In the Classroom
The Colligative Property of Walther Nernst Herbert Beall* and Patrick A. Riccardino Department of Chemistry and Biochemistry, Worcester Polytechnic Institute, Worcester, MA 01609; *
[email protected] The achievements of Walther Nernst (1864–1942) qualify him as one of the giants of late 19th and early 20th century chemistry. His famous equation that relates cell potentials to electrolyte concentrations and his work on the concept of absolute entropy stand out as milestones in the history of science. In this paper we would like to explore a very little known aspect of his wide range of achievements. In 1890 Nernst described a colligative property that he called “reduction of solubility” as a method of determining molecular masses (1), something different from the other well-known colligative properties. In his method, Nernst made a binary liquid phase mixture of an organic solvent and water, which he shook and then determined the concentration of the organic solvent in the water after equilibration had occurred. A known mass of a substance of unknown molecular mass was then dissolved in the organic phase of the liquid– liquid system. It was necessary that this substance be soluble in the organic phase but only very slightly soluble in the water phase. After shaking and equilibration, the concentration of the organic phase in the water phase was again determined. (In our determinations we found that one hour was more than sufficient time for equilibrium to be achieved.) The presence of the unknown solute in the organic phase reduces the mole fraction of the organic solvent in this phase. Assuming ideal solutions, since there are fewer organic solvent molecules per unit volume of organic phase to cross the phase boundary, there should be a proportional decrease in the concentration of the organic solvent in the water phase of the system. Assuming the ideal conditions of Raoult’s law, 0 Csolvent = C solvent Xsolvent 0 where C solvent is the concentration of the organic solvent in the aqueous phase before the unknown solute has been added, Csolvent is the concentration of the organic solvent in the aqueous phase after the unknown solute is added, and Xsolvent is the concentration in mole fraction of the organic solvent in the organic phase. The molar mass of the unknown can be determined in a manner exactly analogous to the calculation of molar mass used with Raoult’s law. Sources of error include (i) nonideality of the solution, (ii) dissolving of the organic solvent in the aqueous phase, affecting the organic phase volume and the concentration of the unknown in the organic phase, and (iii) dissolving of the unknown solute in the aqueous phase, affecting its concentration in the organic phase. One published modification to Nernst’s procedure involved using phenol and water saturated with NaCl as the two phases and titrating the phenol concentration in the aqueous phase with standard base (2). Another modification employed ether and a large volume of water as the two phases and the ether solubility in the aqueous phase was determined directly by the change in volume of the water (3). Acceptance of Nernst’s method was limited. He certainly referred to his method in his own textbook, and his method was described in at least one monograph (4). We located one text in which the phenom-
enon of reduction of solubility was described but without listing it as a colligative property capable of being used for determination of molar mass (5). Other roughly contemporary texts ignored his method and listed only the four familiar colligative properties, osmotic pressure and the changes in freezing point, boiling point, and vapor pressure (6 ). Now, 110 years later, we revisited this experiment to examine its accuracy and its possible pedagogic use. In most of his experiments Nernst used an organic acid as the nonaqueous phase, allowing him to titrate the concentration of the acid in the water layer with a standard base using an indicator. For nonacidic organic phases he took an aliquot of the aqueous layer and used the freezing-point depression of the water to determine the concentration of the organic solvent in the aqueous phase (7 ). However, this method of using one colligative property to determine another seems redundant and would only compound errors if Nernst’s method were being used to determine molar masses. With an organic acid as the aqueous phase, the molar mass of the unknown can be calculated from the volumes of standard base used to titrate the aqueous phase. Let V 0 be the volume of standard base used to titrate the aqueous solution before the addition of unknown solute to the organic phase and V be the volume of standard base used to titrate the aqueous phase after addition of the unknown. The volumes of standard solutions are proportional to the concentrations of organic solvent in the aqueous phase before and after addition of the unknown, and ∆V is proportional to ∆Csolvent , the lowering of the concentration of the organic solvent in the aqueous phase. Making the assumptions of Raoult’s law, the Csolvent and therefore V will be proportional to the mole fraction of organic solvent in the organic phase. That is, if there is no solute in the organic phase, V /V 0 will equal one, and if the organic phase is pure unknown solute, V/V 0 will equal zero. If the solution is ideal there should be a linear relationship between these two extremes. Thus,
