roactive opinion Raoults Law Is a Deception Sthepen J. Hawkes Oregon State University, Corvallis, OR 97331
Raoult¶s law should not be in the introductory chemistry curriculum. It 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 it helps. It works only for dilute solutions (and then only for the solvent, not the solute, and not 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-hexane/n-hexadecane (1) or dextrose/water (2). It fails completely when either component is a polymer, even at infinite dilution (3, 4). In many cases it 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 mass fraction relation than to the mole fraction at most concentrations (calculated from the data in (5)). It is not even pedagogically useful. The law illustrates no wider principle. It is not the foundation for any later teaching. It cannot be proved or even made to appear reasonable by any argument that can be fallowed 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 ³mathophobic´, the calculation of the mole fraction is another algorithm to be uncomprehendingly memorized. It is never used again in the introductory course so their education is not furthered by learning it. I do not know that is was ever popular for the determination of approximate molecular weights, but it 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 consulted because their texts, e.g. (6, 7), show how to perform the calculation with more reliable algorithms. Even so, it is better to seek a published table as in (7, 8). These tables usually are not be found in regular chemical engineers. This must mean that 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 is held to small deviations that cause only curvature of the tie line on graphs of vapor pressure against composition thus conveying the impression that
Raoult¶s law is usually a reasonable approximation. Intermolecular interactions are illustrated more usefully by their affect on solubility and the practical problem of choosing a solvent, abandoning archaic ³like dissolves like´ in f avor of a discussion of dipole-dipole, dipole-dipole, dipoledi poleinduced dipole. London, H-bond and electron donoracceptor interactions. Some theory The deviation from Raoult¶s law may be expressed by an activity coefficient thus 0
p= xp
For Raoult¶s law to apply, must be unity. It may be several orders of magnitude in real solutions. For solutions where ³regular solution´ theory (9) applies Is given (9) by logsolvent = V solvent solute (solvent ±
2
solute) /4.575 T T
where is the volume fraction, v is the molal volume, 3 2 and is the solubility parameter in cal/cm ( is the energy of vaporization to the gas at zero pressure, per unit volume). This function is plotted in the figure, which shows that there is only a very limited number even of ³regular´ solutions in which the activity coefficient is less than 1.1 and the error from Raoult¶s law consequently less than 10%. The law is, therefore, a poor approximation even in these cases. The practice in introductory texts of giving results of Raoult¶s law calculations to two or even three significant figures is deceptive to our students, even for ³regular´ solutions. Moreover, if it is insisted that Raoult¶s must be taught then our students also should be instructed and tested on how to decide whether a solution is one to which it can be applied as a reasonable approximation. Moreover, many solutions are to even ³regular´. For these, the activity coefficient may differ from those in ³regular´ solutions by orders of magnitude. A listing of such solutions in (10) shows activity coefficients at infinite dilution with a median value around 15 and a maximum of 27000 (for hexadiene/water). To suggest to students that Raoult¶s law in generally a reasonable approximation is to deceive them. Polymer s
In the extreme case where a polymer is dissolved in a monomeric solvent, the equations shown in reference (9) reduce to Psolvent
When
= solvent Posolvent
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. It other conditions,
roactive opinion the formula is more complex, and I have been unable to reduce polymers, 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 P solute=
0
solute P solute
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. 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. It also figures into the calculation of weather patterns, though the 2% is smaller than the present uncertainty of the calculations. 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 that ionized reduce vapor pressure more than covalent compounds. W hen antifreeze is added to water, the vapor pressure is lowered so that it evaporates less and is less likely to boil. The lowering of vapor pressure by the solute causes an 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 depression is a consequence of the vapor pressure lowering. The freezing point is depressed even in a completely filled container where there is no vapor. The cause is that solute molecules hinder the formation of crystals of the solvent. Conclusion
The reform of introductory chemistry poses repeatedly the hard questions of what must be left out, and subjects for omission must be sought. Raoult¶s law is one fragment of the curriculum that deceives more than it enlightens and should be omitted.
