June, 1922
THE JOURNAL OF 111-DUSTRIAL AXD ENGINEERING CHEMISTRY
The Molal Entropy of Vaporization as a Means of Determination of Heats of Vaporization B y W. K. Lewis and H.C. Weber DEPARTMENT OF C H E M I C A L
ENGINEERING, MASSACHUSETTS INSTITUTE OF ?IECHNOI.OGY, C A M B R I D G E , M A S S .
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N 1915, Prof. J. H. Hildebrandl pointed out that the molal entropy of vaporization, that is, the latent heat of vaporization of one mole of any liquid divided by the absolute temperature a t which vaporization takes place, was nearly identical for all liquids when compared at identical values of vapor concentration. Professor Hildebrand showed data substantiating the claim for the particular concentration of 0 00507 mole per liter. The authors have found this rdationship extremely helpful in estimating the heat of vaporization of liquids, but because one almost never wants the heat of vaporization a t this particular concentration, we have found it advantageous to plot what me term the Hildebrand function. I n the plots that follow, the ratio of molal heat of vaporization to absolute temperatures a t which vaporization takes place has been plotted against the ratio of the pressure a t which vaporization takes place (expressed in atmospheres) to the absolute temperature. As a matter of convenience, this latter ratio has been multiplied by 1000.
RANGECOVERED BY DATA The data include a list of substances whose boiling points range from that of liquid nitrogen to that of boiling cadmium and zinc. The list includes elements, organic liquids, and inorganic liquids. Even such substances as stannous chloride, ether, and water fall within the range of the curves indicated in the plots. I n choosing the data the authors have, however, limited themselves to pressures of about 1 atmosphere or less, but this is no very serious disadvantage because in chemical practice one seldom has need of heats of vaporization a t pressures greater than one atmosphere. I n the case of water, ammonia, and similar substances in common use, tables are available which give the necessary data a t higher pressures. We do feel, however, that the data can be safely extrapolated to pressures somewhat in excess of one atmosphere with a fair degree of accuracy.
INTERPRETATION OF PLOTS
We have indicated on Plot 1 the location of some fifty-odd points.2 It will be noted that the points fall in a belt about four units wide measured on the vertical scale. It will, of course, be found that a curve drawn through the uppermost points will include data belonging to water, ammonia, alcohol, and other such liquids of an associating or complex nature. A curve drawn through the lowermost points will include all data belonging to the hydrocarbons and nonassociating liquids. In Plot 2 the writers have drawn three such curves and have indicated by method of plotting to which substances the various points apply. The determination of the heat of vaporization of a substance consists in deciding first of all whether the liquid is likely to be associated. If so, use the upper curve; if not, use the lower curve. Having decided which curve to use, locate on the horizontal margin the value of the ratio P/T (pressure in atmospheres divided by absolute temperature, T). Find by the curve the corresponding value 1
J . Ana. Chem. Soc., 37 (1915), 970.
* Hildebrand, and Landolt-Bdmstein-Meyerhofer “Tabellen,” 1912.
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for Q/T on the vertical scale. Multiplying the latter value by T (the absolute temperature) gives the molal heat of vaporization for the unknown substance. If one is dealing with a given class of compounds, a curve can be drawn for this class which is more definite than if a number of types of compounds are included. Plot 3 shows the data for hydrocarbons, including saturated, unsaturated, and cyclic compounds. It vi11 be noted that no points deTiate more than one unit from the full curve drawn among them, i. e., the error in no rase exceeds 5 per cent. The dotted curve represents the heat of vaporization calculated f r o m the vapor pressure curves of various hydrocarbons by the method of the following article.