V =X solvent V0 and V = V 0Xsolvent ∆V = V 0 – V = V 0 – V 0Xsolvent = V 0(1 – Xsolvent) = V 0Xsolute Now,
X solute =
n solute n solute + n solvent
where n represents the numbers of moles of solute and solvent in the organic phase. This reduces to
X solute =
n solute n solvent
JChemEd.chem.wisc.edu • Vol. 78 No. 4 April 2001 • Journal of Chemical Education
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In the Classroom
if the concentration of the solute is small compared to the concentration of solvent. The value of nsolute is
n solute =
V 0 m solute M solute n solvent
M solute =
V 0 m solute ∆Vn solvent
If the assumption that nsolute is much less than nsolvent is not made, the expression for the molar mass of the solute is 0
V m – m∆V ∆Vn solvent
where m is msolute. This reduces to the previous expression when m and ∆V are both very small, and, therefore, m∆V becomes negligible. The organic acid Nernst employed was valeric acid, and this was the one commonly available acid that we found to be satisfactory—although the stench was a considerable drawback. The molar masses of five solutes, naphthalene, menthol, isoborneol, camphor and phenanthrene, were determined using valeric acid. The concentration of the valeric acid in the aqueous layer was determined by titration with standardized 0.5 M sodium hydroxide and phenolphthalein indicator. On averaging three determinations for each solute the results were as shown in Table 1. These data demonstrate that Nernst’s method does give reasonable results, particularly considering the possible sources of error. Extension of the method to other systems, however, is not promising. The stench of valeric acid deters its use. Searches for other commonly available compounds satisfactory for the organic phase were not successful. An organic base could be titrated in the aqueous phase, but no
512
Naphthalene
126.8
128.17
1.0
Menthol
150.1
156.27
4.0
Isoborneol
150.7
154.24
2.3
Camphor
142.0
152.23
6.7
Phenanthrene
173.9
178.22
2.4
M solute n solvent
Solving for Msolute gives
M=
Error (%)
M solvent
Substituting this into the equation for ∆V gives
∆V =
Actual
Solute
m solute
Molar Mass Average
m solute
where msolute is the mass of the solute and Msolute is its molar mass. The amount and molar mass of the organic solvent is known, and so the value of nsolvent is known. Thus,
X solute =
Table 1. Molar Mass of Solute Determined from Concentration of Valeric Acid in Aqueous Layer
satisfactory base was found for molar mass determination by Nernst’s method. Thus Nernst’s colligative property will likely remain a curiosity and serves as an example of the nature of scientific research, which includes large and small discoveries, sometimes leading up blind alleys and sometimes opening vistas that change the nature of human exploration and thought. Clearly, Walther Nernst’s work spans the gamut of these possibilities. Literature Cited 1. Nernst, W. Z. Phys. Chem. 1890, 6, 16. Nernst, W. Theoretical Chemistry; Codd, L. W., Translator; Macmillan: London, 1923; pp 312–313. 2. Küster, F. W. Berichte 1894, 27, 324, 328. 3. Tolloczko, St. Z. Phys. Chem. 1896, 20, 389. 4. Young, S. Stoichiometry; Longmans-Green: London, 1918; pp 312–313, 345–346. 5. Friend, J. N. A Text-Book of Physical Chemistry, Vol. 1; Griffin: London, 1932; p 360. 6. Whetham, W. C. A Treatise on the Theory of Solution; Cambridge University Press: Cambridge, 1902; pp 95–164. Ostwald, W. The Fundamental Principles of Chemistry; Longmans-Green: London, 1909; pp 265–289. Ewell, A. W. A Textbook of Physical Chemistry, Theory and Practice; Blakiston: Philadelphia, 1909; pp 150–180. Getman, F. H. Outlines of Theoretical Chemistry; Wiley: New York, 1913; pp 165–202. Washburn, E. W. An Introduction to the Principles of Physical Chemistry; McGraw-Hill: London, 1915; pp 143–178. Lewis, W. C. McC. A System of Physical Chemistry, Vol. 1; Longmans-Green: London, 1921; pp 162–187. Findlay, A. Practical Physical Chemistry; LongmansGreen: New York, 1923; pp 112–136. Partington, J. R. Chemical Thermodynamics; Van Nostrand: New York, 1924; pp 94–105. Getman, F. H.; Daniels, F. Outlines of Physical Chemistry; Wiley: New York, 1931; pp 162–178. 7. Nernst, W. Z. Phys. Chem. 1890, 6, 573.
Journal of Chemical Education • Vol. 78 No. 4 April 2001 • JChemEd.chem.wisc.edu
