The'Binary Liquid-Solid Phase Diagram of klaphthalene-pdichlorobenzene A Physical Chemistry Laboratory Experiment Paul P. Blanchette St. Mary's College of Maryland, St. Mary's City, MD 20686 The liquid-solid phase diagram of the binary system, naphthalene-p-dichlorobenzene,is obtained quite easily by thermal analysis methods with minimum laboratory equipment. The advantages of this system over other suggested systems (e.g., naphthalene-dipheuylamine (I), tin-lead (2), and phenol-p-toluidine (3))include the use of inexpensive, stable, and relatively safe (4) chemicals and a temperature range accessible with a mercury thermometer. In addition to obtaining the liquid-solid phase diagram, perhaps the real underlying beauty of this experiment is that i t ~rovidesa whole treasurv of thermodvnamic information. Specifically, the student can ohtain reasonable estimates of the heat or fusion (and differential hear of solution). . . entrow -. of fusion, freezing-point-depression constant, and solvent activity coefficients for each component. The data may be exploited further to yield estimations of purity and the "true" melting point (5).
manner using a modified Beckmann apparatus (1,8). A total of 11samples of varying composition is sufficient to define the shape of the phase diagram. Convenient mole fractions for naphthalene are 1.00,0.95,0.90,0.75,0.55, and 0.45, while convenient mole fractions for p-dichlorobenzene, include 1.00, 0.95, 0.90, 0.80, and 0.70. By performing the first determination on 5.00 g of pure solvent, for example, naphthalene, other naphthalene-rich solutions can be prepared by successive additions of previously determined and accurately weighed portions of p-dichlorobenzene to the preceding sample. Paradichlorobenzene-rich solutions can be prepared in an analogous fashion. S a m ~ l ethat s are too dilute do not contain enoueh solution of euteitic composition in order to observe a euyectic halt. However, intermediate solutions from Xnanh= 0.2 ~ 0 . 7 are 5 suitable for such analysis and should be-&led long enough until a eutectic halt appears.
Theory The curve NE in the figure may be thought of as the freezing point depression curve of naphthalene due to added p-dichlorobenzene, and i t may also be thought of as the solubility of naphthalene inp-dichlorobenzene as a function of temperature. Likewise, curve P E may be interpreted as the freezing point depression of p-dichlorobenzene due to added na~hthaleneas well as the solubilitv . of .o-dichlorobenzene in naphthalene as a function of temperarure. Derivation of a suitable eauation to descrihe curves such as NE or P E can be achievedby either approach (6, 7). When pure solid A is in equilibrium with a liquid solution containing component A, the molar Gibbs free energy of A is the same in each phase. Thus,
Results and Discussion The experimental phase diagram of the naphthalenepdichlorobenzene system is shown in the figure. The points shown are a pool of break and arrest temperatures extracted from cooling curves for various solution compositions. These data are a composite obtained by four experimenters. The general appearance is that of a simple eutectic system with the eutectic point occurring a t 29.5 "C and XPDCB= 0.64. Enthalpies and entropies of fusion, and freezing-pointdepression constants for naphthalene and p-dichlorobenzene are presented in Table 1.By method I the enthalpies of fusion were calculated from the limiting slopes of curves NE and P E (I). Method I1 values were calculated with eq 2 using points extracted from a "best fit" curve to the composite data set in the range X.,iWt = 1.0 to 0.9, where the solvent activity coefficient was assigned a value of unity. Methods I and I1 seem to yield reasonably accurate values for a t f , although they tend to be slightly high. The relatively large values of AfTfff calculated by Method I are re-
GA(s)= GA(soln)= GA(l)+ RTlnrAXA
(1)
where rA(s) and rA(l) are the molar Gibhs free energies of the pure solid and pure liquid, respectively, XA is the mote fraction of component A in solution, and 7 A is the solvent mole-fraction-scale activity coefficient. Application of the Gibbs-Helmholtz equation to eq 1, followed by integration and neglect of the temperature dependence of the enthalpy of fusion yields: R In YAXA = A&us(Tm)(l/Tm - 1/T)
(2)
where A~TE~(T,) is the heat of fusion of component A a t its normal melting point, T,. Equation 2 can be used to obtain the heat of fusion and activity coefficients for each component. The mold freezing-point-depressionconstant, k t for component A can he calculated from where MA is the molecular weight of A. Experimental
Freezing points and eutectic halts are extracted from cooling curves (temperature versus time) obtained in the usual
I
0.0
0.5 M O L E FRACTION P D C B
I 1.0
Experimental phase diagram d naphthalene-~lchloroben~ene(PDCB) Volume 64
Number 3 March 1967
267
Table 1.
