provocative opinion Raoult's Law Is a Deception Stephen J. Hawkes Oregon State University, Cowallis, OR 97331
Raoult's law should not be in the introductory chemistry curriculum. I t is unlikely that a student ever will need to know the vapor pressure of a solution and, if they do, Raoult's unreliable guidance will deceive more often than i t helps. I t works only for dilute solutions (and then only for the solvent, not the solute, and not for polymers) or for solutions in which the intermolecular forces within the pure solute and solvent are very similar to those between the solvent and solute in the solution. This is the case, for example, with n-hexaneln-hexadecane ( 1 ) or dextroselwater (2).I t fails completely when either component i s a polymer, even a t infinite dilution (3, 4). I n many cases i t is not even the best guess. For polymers, the volume fraction gives better guidance than the mole fraction (3, 4). Solutions of perfluorobutane in n-butane conform better to a mass fraction relation than to the mole fraction a t most concentrations (calculated from the data in (5)). I t is not even pedagogically useful. The law illustrates no wider principle. I t is not the foundation for any later teaching. It cannot be proved or even made to appear reasonable by any argument that can be followed by undergraduates (the statistical proof is the subject of a graduate course). Intuitive argument based on the area available for evaporation suggests the volume fraction rather than the mole fraction, and is correct in the case of polymers. For the substantial number of students who are "mathophobic", the calculation of the mole fraction is another algorithm to be uncomprehendingly memorized. I t is never used again in the introductory course so their education is not furthered by learning it. I do not know that i t was ever popular for the determination of approximate molecular weights, but i t is seldom used for that purpose now. If a need should arise to calculate the vapor pressure of a solution, a chemical engineer should be consulted because their texts, e.g. (6, 7), show how to oerform the calculation with more reliable akor~thrnsEven so, it is better to jerk :I pul~lishcdt:il~lt,as in r7. .Y . T h ( w tal1l6:i usunlh arc not to he found in reaular chemical literature but a r e i n t h e referenceworks of chemical engineers. This must mean t h a t chemists and most other people who use chemistry do not use the data so the law and its corrections are not worth learning. Its unreliability does not resemble the unreliability of the ideal gas law. Most gases behave nearly ideally in situations that students are likely to meet; whereas, most solutions behave non-ideally. Deviations from Raoult's law are occasionally used to illustrate the effect of intermolecular interaction between solute and solvent. The discussion always i s held to small deviations t h a t cause only curvature of the tie line on graphs of vapor pressure against composition thus conveyinn the imoression that Raoult's law is usuallv a reasonnhle approximotion. lntermoleculnr intrrn~.tionsare il.ustr:it(d more usefullv hv their t+fi!ct on wluhilit\. and the practical problem ofehoosing a solvent, abandoning the ar-
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Journal of Chemical Education
0.2
0.4
0.6
0.8
if
Activitv coefficients -1 for "reaular solutions at 25 "C assumino molar . n moer vo Jme = 100 cr'? a q nsl .o ..me 1rar.I on o o' sc ~ cTne aga nsl eacn I ne s me o Herence oelneen lnc so .u i y paramelers S for solute and solvent chaic "like dissolves like" in favor of a discussion of dipoledipole, dipole-induced dipole, London, H-bond and electron donor-acceptor interactions. Some Theory The deviation from Raoult's law may be expressed by an activity coeff~cienty thus 0
P=YxP
For Raoult's law to aoolv. .. .. r.m u s t be unitv. I t mav be several orders of mabmitudt: in rce1 sdutionj. For solutions \vhere'.remlar solut~on"t h c o n 4 ; t ~ ~ l i w .
