° values calculated from the line fits using 298 K. The determined thermodynamic constants are summarized in Table 2 for both the authors’ data and for 3 student sections with the calculational errors corrected. Many groups have studied the thermodynamics of this chemical system, but the values of the constants found vary greatly depending on solvent, ionic strength, and the chloride concentration in use. The most comparable literature value for ΔG° at 298 K was taken from Bjerrum et al.,9 and for ΔH° and 635
dx.doi.org/10.1021/ed100833x |J. Chem. Educ. 2011, 88, 634–636
Journal of Chemical Education
LABORATORY EXPERIMENT
Table 2. Thermodynamic Constants ΔH°/(kJ mol-1)
ΔS°/(J mol-1 K-1)
ΔG298°/(kJ mol-1)
Method A, raw data (extracted from Figure 2)
36
27
28
Method B, raw data (extracted from Figure 2)
37
34
27
Method A, corrected student mean
36
30
28
Method B, corrected student mean
38
40
27
Method A, Figure 2 data, activity corrected
61
73
39
Method B, Figure 2 data, activity corrected
62
80
38
Method A, corrected student mean, activity corrected
65
90
39
Method B, corrected student mean, activity corrected Literature Values, Bjerrum et al.9
67
100
Literature Values, Zeltmann et al.10
71.5
ΔS° from Zeltmann et al.;10 these values are also given in Table 2. At first glance it appears as if the experimental values for the thermodynamic constants are greatly removed from the literature values, but a perusal of the literature sources shows that significant corrections are needed because the activity of chloride was greatly different than the concentration of chloride under these conditions. Activity coefficients for the [Cl-] and T values in use were taken from Akerl€of et al.11 and the calculations redone. The experimental data in Table 2 and plots in Figure 2 have been updated after activity correction. These values compare much more favorably with the literature data. The activity corrections were deemed inappropriate for a general chemistry audience; they have been included to allow comparison of experimental outcomes with the literature values. Should this system be studied by students in an advanced course, this would make an interesting addition, along with some of the aspects of trying to correct for water activity,10 and looking at activity changes as a function of ionic strength and source of chloride.9 The students were not asked to compare their outcomes to the literature, given the need for activity correction. However, from an intuitive perspective, the signs of the calculated thermodynamic parameters made sense. The students consistently obtained positive ΔG° values for the reaction. They could see that they had a mix of both the red and blue forms of cobalt, yet they had a massive excess of chloride present to push the reaction forward to that point via Le Chatelier’s principle. This would suggest an unfavorable, nonspontaneous reaction with a positive ΔG°, matching the experimental outcome. Equation 2 converts 5 reactant species to 7 products, so a positive ΔS° value was expected and obtained in practice. With a positive ΔG° and a positive ΔS°, the students could deduce that ΔH° had to also be positive, which was again consistent with their laboratory findings.
38 37.8
83.7
’ ASSOCIATED CONTENT
bS
Supporting Information Student handout; notes for the instructor. This material is available via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT We would like to acknowledge financial support from Knox College. ’ REFERENCES (1) Kildahl, N.; Varco-Shea, T. Explorations in Chemistry: A Manual for Discovery; Wiley: New York, 1996. (2) Szafran, Z.; Pike, R. M.; Foster, J. C. Microscale General Chemistry Laboratory; Wiley: New York, 1993. (3) Beaulieu, L. P. J. Chem. Educ. 1978, 55, 53–54. (4) Pickering, M. J. Chem. Educ. 1987, 64, 723–724. (5) Liberko, C. A.; Terry, S. J. Chem. Educ. 2001, 78, 1087–1088. (6) Silberman, R. G. J. Chem. Educ. 1996, 73, 426–427. (7) Euler, W. B.; Kirschenbaum, L. J.; Ruekberg, B. J. Chem. Educ. 2000, 77, 1039–1040. (8) Shakhashiri, B. Z. Chemical Demonstrations; The University of Wisconsin Press: Madison, WI, 1983; Vol. 1, pp 280-285. (9) Bjerrum, J.; Halonin, A. S.; Skibsted, L. H. Acta Chem. Scand. A 1975, 29, 326–332. (10) Zeltmann, A. H.; Matwiyoff, N. A.; Morgan, L. O. J. Phys. Chem. 1968, 72, 121–127. (11) Akerl€ of, G.; Teare, J. W. J. Am. Chem. Soc. 1937, 59, 1855–1868.
’ CONCLUSIONS The aqueous cobalt-chloride complexation system provides an avenue to both observe a shift in equilibrium with temperature and calculate the associated thermodynamic parameters. The data produced by the students compared favorably with literature sources when chloride activity corrections were applied. Although not comparable without these corrections, the raw uncorrected data produced consistent ΔG° versus T plots and gave calculated thermodynamic parameters that were of a reasonable magnitude and correct in sign. 636
dx.doi.org/10.1021/ed100833x |J. Chem. Educ. 2011, 88, 634–636
