Nomograph for the ClausiusClapeyron Equation CLARENCE L. CRAWFORD', Case School of Applied Science, Cleveland, Ohio
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ECAUSE of the inadequacy of vapor pressure data, various methods have been devised for the interpolation from existg., Cox chart, ing data plotted on straight-line graphs-. Duhring rule, and the plot of log P us. 1 / T , where T is the absolute temperature a t which a substance has the vapor pressure, P. On the latter plot, according to the equation, In P = -L/RT
+C
the slope of the line is proportional to L, the latent heat of vaporization. Therefore, the latent heat can be calculated from the measured slope or the slope can be calculated from the experimental latent heat. The line is determined by two points or one point and the slope, all of which require some calculation from experimental data. Figure 1 is a modification eliminating the calculation of the points and/or the slope, the points being plotted directly in mm. and C., and the molar latent heat being plotted on or read from its line. The two points establishing the line may be the vapor g., the boiling point-and the pressure at one temperature-. molar latent heat of vaporization, or as before, the vapor pressures at two temperatures. The range of the chart may be extended by multiplyin all pressures by a constant (including conversion t o other units7 since P enters the equation as a ratio. The accuracy of the chart is limited by the accuracy of the Clausius-Clapeyron equation : 1 Present address, Gulf Research and Development Company, Pittsburgh. Penna.
Error-producing assumptions made in the derivation of the equation are: (1) The latent heat of vaporization of any substance i s constant; (2) the volume of the liquid is negligible in comparison with that of the vapor obtained therefrom; and (3) the perfect gas law (PV = nRT) holds. The error produced may be considerable, for the latent heat is liable t o wide variation; near t h e critical point assumption 2 is not valid; and the simple gas law is subject to great deviation. Data not obeying the equation will, naturally, not fit the chart. Plotting of experimental data on t h e chart indicates general applicability with certain exceptions, notably acetic acid, whose latent heat of vaporization is actually about half t h a t given by the equation from vapor pressure data. Thus the chart should be used judiciously. Using acetone as an example, under a vapor pressure of 184.8 mm. of mercury at 20" C. and of 860.6 mm. a t 60" C., By equation: L, = 7490 cal./gram-mole L, = 7500 cal./gram-mole By chart: By experimental data: L, = 7220 cal./gram-mole
Acknowledgment The author appreciates the help of 0. E. Brown, Case School of Applied Science, in the preparation of this chart. All data used were taken from Lange's Handbook of Chemistry.
4 5000
6000 7000 8000
FOR THE CLAUSIUS-CLAPEYRON EQUATION FIGURE 1. NOMOGRAPH Locate PI at TIand PS at TZin the net, and latent heat of vaporization on the L, scale. 1280