where r$ i s the volume fraction, u is the molal volume, and 6 i s the solubility parameter in cal/cm3 (@ is the energy of vaporization to the gas a t zero pressure, per unit of volume). This function is plotted in the figure, which shows that there is only a very limited number even of "regular" solutions in which the activity coefficient y is less than 1.1 and the error from Raoult's law consequently less than 10%. The law is, therefore, a poor approximation even i n these cases. The practice i n introductory texts of givingresults of Raoult's law calculations to two or even three significant figures is deceptive to our students, even for "regular" solutions. Moreover, if i t is insisted that Raoult's law must be
taught then our students also should be instructed and tested on how to decide whether a solution is one to which i t can be applied as a reasonable approximation. Moreover, many solutions are not even "regular". For these, the activity coefficient may differ from those i n "regular" solutions by orders of magnitude. A listing of such solutions in (10)shows activity coefficients a t infinite dilution with a median value around 15 and a maximum of 27000 (for hexadiendwater). To suggest to students that Raoult's law is generally a reasonable approximation is to deceive them. Polymers In the extreme case where a polymer is dissolved in a monomeric solvent, the equations shown i n reference (9) reduce to
when the polymer has much higher molecular weight than the solvent, the solution is dilute, and the polymer and solvent are sufficiently chemically similar that the Flory interaction parameter is unity. I n other conditions, the formula i s more complex, and I have been unable to reduce i t to Raoult's law in any case that I could conceive. For polymers, Raoult's law is unambiguously false and is not even a poor approximation. The same relation applies (3, 4 ) to solutions of volatile substances in polymeric solvents. Then
and Raoult's law is again false. These two equations for polymer solutions are derived rigorously but also result from the simplistic argument that evaporation rates are proportional to the area of the solution surface occupied by the evaporating substance.'
The vapor pressure of strong sucrose solutions is so low that spilled pop never dries completely. Because the lowering of the vapor pressure depends on the number of molecules or ions, other things being equal, small molecule substances lower vapor pressure more than similar masses of larger molecules. For the same reason, substances that ionize reduce vapor pressure more than covalent compounds. When antifreeze is added to water, the vapor pressure is lowered so that i t evaporates less and is less likely to boil. The lowering of vapor pressure by the solute causes a n increase in boiling point because a higher temperature is needed for the vapor pressure to equal the atmospheric pressure. Some texts use the vapor pressure lowering to prove that the solute also will reduce the freezing point. The proof is sound and the approach is rational but it becomes irrational when they imply that the freezing point deoression is aconseouence of the vaoor lowering. . oressure . The freezing point is depressed even in a completely filled container where there i s no vaoor. The cause is that solute molecules hinder the formation of crystals of the solvent. Conclusion The reform of introductorv chemistry Doses r e o e a t e d l ~ t l ~ hard c question of what m;st In! left &t', and subjects fo-r omiision must be wurht. Raoult's law IS one framienr of the curriculum that deceives more than i t enlightens and should be omitted. Literature Cited I. Hildebrand. J. H.; Sweny J. W. J. Phys. Chem. 1939.4,3.297. 2. Torgesen.J. L.:Bower,V E.; Smith. E. R. J. Res. Not. Bur: Stondoids 1950,45,458. 3. Patterran. D.:Tewari.Y. B.; Schreibe~H. PMocrnmobcubs 1972.4.3Sfi. 4. Roberts, G. L.; Hawkes, S. J. J. Chromoiog Sci. 1973.11.16. 5. Simons,J. H.: Mausteller, J. W. J. Chem. Phys 1952,20. 1516. 6. h i d , R. c.;~ r a u m i t zJ. , M.:shenvoad.T K ~ h Prnpenles r orcnses end Liquids, 3ded.; McGraw-Hill: New York. 1977. 7. Hiram. M.; Ohe. S.: Nsgahama. K. Compul~rAidedData B w b of Vnpor-Liquid Equiiibrio; Kodansha, Takyo and Elsener Stientifie: Amsterdam, 1976. 8. Perry R. H.; Green. D. P o v ' s Charn~ealEngrneem Handbook; McGraw-Hill: New 70% .".n,..,"-.
" " d ,
Qualitative Discussion Vapor pressure lowering by a solute is interesting and perhaps mildly important, and the fact that it is not easily calculated does not reduce its interest. Seawater has 2% lower vapor pressure than lakewater (11) and this slightly increases the humidity around the Great Lakes compared to places near oceans. I t also figures into the calculation of weather patterns, though the 2% is smaller than the present uncertainty of the calculations.
9. Hildebrand, J. H.: Prausnitz. J. M.; Scott, R. L. Regular nndReloted Soiulions. 3rd ed.:Van Nostrand Reinhold: New York. 1970. p 110. lo. Frededund. A,: Jones. R. L.; Prausnitz. J. M. Amer Inst Chzm Ens 1975.276.
,"*a 11. Millero, F J.: Leung,W H.Amer J Sci. 1976,276, 1063.
'I was appalled by a reviewer's suggestion that instructors should focus on volume fraction rather than mole fraction. This would give correct answers for uncomplicated polymer solutions, but wrong answers for the solutions mentioned earlier where Raoult's law works we Introoxlon, chern sl~ysno. d no1 nclme any atlernpt lo qdantcly vapor presswe lower ng
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