Solution Calorimetry Experiments for Physical Deborah A. Raizen, B. M. Fung,' and Sherril D. Christian University of Oklahoma, Norman, OK 73019 The measurement of the heat of combustion hv wine a bomb calorimeter is a standard experiment in thephgsi'cal chemistrv lahoratorv. Even though reactions in the liquid phase under constant pressure are far more general than constant-volume combustion reactions, thermodynamic measurements on solutions are not very common in the undergraduate physical chemistry curriculum. To remedy this deficiency, we have developed two solution calorimetry experiments for our physical chemistry laboratory. The first one measures the heat of an exothermic reaction, the reduction of permanganate by the ferrous ion. The second one measures the heat of an endothermic process, the mixing of ethanol and cyclohexane. In addition to enhancing students' understandine of the thermodvnamic . properties of solu. tions, the experiment gives them experience with a useful lahoratorv technique. The second experiment also demonstrates that solutions can deviate s&.tantially from the ideal behavior, reminding future chemists and engineers that wider possibilities exist than those treated in an introductory lecture course.
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Standardlzatlon of the Calorimeter Either a commercial or a "home-built" solution calorimeter2 can be used. The Parr 1451 solution calorimeter used in our experiments is shown schematicallv in Fieure 1. I t is stand&dized hy neutralization of l'ris (t&(hyd&xymethyl) aminomethane, with 0.100 21 HCI. The procedure for standardizing the calorimeter is given in the-instructional manual. Reduction of Permanganate by Fe(1l) Ion A chemical reaction to be studied by solution calorimetry in a student laboratory should he fast and complete, and the components should he simple and easy to handle. After experimenting with several systems, we have chosen the reduction of permanganate (Mn04-) hy the ferrous ion (Fez+).An excess amount of the latter is used, so that stoichiometric calculations can be based upon the amount of potassium permanganate weighed out. Ferrous sulfate (1.5 g of FeS04.7H20) is stirred into 150 mL of 1.0 N sulfuric acid. After the solution is left a t room temperature for about 20 min to reach thermal equilibrium, 100 mL is pipetted into the Dewar. A small amount of KMn04is crushed, and 4 . 1 g is weighed accurately into the Teflon dish. The glass bell is pressed over the dish, 10.0 mL of 1.0 N sulfuric acid are pipetted into the bell, and the bell is shaken vigorously. The shaking is repeated several times during the next 20 min to ensure complete dissolution. The hell and Dewar are assembled in the calorimeter, and the recorder range is set a t 100 mV (1 "C full range). After the
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Author to whom correspondence should be addressed. 2Clevette,D. J.; Bauman, J. E. Am. Lab. 1987 (6), 19-24. Earner, H. E.; Scheuerman, R. V. Handbook of Thermochemical Data for Compounds and Aqueous Species; Wiley: New York, 1978. "tokes, R. H.: Adamson, M.J. Chem. Soc., Faraday Trans. 11977, 73. 1232-8.
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Journal of Chemical Education
Figure I. Schematic diagram 01 the Parr 1451 solution calorimeter.
system reaches equilibrium, the reactants are mixed by pressing the push rod to release the dish, and the temperature change is recorded. For data treatment, students are asked to calculate the enthalpy change of the reaction by using the heat capacity of 4.00 J.K-'.mL-' for 1N H2SOc They are also asked to write the equation of reaction and look up for Fe(II), Fe(III), Mn(II), and H20. Given t h a t AH,(MnO;) = -541.4 k J . m ~ l - l ,they ~ should be able to calculate AHo of the reaction and compare it with their own experimental value.
qf
Mixing Ethanol with Cyclohexane The extreme nonideality of a mixture of an alcohol and a nonpolar solvent allows for easy, reproducible measurements. While an ideal system has no enthalpy change on mixing (AH= O), the system of ethanol/cyclohexane is highly endothermic, giving a sizable temperature drop even for mole fractions of ethanol as small as 0.02 and as large as 0.98 (-1 "C and -0.3 O C , respectively, using the Parr 1451 solution calorimeter). The measurements are accurate enough to allow for the plottingof a reasonably smooth curve of enthalpy versus mole fraction (Fig. 2). Good results can be obtained not only for measurements made by mixing different volumes of pure enthanol and cyclohexane, hut also for the few measurements made by adding pure ethanol or cyclohexane to a mixture. Cyclohexane (50 mL) is pipetted into the Dewar, and different volumes of 100%ethanol are pipetted into the hell for a series of measurements. A second series of measurements is done with ethanol in the Dewar and cyclohexane in the hell. Two other measurements are done by pipetting 50 mL of a mixture into the Dewar and a pure component into the hell. Since the process is endothermic, the recorder pen should he positioned to respond to a temperature drop after mixing.
