Laboratory Experiment pubs.acs.org/jchemeduc
Thermodynamics of the [CoCl(iPrOH)3]+ to [CoCl(iPrOH)2(MeOH)3]+ Reaction: A General Chemistry Laboratory Exercise Frazier Nyasulu,* Daniel Nething, Rebecca Barlag, Lindy Wise, and Phyllis Arthasery Department of Chemistry and Biochemistry, Ohio University, Athens, Ohio 45701, United States S Supporting Information *
ABSTRACT: In this general chemistry laboratory exercise, the absorbance of [CoCl(iPrOH)3]+, where iPrOH is isopropyl alcohol, is used to determine the equilibrium constants for its reaction with methanol to form [CoCl(iPrOH)2(MeOH)3]+ in the temperature range ∼10 to 20 °C. The absorbance versus concentration calibration plot is determined by sequential additions of a concentrated [CoCl(iPrOH)3]Cl standard to iPrOH. The equilibrium mixture is cooled in a CaCl2− ice bath, and measurements of temperature and absorbance are made at various time intervals as the solution warms to room temperature. The variation in the equilibrium constant as a function of temperature is used to determine the Gibbs energy, enthalpy, and entropy.
KEYWORDS: First-Year Undergraduate/General, Laboratory Instruction, Physical Chemistry, Hands-On Learning/Manipulatives, Coordination Compounds, Equilibrium, Laboratory Equipment/Apparatus, Spectroscopy, Thermodynamics, UV−Vis Spectroscopy found to be 8.4 ± 0.2 kJ/mol, and as eq 1 indicates, ΔS° cannot be determined because the constant is not known. The effect of temperature on the absorbance of [CoCl2(H2O)2]+ in the [CoCl(H2O)5]+/[CoCl2(H2O)2]+ equilibrium mixture has been reported by Brown et al.11 With the thermosiphon phenomenon as the main focus, data analysis to interrelate K, ΔG, ΔH, and ΔS was not explored. An interesting variation to the above examples is a lab in which the potentials of a Zn|Zn2+∥Cu2+|Cu voltaic cell were used to explore the interrelationships between K, ΔG, ΔH, and ΔS.12 Because of the inherent simplicity of analysis, most solubility product laboratories investigating the interrelationships between K, ΔG, ΔH, and ΔS are based on weak acids or weak bases that have limited solubility. Aliquots from the equilibrium mixture at various temperatures are titrated; acids are titrated with a strong base, and bases are titrated using a strong acid. In the case of salicylic acid, colorimetric analysis after the addition of Fe3+ to an aliquot taken from the equilibrium mixture has been reported.6 For KNO3, a substance with high solubility in water, increasingly larger known masses of KNO3(s) are added to a small volume of water and the temperature at which the solution becomes cloudy (onset of saturation) is determined.7 Of the analytical methods typically available in general chemistry laboratories, colorimetric analysis may well be the single analytical tool that has a signal independent of temperature. In this laboratory exercise, in situ temperature and absorbance measurements on a cobalt−chloride−alcohol complex are obtained with the goal of interrelating K, ΔG, ΔH, and ΔS.
T
he equilibrium constant (K), Gibbs energy (ΔG), enthalpy (ΔH), entropy (ΔS), and their interrelationships are important thermodynamic concepts in the general chemistry curriculum. Although nearly every lab manual has an exercise in which an equilibrium constant is determined, there are relatively few in which the interrelationships between K, ΔG, ΔH, and ΔS are explored.1−10 One way to explore these interrelationships is to determine the effect of temperature on the equilibrium constant. Conventionally, this is performed using a number of different temperature baths. Owing to the high cost of equipping general chemistry laboratories with commercial temperature baths, the temperature of the water baths is often controlled manually. Most of the lab exercises that explore the effect of temperature on K are based on solubility product1−7 or vapor pressure,8,9 both physical phenomena. An example of a lab exercise in which a chemical reaction is performed is the [Co(H2O)6]2+ plus Cl− reaction; the Cl− replaces the water in a series of steps, and it is the second step from [CoCl(H2O)5]+ to [CoCl2(H2O)2]+ that results in a color change of pink (octahedral) to blue (tetrahedral).10 The chloride concentration is varied, and the temperature (Td) at which the solution turns from pink to blue is measured. The applicable van’t Hoff equation from the work of Koga and co-workers is
ln(K2) = − ln
ΔH2° ΔS2° + RTd R
ΔH2° ΔS2° 1 + + const − = − RTd R [Cl ]
(1)
where R is the gas constant and the subscript 2 refers to the second step in the reaction sequence. The value of ΔH° was © 2012 American Chemical Society and Division of Chemical Education, Inc.
