In the Laboratory
Calorimetric Determination of Aqueous Ion Enthalpies Paul Siders Department of Chemistry, University of Minnesota–Duluth, Duluth, MN 55812 Formation enthalpies of aqueous ions are discussed in general and physical chemistry textbooks and can readily be measured in a physical chemistry laboratory. A solution-calorimetry experiment to determine enthalpies of formation of aqueous Na+ , K+, Cl{, and I{ is described below. Other solution-calorimetry laboratory experiments have been published in this Journal. Experiments described by Raizen, Fung, and Christian (1) measure the enthalpy of reduction of permanganate by iron(II), and the enthalpy of mixing of ethanol and cyclohexane. The experiments of Diogo et al. (2) address solute–solvent interactions and lattice energies. Our laboratory uses the Parr 1455 Solution Calorimeter. An insulated Dewar flask is filled with 100 mL of water or aqueous HCl. The solid sample to be dissolved is placed on a covered sample dish that rotates in the solution. The solution’s temperature is measured with a thermistor. The sample dish can be released into the solution with a push rod. The calorimeter is controlled and data are recorded by a computer attached to the calorimeter’s serial port. The Parr serial port accepts an RJ-45 connector. A BASIC program gives students a menu with selections to record, list, and plot data and to send control codes to the calorimeter (e.g., to start and stop the stirrer). The program also creates a data file in comma-quote format for easy import to a spreadsheet. The program was written in BASIC for portability among DOS machines; we have used it on a single-floppy 8088 computer and a dual-floppy 80386. The BASIC code and pin assignments for a cable from the calorimeter’s RJ-45 port to a 25-pin serial port are available from the author. The calorimeter is standardized by reacting about 0.5 g of tris(hydroxymethyl)aminomethane (“Tris”) with 100.0 mL (a stoichiometric excess) of 0.1000M HCl, as described in the Parr manual. The enthalpy of neutralization of solid Tris by 0.10 M HCl is 245.76 J per gram of Tris at 25 °C. A small correction is applied if the reaction temperature is not 25 °C. The enthalpy change of the neutralization, in joules, is Q p = m[ 245.76 + 1.436(25.0 – T 0.63R) ], where m is the mass of Tris in grams and T 0.63R is the Celsius temperature at 63% of the rise. Finally, the heat capacity of the calorimeter, Cp,cal , is calculated from the relation Qp /∆T = Cp,cal + Cp,soln , where Cp,soln , the heat capacity of the solution, is taken to be 4.190 J?K{1?mL{1. The temperature change, ∆T, is calculated at the time at which the temperature rise is 63% complete. For our calorimeter, C p,cal = 91 J/K. After standardizing the calorimeter (three repetitions), four reactions are run in duplicate to determine enthalpies of four aqueous ions. Enthalpies of aqueous ions are taken relative to the reference choice ∆Hf°( H+,aq) ≡ 0 at infinite dilution (3). The first reaction involves H+, for which the enthalpy is zero by convention.
peratures obtained from dissolution of 1.3584 g of NaC2H3O2?3H2O in 100.0 mL of 0.2000 M HCl. ∆T is calculated between the regression lines at the point of 63% temperature change, as suggested in the Parr instruction manual. The aqueous acetate ion does not enter the reaction appreciably because the acetic acid is negligibly ionized in the excess HCl. Students are asked to calculate the percent ionization of acetic acid under their experimental conditions. The enthalpy of Na+(aq) is calculated from the measured ∆H1 and tabulated formation enthalpies of sodium acetate trihydrate and acetic acid. Students then measure in duplicate the enthalpies of dissolving 0.010 mol of three salts in 100.0 mL of water in the calorimeter: NaI, KI, and KCl. The only salt requiring special handling is NaI, which absorbs water with great effect on heat of solution. We grind NaI, dry it at 160 °C for 2 hours, and thereafter store it in a desiccator. For every run, students use a spreadsheet to fit linear regression lines through early and late temperature data, and calculate ∆T at the point of 63% temperature change. For simplicity, the heat capacity of all aqueous solutions is taken to be 4.190 J?K{1?mL{1. The three solution enthalpies of NaI, KI, and KCl plus the Na+ enthalpy obtained from reaction 1 along with tabulated enthalpies of the crystalline salts allow students to calculate enthalpies of the aqueous ions I{, K+, and Cl{. This experiment has been done in two 3-hour lab periods. It could be shortTable 1. Aqueous Ion Enthalpies ∆H °f (kJ/mol) Ion
Experimental
Na +
{241.0
Tabulated (3 ) {240.1
I{
{54.5
{55.2
K+
{252.8
{252.4
Cl{
{165.3
{167.2
+ H (aq) + NaC2H3O2?3H2O(s) → + Na (aq) + HC2H3O2(aq) + 3H2O(l); ∆H1
(1)
The enthalpy of reaction 1 is measured directly by reacting solid sodium acetate trihydrate with excess hydrochloric acid in the calorimeter. Figure 1 shows tem-
Figure 1. Dissolution of NaC2H3O 2?3H2O in HCl.
Vol. 74 No. 2 February 1997 • Journal of Chemical Education
235
In the Laboratory
ened by reducing the number of ions for which enthalpies are determined. In order to compare student data with tabulated values at 25 °C, the dissolutions should be run near 25 °C. This is accomplished by filling the calorimeter with water or HCl solution that has been warmed in a water bath. Another possible difficulty in comparing results to literature values is that the final ion molalities in this experiment are about 0.1—far from infinite dilution. Enthalpies might be corrected to infinite dilution using a simple equation based on the Debye–Hückel limiting law: lim ∆Hdissolution as m → 0 = ∆Hdissolution (m) + ∆H dilution (2)
ficient data to reliably correct all four solution enthalpies to zero concentration are not available, so concentration effects are neglected in this experiment. Aqueous ion enthalpies calculated from enthalpies of solution measured in the lab are given in Table 1, along with literature values. Errors less than 2% were easily obtained. The simple experiment described above yields accurate results and reinforces the discussion of aqueous ion enthalpies in the physical chemistry lecture class. A detailed laboratory write-up is available from the author. Literature Cited
where 1/
∆Hdilution ≈ {S (m)
2
(3)
For 1:1 electrolyte in water at 25 °C, the proportionality constant S is approximately 2.01 kJ?mol{1?molal{1/2 (4, 5). However, eq 3 is applicable (with constant S) only up to about 0.01 m. Data at higher concentrations are discussed by Whalen (5) and by Young and Seligmann (6). Enthalpies of dilution from 0.10 m to zero are {0.26 and {0.32 kJ/mol for NaI and KCl, respectively (7). Suf-
236
1. Raizen, D. A.; Fung, B. M.; Christian, S. D. J. Chem. Educ. 1988, 65, 932–933. 2. Diogo, H. P.; Minas da Piedade, M. E.; Moura Ramos, J. J.; Simoni, J. A.; Martinho Simoes, J. A. J. Chem. Educ. 1993, 70, A227–A233. 3. Atkins, P. W. Physical Chemistry, 5th ed.; Freeman: New York, 1994. 4. Moelwyn-Hughes, E. A. Physical Chemistry, 2nd ed.; Pergamon: Oxford, 1961; Chapter 18. 5. Whalen, J. W. Molecular Thermodynamics: A Statistical Approach; Wiley: New York, 1991; p 79. 6. Young, T. F.; Seligmann, P. J. Am. Chem. Soc. 1938, 60, 2379–2383. 7. Lange, E.; Robinson, A. L. Chem. Rev. 1931, 9, 89–116.
Journal of Chemical Education • Vol. 74 No. 2 February 1997
