I Phase Equilibrium, Chemical Equilibrium,
Walter Dannhauser SUNY at Buffalo Buffalo. NY 14214
I I
and a Test of the Third Law Experiments for physical chemistry
An ideal nhvsical chemistrv laboratow should . experiment . introduce skdents t o various laboratory techniques within a unifying theoretical framework such as, for example, the laws of thermodynamics. This goal is seldom even approached: rather, we usually content ourselves with assigning a number of essentially unrelated experiments which do little to provide the broad perspective that students need so badly. The experiments outlined below were designed to provide an experimental basis for such a unifying point of view, and I believe they are reasonably successful in doing so. IntroducIlon to the Experiments The "obvious." direct, wav of evaluating the equilibrium constant of a reaction is to measure the equilibrium concentrations (more precisely, the activities) of all the reactants and products and to substitute these values in the reaction quotient of concentrations (activities). This method is adequately illustrated by various experiments in most laboratory manuals. If the eauilihrium constant is measured as a function of temperature, then application of the Gibbs-Helmholtz eauation nermits evaluation of the thermal parameters which cdaractehze the reaction-the standard enthalpy and standard entropy of reaction. This, too, is a standard experiment. Can the procedure he reversed? In other words, can one evaluate the equilibrium constant for a reaction from purely thermal, ie., calorimetric, measurements? The answer is, "Yes," if the Third Law applies for each reactant and product. Castellan ( I ) provides a particularly good discussion of this matter. In summary he states: "The validity of the Third Law is tested by comparing the change in entropy of a reaction computed from the Third Law entropies with the entropy changes computed from equilibrium measurements. Discrepancies appear whenever one of the substances in the reaction does not follow the Third Law." The experiments described below provide the basis for such a test. They are based on a paper by Malcom, Staveley, and Worswick (2) which is one of a series from Staveley's laboratory. The experiments-are directed toward measurements of AGig8,AHlgs, and AS2g8,of reaction 1.
-
KdFe(CNh. 3H20(s) KSe(CNk(s) + 3HzO(g) (1) Malcom, Staveley, and Worswick have nieasured the heat capacity of the trihydrate (KFCT) and the anhydride (KFC) from 10°K to 300DK so that Third-Law entropies may be evaluated. With Sigs of HnO(g) firmly established,' the calorimetric ASO(l)is compared to the experimental (equilibrium) value, and the aforementioned test of the Third Law can he carried out. Presented at the Ninth Northeast Regional meeting, American Chemical Society, Syracuse, New York, October 4,1919. Because of the residual entropy of ice at OK ' due to proton disorder, evaluation of SlgSis not straightforward.If the background of the students permits, a discussion of the statistics involved and a comparison of the calorimetric and statistical mechanical evaluation of So may be appropriate. Temperature changes are never directly measured as such. The electrical calihration is in terms of Joules/(mVbridge unbalance)and ATs ean be estimated from the beat capacity of the calorimeter,ahout 4.2 kJ/K.
-
The interest in this particular system stems from the paraferroelectric transition that KFCT undergoes electric when cooled below 250°K. I t appears as a lambda-transition in the C , versus T curve. X-ray and neutron diffraction studies (2) show that the positions of all atoms other than hvdroeen remain essentiallv unchan~ed.The auestion then does a reaiisesyare the hydrogen atoms ordered a t 0 sidual entrouv due to nroton disorder nersist? The concent of residual entropy is oiten exemplifiedin texts by reference to, and discussion of, ice. The KFCT situation is quite similar and students readily appreciate the qualitative aspects of the problem.
o or
The Experiments We devote one 5-hr laboratory period to each of the two experiments described below. They can be performed entirely independently of one another. In the first experiment, stuof reaction (2) by calorimetry from dents determine mig8 heats of solution.