A%
Calculated Values ol Thermodynamic Properties
Component
Method I*
(kJ/mai) Method ilb
Naphthalene pDichiorobenrene
20.3 i 1.5 18.8 5 1.5
20.3 0.9 18.7 1 0 . 9
*
LitC 18.8 17.9
kd°Clm) Experimentala
e it*
i 0.45 i 0.55
6.98 7.11
6.56 6.96
A% (Jlmoi K) 57.4 57.3
5 4.2 5 4.1
"From llmitlng slopes of cweo NE and PE. 'Fmm eq 2 at & , 0.9 a~, , ? =1 Ref 9. *From eq 3. vef
>
ra.
sponsible for making the calculated A&, a little high and the calculated k f values a little low. The close agreement between the entropies of fusion for the two components is expected due to similarities in intermolecular interactions. Table 2 shows solvent mole-fraction-scale activity coefficients at selected compositions calculated with ea 2. Both components, as solvents, seem to exhibit reasonably ideal behavior at mole fractions above 0.9 hut tend to become less ideal at lower concentrations. Concluslon
The naphthalene-p-dichlorobenzene system lends itself quite easily to thermal analysis methods and provides the student with a wide variety of useful thermodynamic information. Acknowledgment
The author wishes to extend his sincerest thanks to his students, J. Bergmeister, C. Cline, W. Leonard. and S. Rand. for testing thisexperiment and providing the author with suitable data. Literature Clted 1. Sh-maker, D.P.: ef. al. Experiment. in Physic01 Chemistry; McCrsw-Hill: New York, 1981;pp 216223.
268
Journal of Chemical Education
Table 2.
Solvent Mole-Fraction-Scale Actlvlty Coefflclentsa
Naphthalene Mole Fractlon Activity Coeff. 1.00 0.90 0.80 0.70 0.60 0.50 0.40
1.00 0.998 0.981 0.948 0.914 0.874 0.838
pDichiombenzene Mole Fraction Activity Caeff. 1.00 0.90 0.80 0.70
1.00 0.998 0.981 0.946
2. Saiebew,H. W.:sf al.Phydca1 ChsmialryLoborofory; Maanillan: New York, 1919:pp 392394. 3. Daniels, F.;et al. E~perimenfolPhysical Chemiafry; Mecraw-Hill: New York, 1962; pp 116-121. 4. Brotheriek, L., Ed. Hazard8 in the ChemieolLabomtory.The Royal Sodetyof Chemistry: Landon. 1981. 5. Meyor, E.F.: Meyer, J. A. J. Chem. Edue. 1980,57,831. 6. Lewis, G. N.;Randall, M.: Pifper, K.S.; Brewer, L. Thermodywmica: MeGrsw-Hill: NewYork, 1961: pp 227.230, 7. k i n e . I. N. Physical Chemirfry; McCraw-Hill: New York, 1989: pp 309207. 8. Skau, E. L.; Arthur, J. C., Jr.; Wickeharn. H. In Technique 01Orgonic Chemiacry: Weiasbqer, Ed.: Interscience: New York. 1959: Vol. 1,Part 1. Chapter 3. 9. Hondbook olChomirtry ondPhyricr, 64th ed.: CRC Press: Boca Raton. FL.1983. lo. Castellan,C. W.Physicol Chemistry; Addison-Wesley: Reading, MA,1967;p 258.
