Background: The ratio between the amount of product and reactant present at equilibrium is usually dependent upon temperature. This dependence is primarily due to the entropy increase in the surroundings as the temperature is increased. In this study, we will examine the effect of entropy on the equilibrium of the reaction Co(H2O)62+ + 4 Cl1- CoCl42- + 6 H2O High temperatures favor the formation of products while cooler temperatures favor the reactants. The data collected will allow the calculation of ∆Ho, ∆So, ∆Go and the equilibrium constant at 25o C. We will be using the equation ∆Ho-T ∆So = -RT ln K or, when rearranged, ln K = -∆Ho/RT + ∆So/R. In the latter form, a plot of ln K vs 1/T gives -∆Ho /R as the slope of the graph and ∆So/R as the Y intercept.
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Turn on the spectrometer and allow to warm for 15 minutes while carrying out the steps 2 and 3. Place about 100 ml of distilled water into a 150 ml beaker and heat to boiling. Mass 0.2 to 0.3 g of cobalt (II) chloride hexahydrate to the nearest tenth of a milligram. Transfer to a 50 ml beaker. Dissolve the cobalt (II) chloride in 20-30 ml of the stock HCl solution, transfer to a 50 ml volumetric flask, wash the beaker with the stock solution and transfer to the flask. Dilute to the line using the stock HCl solution. Record the concentration of the acid. Set the wavelength to 690 nm (if the spectrometer has a filter, verify that the filter is properly set), set the zero % T value and, using the stock HCl solution, set the 100 % T value. The Logger Pro should be interfaced with both the colorimeter and a Stainless Steel Thermistor. The thermistor should be in a 2 hole size 00 stopper and should protrude about an inch beyond the stopper. The stopper should fit into your cuvette. Click on the Experiment icon and choose ‘Set up Sensors’. Tell the spectrometer which port is connected to the colorimeter (it should recognize the Stainless Steel Thermistor). Click on ‘Calibrate’ and select ‘Colorimeter.’ Click on ‘Calibrate Now’, enter the zero and 100 % values without and with the cuvette and stock HCl solution. Adjust the time so that it collects for at least 20 minutes. Rinse the cuvette twice with the cobalt solution and fill about ¾ full. Place the cuvette and cobalt solution into the boiling water bath. The solution should turn blue. When the temperature of the cobalt solution reaches 90o C, remove from the bath, wipe quickly with a dry paper towel, place in the colorimeter and click on ‘Collect’. After the temperature drops below 30o C, click ‘Stop’ and save the data for later analysis. Use an appropriate title for the data.
Analysis: Calculate the initial concentration of cobalt(II) chloride. Note that the solid is a hexahydrate. Eb for the complex ion is about 552 M-1. Using the ‘Calculate new column’ and Eb calculate the concentration of the complex ion at each absorbance value. Likewise, calculate the [ Co(H2O)62+] at each absorbance value. The [ Cl1-] is effectively the concentration of the HCl stock solution since the additional ions from the dissolved solid and the loss of ions due to complex formation are small quantities. Calculate K at each reading where K= [CoCl42-]/([ Co(H2O)62+][ Cl1-]4). Calculate ln(K) and 1/Temperature for each reading. Be certain T is in Kelvin. Plot ln(K) vs 1/T and determine the slope and intercept for the graph. Determine the values of ∆Ho, ∆So, ∆Go and the equilibrium constant at 25o C.
Instructor Notes Students can reach the data gathering stage in about 30 minutes and thus complete the lab procedure in one hour. Stock HCl solutions should be 4 M to 5 M. The actual concentration may be determined via titration with a known base solution. This work may be included as part of the experiment or may be provided by the instructor. The student procedure provided uses an instructor calibrated stock solution. The Spec 20 or Spec20D may be interfaced to the Logger Pro with an SPC-DIN or SPC-BTA connector available through Vernier Corporation. The thermistor should be placed so that the tip is immersed in the solution yet does not protrude into the light path. It is important that the students calibrate the colorimeter with the computer.