Table 1. Suggested Volumes To Be Used for the Mlxlng ot Ethanol and Cyclohexane In a Parr Solutlon Calorlmeter Ethanol (mL)
(d)
0.5 1.0 2.0 5.0
(8)
15.0
50.0 50.0 50.0 50.0 50.0
(1) (g) (h) (i) (j) (k)
15.0 10.0 50.0 50.0 50.0 50.0
50.0 2.0 5.0 10.0 15.0
(a) Ib) (C)
M o l e Fraction of
Ethanol
Figwe 2. mermodynamic data for mtt mixing of ethanol and cyclohexane at -298 K. (A) AH(experimenta1): (8) TAS (experimental); (C) TAS (ideal). The solid curves are least-squares fits of the data in Stokes and Adamson.' The open symbols are a student's data; the closed symbols are TAS values calculated by subtracting the A G values in Table 1 from the studenVs data of AH. The circles are values obtained from mixing pure components: the diamonds are values obtained ham mixing a pure component with a mixture.
The suggested volumes of each component to he used in this experiment are listed in Tahle 1. Measurements on (a)-(f) . . . . can he performed on one day, and (g)-(I) on another day. ~ l t e r n a t k e lthe ~ , measurements can he made hv two erouvs of students on the same day, and the data can hk pooGd. The calculations for the mixing of pure components are straightforward. The heat capacity of the mixture is calculated by assuming the heat~apacitiesof the components to he linear, C,(mixture) = nlCP1 nzC,n The molar enthalpy of mixing is readily calculated by
ill
Miaure
Cyclohexane (mL)
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Range (OC)
50.0 mL of (0) -
50.0 mL of lkl
15.0
2 2 2 5 5 2
5 1 2
2 5
2
Table 2. Values ot Aaexcess) and AG(total)*as Functions 01 the Mole Fraction ot Ethanol lor Mlxlng Ethanol and Cyclohexane
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'me values of A U e x ~ s swere l calculated horn me data in Stokes a M Adamrm'. and Aqtolal) = Aqexceos) RT(X, in X, X2 In X,). with T= 298.2 K.
+
where nl and nz are the numbers of moles of each component. The molar enthalpy of mixing is then plotted against the mole fraction of ethanol. The calculations for the two"walk-across" steps ( 0 and (1) demonstrate an important principle: the total enthalpy change of a series of steps is equal to the sum of the enthalpy changes in each individual step (an illustration of Hess's law). For example, in part ( 0 ,
where n. is the number of moles of mixture formed in step (e), nr is the number of moles of the same mixture used in step (0, and nlis the number of moles of pure ethanol used in step (0. When AH is plotted against the mole fraction of ethanol, i t falls on the same curve as the other data points (Fig. 2), givinga nice confirmation of the principle. To calculate nr, i t is necessary to know the density of the mixture ( p ) and the mole fraction of each pure component ( x i ) used in step (e):
where ur is the volume of the mixture used in step ( 0 and MI and M2 are the molecular weights of the two components. ~ e c a u s eit may not hecont,enient todetermine the \,slue ofp directly, one can use the approximate relation nt n,
uf u,
(4)
where u, is the sum of the volumes of the pure components mixed in step (e): ur = 50.0 mL and u. = 65.0 mL in our case. The approximation turns out to he quite good, producing negligible errors in calculating the value of AH. The calcula-
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tion for step (1) is similar, except that nz (for pure cyclohexane) is used instead of nl in eq 2. The data from a student's trial run, which were collected from more measurements than those required in the above vrocedure, azree well with literature data4 as shown in Figi r e 2. hes sake reference also gives the nonideal free energy data. The curve for the nonideal entropy changes (multiplied hy temperature) in Figure 2 wasvhtiined hy suhtracting AG from AH. T o facilitate the calculation of TAS from the ex~erimentalvalues of AH. we have tabulated values of AC&&dated from the workofstokes andAdamson4for the ethanol/cyclohexane system (Table 2). For an ideal system, A G = RT(r, In r,
+ x, in x,)
(6)
and TAS=AH-AG=-AG
(7)
The large deviations of AH from zero and T A S from its ideal value (Fig. 2) illustrate the nonideal behavior of this system. The students are asked tointerpret these deviations in terms of the change of hydrogen bonding during the mixing of the two components. Complementing thermodynamic material covered in the physical chemistry lecture course, this experiment touches on a wide range of thermodynamic principles and gives students experience in using them to handle data. We feel that students will learn a great deal more from the experiment than from thermochemical experiments we have used in the past, and we hope that other instructors will find it useful too. A detailed write-up for these two experiments is availhle on request. Volume 65
Number 10
October 1988
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