Published: January 13, 2012 536
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EXPERIMENTAL OVERVIEW In isopropyl alcohol (iPrOH), cobalt(II) chloride retains one chloride ion and complexes three molecules of isopropyl alcohol to form a blue-colored tetrahedral complex, [CoCl(iPrOH)3]+. In a methanol solution, cobalt(II) chloride retains one chloride ion and complexes five MeOH molecules to form a pink-colored octahedral complex, [CoCl(MeOH)5]+. When MeOH is added to [CoCl(iPrOH)3]+ in i PrOH, the following reaction occurs to give a pink-colored octahedral complex:
Pasco Scientific datalogger, Pasco Scientific colorimeter sensor, Pasco Scientific temperature sensor (fast responding small sensor), 1.00 mL variable volume autopipettor, Pasco Scientific cuvettes (∼7 mL capacity), CoCl2·6H2O, methanol, and isopropyl alcohol were used. Calibration Plot
The target concentration of [CoCl(iPrOH)3]Cl stock solution is 0.010 M ± 15% in isopropyl alcohol (iPrOH). The concentration herein is 0.00890 M. After calibrating the colorimeter (0% and 100% transmittance) with iPrOH, a 0.10 mL aliquot of the stock solution is added to 4.00 mL of iPrOH in a cuvette, and after stirring (a small stir bar is placed into the cuvette), the absorbance at 610 nm is measured. The 0.10 mL aliquot additions of the [CoCl(iPrOH)3]Cl stock solution are continued until 12 additions have been made or the absorbance exceeds 1.2.
blue
⇌ [CoCl(iPrOH)2 (MeOH)3 ]+ + iPrOH (2)
The equilibrium constant can be expressed as
K=
[[CoCl(iPrOH)2 (MeOH)3 ]+ ][iPrOH] [[CoCl(iPrOH)3 ]+ ][MeOH]3
Effect of Temperature on K
(3)
The calibration of the colorimeter (0% and 100% transmittance) is performed using a solution consisting of 5.00 mL iPrOH and 1.00 mL MeOH. The equilibrium mixture is prepared by adding 2.00 mL of 0.00890 M [CoCl(iPrOH)3]Cl (iPrOH is the solvent), 3.00 of mL iPrOH, and 1.00 mL of MeOH into a cuvette. A small stir bar is placed in the cuvette, and, using tongs, the cuvette is held in a CaCl2−ice bath for 45−60 s. The cooled mixture is intermittently removed and stirred. The cooling and stirring is continued until the original blue color has changed to a pink color. Prior to placing the cuvette into the colorimeter, the cuvette is dried with a paper towel. A small hole is predrilled into the cover of the colorimeter to accommodate a temperature sensor. The setup is shown in Figure 1. The temperature sensor
The colorimetric determination of this equilibrium constant is performed as a general chemistry laboratory exercise.15 Equilibrium mixtures of this reaction show sharp color changes for small changes in temperature indicating that this reaction could be used to investigate colorimetric-based interrelationships between K, ΔG, ΔH, and ΔS. The speed and ease with which absorbance measurements can be performed is greatly improved by preparing calibration and equilibrium solutions in a cuvette.16 In this lab exercise, the calibration plot is obtained by adding small volumes of a concentrated standard of [CoCl(iPrOH)3]Cl (iPrOH is the solvent) to a blank solution of iPrOH in a cuvette. The equilibrium mixture is made by mixing a solution of [CoCl(iPrOH)3]Cl, iPrOH, and MeOH. It is assumed that these volume additions of alcohols are additive. After cooling the equilibrium mixture in a CaCl2−ice bath, absorbance (610 nm) and temperature (°C) are measured at 15 s intervals as the solution warms to room temperature. In making these measurements, it is also assumed that the equilibrium adjusts rapidly to be close to what it would be if the temperature was fixed at each of the measurement temperatures. The thermodynamic equations of interest are
ΔG° = − RT ln(K ) = ΔH ° − T ΔS°
(4)
where the degree symbol pertains to the corresponding quantity at standard concentrations. As long as the temperature change is small, ΔH° and ΔS° can be considered to be constant. Rearranging eq 4 yields the equation used to determine ΔH° and ΔS°:
ln K = −
ΔH ° ΔS° + RT R
Figure 1. Setup for the measurement of absorbance and temperature.
is inserted through the colorimeter sensor cover hole into the solution in the cuvette such that the sensor does not interfere with the colorimeter light path. Duct tape is used to secure the temperature sensor to the colorimeter cover and also to keep out stray light. The wood undersupport is used to raise the datalogger so that the colorimeter is barely above the stirrer. The datalogger is programmed to record temperature (±0.01 °C) and absorbance (±0.001) at 15 s intervals and displays a plot of absorbance versus temperature. Data collection is continued until a temperature change of 15 to 20 °C is achieved. Data is saved to a USB flashdrive. The solution is recooled, and the measurements are repeated.
