William Francis Giauque received the Nobel Prize in Chemistry in 1949. Giauque was given the Nobel Prize for his work the Third Law of Thermodynamics. This research included relative entropies and experimental proof of the Third Law of Thermodynamics. Particularly, Giauque added considerably to the knowledge of the entropy of chemical substances at very low temperatures. This leads to another area that contributed to Giauque's Nobel Prize. Giauque was able to develop new methods of magnetic cooling that allowed temperatures nearer to absolute zero to be reached. Another aspect of Giauque's work that was recognized at the presentation of the Nobel Prize was his methods for measuring temperatures just above absolute zero. Nonetheless, the real basis for the Nobel Prize was Giauque's work with entropy measurements. In this work he was able to reach accuracy ten times greater than the best earlier measurements. The result of this was the proof of the Third Law of Thermodynamics, and the ability to calculate chemical equilibria. One last area that was cited was Giauque's work in the comparison of Third Law entropies to known spectroscopic data.
One of the elements for which Giauque compared Third Law entropy with know spectoscopic data was chlorine. This was presented with T. M. Powell in an article in the Journal of the American Chemical Society titled "Chlorine. The Heat Capacity, Vapor Pressure, Heats of Fusion and Vaporization, and Entropy. In this article Giauque demonstrates his technique for comparing Third Law entropies to those of known spectroscopic data.
The first step in this study was to prepare the chlorine. This was done by dropping 3 M HCl on manganese dioxide. The HCl gas was removed and the chlorine was dried. At this point the chlorine was purified to the 3 moles of impurity to 100,000 moles of chlorine. Now that a satisfactory purity of chlorine had been obtained, the vapor pressure of chlorine was experimentally determined. These measurements were made in a calorimetric apparatus because it allowed good temperature control. From these vapor pressures, the melting and boiling point of chlorine was found to be 172.12 K and 239.05 K respectively. After the vapor pressure data was obtained, calorimetric data was experimentally determined. The purpose of this calorimetric data was to determine the heat capacity at different temperatures. Helium gas was used for the purpose of assisting thermal equilibrium at low temperatures and a correction was used for changing vapor pressure of the liquid. Giauque uses this heat capacity data to plot a curve that displays that heat capacity increases with temperature. The next step in this paper is the determination of the heat of fusion of chlorine. This was done by adding heat at a point below the melting point and continuing until a number of degrees above the melting point. Giauque determined the heat of fusion to be 1531 cal/mole. After this the heat of vaporization was determined. In the calculation of the heat of vaporization Giauque used delta P/delta T and determined the heat of vaporization to be 4878 calories/mole. This varied within error limits with the value of 4851 calories/ mole that was obtained from the vapor pressure equation.
The final part of this article details the determination of the entropy of chlorine. This may be considered the most fascinating part of this article. For Giauque was able to calculate the entropy of chlorine to within 0.01 cal./K*mole of the known spectroscopic values. Giauque does this by making used of the Maxwell equation (delta S/delta P)constant T = -(delta V/delta T)constant P. This corrected to the ideal gas state of chlorine along with Berthelot's equation of state. Berthelot's equation was the following, delta S = S(ideal) - S(actual) = 27RT(critical)^3P/32T^3P(critical). The following table ( Table VIII pp.1973) shows the method of Giauque's calculation of the entropy:
The Entropy of Chlorine
0-15 K., Debye function hcv/k=115 0.331
15-172.12 K., graphical 16.573
Fusion 1531/172.12 8.895
172.12-239.05 K., graphical 5.231
Vaporization 4878/239.05 20.406
Entropy of actual gas at boiling point 51.44
Correction for gas imperfection 0.12
Entropy of ideal gas at boiling point 51.56 cal./deg*mole
This entropy was determined for chlorine at its boiling point, the entropy at 298.10 K. was also determined to be 53.32 cal./deg*mole from the calorimetric data. These two values compare almost unbelievably with the corresponding spectroscopic values of 51.55 cal./deg*mole and 53.31 cal./deg*mole. This table clearly shows how Giauque's ability to make very precise measurements allowed him to determine an extremely accurate entropy from experimental data. For all those chemists out there, imagine the difficulty in the precision of this work and it is clear why Giauque should be appropriately lauded. The fact that his value is very close to the spectroscopic value deserves further praise, which was received in the form of the Nobel Prize as we have mentioned before.
In this article Giauque has determined vapor pressure values at various temperature. Then he determined heat capacity values at various temperatures. Next, the heat of fusion of chlorine was determined. After this step the heat of vaporization was determined. From this experimental data Giauque, along with a little help from the Debye function, was able to calculate extremely precise values for the entropy of chlorine. This is one of the many reason that William Francis Giauque was what we know him as today, a great chemist and a nobel laureate.
Giauque, W.F. and Powell, T.M.; U. of California: "Chlorine. The Heat of Capacity, Vapor Pressure, Heats of Fusion and Vaporization, and Entropy." J. Am. Chem. Soc.; Vol. 61; pp.1970-74 (1939).
Nobel Prize in Chemistry 1949 [online] Available: 12/7/99 8:32 PM
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