We have noted (3) previously that this is a particularly attrartive experiment he(!ause of the rapidity and endothermicity uf both sulution reactions. Consequently, the ralorimccer can he quite rudimenrary: we use a 2-1 plastir Ikwar flask to eliminate breakage problems. A 10-ohm Nichnme heater. sheathed in pulyethylene surgical tubing, is wound around a plastir mandrel which also irrves as the bushing for a glass stirrer driven by an rxternal motor. Temperature chungur are measured with a IOK-ohm thermistor which is made one arm of u simple DC Wheatstone bridge. Hecause the small ATs involvrd, the bridge is not used as a null device; rather, the bridge unbalance voltage is a linear measure of AT. Thus the bridge balance potentiometers, which are used merely to set the range of the bridge, need be neither precision grade nor calibrated, greatly simplifying the bridge and reducing its cost. A mercury D-cell provides an adequately stable source of bridge EMF. If a 5 mV recorder is available, the bridge unbalance can be directly displayed as a function of time, greatly simplifying analysis of the data. Otherwise, point-hy-point recording (a digital millivoltmeter is convenient) is entirely satisfactory. Because AH > 0, the electrical calibration of the calorimeter is straiehtforward: it is virtuallv trivial if a constant current jourceis a\,ailable. We easily detect millidegree .lTs.'Thus. rr,ith 1 I nf solution in the calorimeter our urecision is about f3 Joules. Reagent arade KFCT is pulverized, heated to constant weighcn a vacuum oven, andstored in desiccator. Five 10-g aliquots are added sequentially to the calorimeter merely by pouring them through a powder funnel so positioned that the sample falls directly into the solution. Electrical calibration follows each aliquot. The experiment is repeated with samples of the pulverized hydrate. The integral heat of solution is evaluated at each concentration for each solute and AH(2) = AHdhydrate) AHdanhvdride). a neat annlication of Hess' Law. The me&& jleats df solution are essentislly independent of concentration, makine the reauired extrapolation to infinite dilution a seeminglytrivial task. Actually, the heats of dilution are very large (4)hut happen topass through a maximum just
a
Volume 57, Number 9, September 1980 / 681
in our concentration range! The data should he shown to the students to illustrate the hazards of extranolation. In anv event, hecause the heats of dilution cancel exactly for K F C ' ~ and KFC. AHD(2)can be evaluated3 easilv and student results agree well with Hepler's (5). T h e second experiment actually consists of two parts performed in parallel: (a) the vapor pressure of water is measured as a function of temperature, and (h) the dissociation oressure of KFCT is measured as a function of temperature. ~ l ; u sA(?. VI",and hSo at 298°K can he evaluated for reactions (1) . . and
(3).
-
H20(l) HsO(g) (3) T h e vapor pressure measurements are straightforward. We use a n isoteniscoue and find the design " of Steinhere (6) nsrtitularly convenient. The precision of the results is generally limited bv the readahilitv of the manometer (f1torrl. T h e determination o f t h e dissociation pressure is not so simple because eauilihrium is attained verv slowlv (7). The unf&orahle kinetics preclude a direct measirement of the dissociation pressure a t 298'K; rather, measurements are made a t a series of higher temperatures starting a t 40°C and the results are extrapolated to 25'C. If the thermostat holding a previously conditioned4 mixture of KFCT and KFC is brought to 40% by 9 a.m., it appears that sufficient time is available to attain equilibrium b j i p.m., when our laboratory session begins. A sketch of the apparatus is shown in the figure. The mercury levels of the local manometer are read with a cathetometer. The O-ring valves5and joint are excellent whereas prior attempts to use ordinary stopcocks invariably failed after a few heating cycles. At the start of the experiment V2 is closed and V1 is opened to permit evacuation of both legs of the local manometer. Suhsequently, V1 is closed in order to isolate the
-
Degassed Vopor
L -
of^^^^