(5)
With ΔH° and ΔS° constant, a plot of ln(K) versus 1/T is linear with
slope(m) = −
ΔH ° R
Y ‐intercept (b) =
ΔS° R
EXPERIMENTAL DETAILS
Materials and Equipment
[CoCl(iPrOH)3 ]+ + 3MeOH
pink
Laboratory Experiment
(6)
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Laboratory Experiment
HAZARDS Methanol (MeOH) and isopropyl alcohol (iPrOH) are highly flammable. Solutions of cobalt(II) should be handled with care and disposed of properly.
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increases from 0.3 to 0.9 and K values decrease from 0.6 to 0.1. An Excel spreadsheet template is provided (see the Supporting Information) to standardize student data analysis. A plot of ln(K) versus 1/T is shown in Figure 3 from which ΔH° is −49.2 ± 0.3 kJ/mol and ΔS° is −190 ± 11 J/(K mol).
RESULTS AND DISCUSSION
Enthalpy and Entropy
The spectrum of [CoCl(iPrOH)3]+ has λmax at 657 nm and a shoulder peak at 615 nm. The spectrum of [CoCl(iPrOH)2(MeOH)3]+ has λmax at 536 nm. The molar absorptivity (ε) of [CoCl(iPrOH)3]+ is considerably higher. Our dataloggers only work at four wavelengths: 468 nm, 565 nm, 610 nm, and 660 nm. Although the absorbances at 610 and 660 nm are about equal, the calibration plot at 610 nm is more linear (Figure 2).
Figure 3. A plot of ln (K) versus T−1.
Based on class data (N = 48), the enthalpy is −49 ± 4 kJ/mol and the entropy of solution is −199 ± 11 J/(K mol). Although the literature values for this specific reaction are not known, the enthalpy values are comparable to those of cobalt(II) primary alkylamine complexes (30 to 50 kJ/mol) wherein the reaction is from the octahedral complex to the tetrahedral complex.17 Bond Formation Figure 2. Calibration plots at 610 and 660 nm.
One attractive feature of this reaction is that it is possible to estimate the enthalpy change associated with the formation of the Co2+−ligand (MeOH or iPrOH) bond. It is reasonable to assume that the Co2+−iPrOH and the Co2+−MeOH bonds are of about the same strength as both involve a lone pair on the oxygen bonding to the Co2+. Considering the reaction equation, one Co2+−iPrOH bond is broken (ΔH = p) and three Co2+−MeOH bonds are formed ((ΔH = −3p) . Therefore
The calibration equation parameters at 610 nm are
slope (εb) = 374 ± 2L/mol Y ‐intercept = − 0.008 ± 0.003 R2 = 0.9997
(8)
It should be noted that the path length in the cuvette is larger than 1 cm and that the cuvettes are cylindrical in shape. Select temperature and absorbance data are shown in Table 1. For the temperature range (−8 to 10 °C), the absorbance
ΔH °(reaction) =
Table 1. Selected Data and Corresponding Calculated K Values Temp/°C
Absorbance
K
−7.80 −4.90 −3.50 −1.50 0.30 1.30 2.80 4.60 6.30 7.70 8.00 8.30 9.50 9.80 10.40
0.331 0.408 0.458 0.500 0.557 0.590 0.636 0.689 0.737 0.776 0.787 0.797 0.843 0.855 0.877
0.615 0.472 0.405 0.359 0.307 0.281 0.250 0.220 0.195 0.178 0.173 0.169 0.152 0.147 0.140
∑ ΔH(bonds broken) + ∑ ΔH(bonds made)
(9)
ΔH °(reaction) = p − 3p = − 49.2 kJ/mol p = 24.6 kJ/mol
(10)
At 25 kJ per mole, bond enthalpies are less than 10% of ordinary covalent bonds. Spontaneity
The change in the Gibbs energy (ΔG) is useful for determining spontaneity. From their calculated values of ΔG, students observe that the values are positive and that these decrease with decreasing temperature. These observations correlated with what was observed experimentally: the blue color of reactant [CoCl(iPrOH)3]+ decreases as temperature is decreased. The temperature at which ΔG° is zero (K is 1) is about −15 °C and ΔG° at room temperature is 7.3 kJ/mol. 538