The series of calculations leading to the thermodynamic values are as follows: 1) Convert T celcius to T Kelvin and invert to 1/T. 2) Determine the initial molarity of Co+2 ions in the sample. 3) Determine the concentration of complex in the sample by dividing the absorbance by 552 (this is the value of Eb). This, of course, is just Beer’s Law where A = EbC. The cell length, b, has a value of 1.16 cm for standard cylindrical cuvettes provided with the instruments. (1) 4) Determine the value of K by setting K = [CoCl42-]/([ Co(H2O)62+][ Cl1-]4 The chloride concentration from HCl can be used here or it can be calculated as [ Cl1-]o + 2*[Co2+]-4*[CoCl42-]. The correction inherent in the last two terms is less than 1 %. 5) Determine the value of ln(K). 6) Plot ln(K) vs 1/T and determine the equation of the resultant linear graph. Since ln K = -∆Ho/RT + ∆So/R the slope of the resultant line is -∆Ho/R and the Y intercept is ∆So/R. Determine the values of ∆Ho and ∆So. Use these to determine ∆Go and K.
Further Discussion for Instructors The calculations shown reflect the simplified calculations commonly employed in AP and General College Chemistry. That is, they are based solely on molar concentrations not on the activities and molality of the species. This results in some significant differences between the values calculated and the actual values for the system. As noted, K is calculated as K = [CoCl42-]/([ Co(H2O)62+][ Cl1-]4 while the correct statement is K =[ a(CoCl42-)a(H2O)6]/[a(Co(H2O)62+)a(Cl1-)4)] where a represents the activity coefficient and () the molality of the species. The presence of HCl in the solution will cause the mole
fraction of water to decrease to about 0 .95. This causes the a(H2O)6 term to decrease from unity to about 0.75, a 25 % reduction. Likewise, the high concentration of HCl will result in less than 100 % ionization so that the chloride ion term is incorrect. The activity coefficient for HCl rises at concentrations greater than about 0.4 molal and is about 2 at the concentrations used in this experiment (2). This will have a significant effect as the chloride concentration is raised to the fourth power. These corrections will affect the y intercept and, therefore, ∆So and ∆Go but will have minimal effect upon the slope and ∆Ho. As noted in the manuscript, these are topics which should be explored with students in advanced classes such as Physical Chemistry but are beyond the level of students for whom this article is written. Koga notes that the color change occurs when the complex changes from the octahedral to the tetrahedral form, specifically, [CoCl(H2O)5]+ + Cl1- [CoCl2(H2O)2] + 3 H2O and, determines K for the process K=[ [CoCl2(H2O)2]]/[[ CoCl(H2O)5+][ Cl1-]] to be 1.7+0.4 x 10-3 at 300 K and ∆Ho to be 8.8 + 4.2 kJ/mol for this step of the reaction (3). The experimentally determined value of K is in reasonable agreement with the value 2 x 10-5 used by Oxtoby (4).
LITERATURE CITED 1. Private communication, Product Applications Division of Cole-Parmer Instrument Company, August 2010. 2. Kaye and Laby Physical and Chemical Constants, http://www.kayelaby.npl.co.uk/chemistry/3_9/3_9_6.html (accessed August 2010). 3. Koga,N.;Kimizu,T.;Sakamoto,M.;Furukawa,Y., Chem. Educator, (2009), 14, 225. 4. Oxtoby, D.W.; Gillis, H.P.; Nachtrieb, N.H., Principles of Modern Chemistry, 5th Edition; Thomson Brooks/Cole, United States, 2002.
CAS REGISTRY NUMBERS Hydrochloric acid (7647-01-0) Cobalt (II) chloride hexahydrate ( 7791-13-1).
Figure 1 Spectra of cobalt(II) sulfate solution
Figure 2 Spectra of tetrachlorocobaltate(II)