The large heats of dilution and their cancellation in this special ease provides an excellent basis for discussion of the choice of infinite dilution as the standard state for enthalpy. Following Malcom et al., a sample of KFCT is cyded several timea between -78T and room temperature to ensure transformationto the stable monoclinic form. A 3:l mixture of KFCT/KFC is pulverized to a fine powder and enough of the mixture is put into the sample flask to cover the bottom to a depth of a few millimeters. The sample is degassed at O°C or lower, the vacuum being applied for only a few minutes, after which valve V2 is closed. The sample is heated to about 60°C, cooled back to about O0C, and degassed again. It is ready for use after eauilibratine at 4 0 T for about 6 hr. As a check. the dissociation predsure at 40% is 35 tom. We find it desirable to degas the sample uery briefly after a few runs. (This requires increasingly long periods of equilibration at 40°C.) We replace the sariple entirely after about half adozen runs. It is important that V2 be kept closed except during the actual measurement of the dissociation pressure, i.e., that the sample not be pumped on after it has been conditioned. Ace Glass Ineorp., Vineland, N.J. 08360. Type 8195 or equivalent. @Therate is so slow that the system appears to be at equilibrium if the monitoring time is only 15-30 min. The results at 35'C are usually not very g o d and should be weighted lightly in the subsequent analysis. However, the kinetics aspects of the experiment is a definite pedagogic advantage. A major source of student error is the neglect of proper units in these csleulatians. Because the experimental results are expressed in tom, many students simply continue with these units, leading to AG298(3) < 0 for example. The appropriate choice of units and the standard state for gases-and the influence thereof on ASo but not on AHo-is exemplifiedby this aspect of the experiment. sThis aspect of the experiment has been a great disappointment: the students are incredibly careless in the Third Law integrations. Despite our suggestion that they try numerical methods, most use the graphical technique illustrated in all the textbooks. Sloppy graphs (an excellent place to emphasize significant figures!) and a total disregard for units are the most common faults. Since the C, s are given at equal temperature intervals, numerical integration with the trapezoid rule is easily done witha hand calculator. Even for KFCT with its lambda transition, the results agree with Maleom et al. to better than 0.1%. 682 1 Journal of Chemical Education
sample leg of the manometer and V2 is opened. The reference leg is connected to the pump a t all times. After the vapor pressure of water and the dissociation pressure of KFCT have been measured a t 40°C, the bath temperature is raised as quickly as possible to about 50°C and set to regulate f0.1'. Five minutes a t this new temperature is adequate to bring the isoteniscope into thermal equilibrium and the vapor pressure of water can then he measured. Bv then the dissociation pressure has had opportunity to equilibrate, and its value is monitored for about 10-15 min. If it is reasonably constant (we suggest deviations less than lo%),we record the value and the bath is quickly adjusted to 60°C where the procedure is repeated. Then the bath is cooled rapidly to 55", 45", and 35'C and the procedure is again repeated a t each temperature. At 35OC the kinetics are noticeably slow! As much time as possible is allowed for equilihration (overnight would he desirable). From suitable plots or numerical analysis of their data, students evaluate AGO, AHo,and AS0 a t 298'K for reactions (1) and (3h7Asa check, AHO(l)= AH0(3) AH0(2) and the advantage of precise solution calorimetry techniaues becomes obvious. Students are given the ~iteraturk(2) values of AH0(2) = 3.476 kcal and the KFCT dissociation pressure a t 298OK, mia= 13.7 tom. These values provide a comparison with their own experimental results and are also needed for the suhsequent calculations. Malcom, Staveley, and Worswick tabulate smoothed values of C. for KFC and KFCT from 10-300°K in lo0 increments. We provide these data for the students, and they evaluate S& by graphical and/or numerical methods. We also provide the value S2ss(KFC) = 100.17 ~almole-~.K-'sothey can check the accuracy of their integration technique! With S&H20(g)) = 45.10 eu from the literature, the Third Law can now he tested. The students' experimental equilibrium data are generally not adequately precise for a con&sive test. Therefore, we ask them to repeat the calculations with the h i v e d literature value ot' ASOIL). . . If their Third-Law integrations have heen precise, they will duplicate Malcom, Staveley, and Worswick's finding that A S o ( l ) is essentially the same for the equilibrium and calorimetric experiments: thus, KFCT is an ordered phase a t 0°K.
+
Literature Cited (1) Castellan, 0. W.. "Physical Chemistry:
2nd Ed., Addinon-Wesley. 1971. See sections 11-9, -14,-15,and espacially 11~17. (2) Malmrn. I. R.,Stsudey,L. A. K.,and Worawick.R. D., J C h m Soe Trans. Farad. Soc. 1.69.1532 11973). SeeaLsoN. G. Parsonageand L. A. K. Staueley,"Disorder inCr)ufals? Oxford University Plors, 1978. Similar experiments have bean reported by Giauque, W. F., st. ol. J . A m w Chem. So