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(6) Barreto, J. C.; Dubetz, T.; Brown, D. W.; Barreto, P. D.; Coates, C. M.; Cob, A. Chem. Educ. 2007, 12, 18−21. (7) Silberman, R. G. J. Chem. Educ. 1996, 73, 426−427. (8) Nyasulu, F. W.; Cusworth, W.; Weiner, J.; Lindquist, D.; Macklin, J. Chem. Educ. 2005, 10, 303−305. (9) Holt, J. S.; Grabow, R.; Pursell, C. J. Chem. Educ. 2003, 8, 327− 3293. (10) Koga, N; Kimizu, T.; Sakamoto, M.; Furukawa, Y. Chem. Educ. 2009, 14, 225−228. (11) Brown, J. L.; Battino, R.; Krause, P. F. J. Chem. Educ. 1993, 70, 153−154. (12) Szafran, Z.; Pike, R. M.; Foster, J. C. Microscale General Chemistry Laboratory With Selected Macroscale Experiments; Wiley: New York, 1993; pp 329−339. (13) Shakhashiri, B. Z. Chemical Demonstrations, A Handbook for Teachers of Chemistry; University of Wisconsin Press: Madison, WI, 1983; Vol. 1, pp 280−285. (14) Bare, W. D.; Mellon, E. K. J. Chem. Educ. 1991, 68, 779−780. (15) http://www.ars-chemia.net/Classes/102/manual/102_ Complete_Manual.pdf (accessed Nov 2011). (16) Nyasulu, F.; Barlag, R. J. Chem. Educ. 2011, 88, 313−314. (17) Aizawa, S.; Funahashi, S. Inorg. Chem. 2002, 41, 4555−4559.
CONCLUSIONS The ability of the autopipettors to dispense small volumes of solutions quickly and accurately means that solutions of varying concentration can be made quickly and easily by adding small aliquots of a concentrated standard to the same blank solution. In this lab, aliquots of a concentrated solution of [CoCl(iPrOH)3]+ in PrOH are added to a iPrOH in a cuvette to generate solutions with varying [CoCl(iPrOH)3]+ concentrations. Absorbance measurements are made after each addition, and with these measurements a calibration plot of absorbance versus [CoCl(iPrOH)3]+ can be implemented. This is a workable approach to generate calibration plots as long as the measurement procedure does not consume the calibration solution. Given the numbers of students in general chemistry, this approach leads to savings in reagents and waste generation. In the modern era of autopipettors, calculators, and computer spreadsheets, it is not necessary to prepare calibration standards with the same total volume. Because the starting equilibrium solution has very small concentrations of the pink [CoCl(iPrOH)2(MeOH)3]+ at room temperature, heating the equilibrium mixture is not a good option because it will just lead to very small increases in the concentrations of the blue [CoCl(iPrOH)3]+. Regarding the assumption that the equilibrium shifts quickly, preliminary indications are that it is valid. Rapid color changes are observed when the temperature is decreased more sharply than executed in this experiment (cuvette placed in the acetone−CO2(s) ice bath). With high-speed, high-accuracy measurement tools, the effect of temperature on a select group of measured parameters, such as absorbance and pressure, can be accomplished simply by letting the reaction temperature return to room temperature. In designing this laboratory exercise, procedures were developed that execute quickly, use minimal reagents, yield good results, and accentuate the properties of the autopipettor, datalogger, colorimeter, and temperature sensors. Students complete this lab in about 1.25 h, and with this they have enough time to complete the data analysis in the Excel spreadsheet within the three hour laboratory time period. This lab exercise affords our students an opportunity to consolidate their understanding of the interrelationships between the equilibrium constant (K), Gibbs energy (ΔG°), enthalpy (ΔH°) and entropy (ΔS°).
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ASSOCIATED CONTENT
S Supporting Information *
CAS registry numbers; student handouts; notes for the instructor. This material is available via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected].
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REFERENCES
(1) Murov, S. L. Experiments in General Chemistry, 3rd ed.; Brooks/ Cole: Monterey, CA,1999; pp 333−348. (2) Euler, W. B.; Kirschenbaum, L. J.; Ruekberg, B. J. Chem. Educ. 2000, 77, 1039−1040. (3) Beran, J. A. Laboratory Manual for Principles of General Chemistry, 7th ed.; Wiley: New York, 2004; pp 347−356. (4) Block, T. F.; McKelvy, G. M. Laboratory Experiments for General Chemistry, 5th ed.; Brooks/Cole: Monterey, CA, 2006; pp 261−270. (5) Nyasulu, F. W.; Cusworth, W; Lindquist, D.; Macklin, J J. Chem. Educ. 2007, 84, 456−458. 539
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