8
CORRECTION OF BOILING POINTS FOR VARIATION I N BAROMETRIC PRESSURE REIN0 W. HAKALA S y r a c u s e University, Syracuse,
CRA~TS'S rule,' which can be written Ts = T [ 1 + C(760 - p-.)I
(1)
is much used in the organic chemistry laboratory to correct boiling points to one atmosphere. Crafts's constant, C = RTb/760AH,,. = (dt/dp,,.)b/Tb, has the value 0.00012 for substances that obey Trouton's rule. Crafts's rule was deduced from that of Ramsay and Young, and can also be derived, as is well known, from the Clapeyron-Clausius equation and Trouton's rule (in an approximate manner). The formula
New York
the two equations are combined to eliminate log PC,the analogous expression log ( P ~ / P )= (fTr/Tb)(Tb/T- 1)
(4)
results. It is readily rearranged to Tb = 2'11
+ (Tb/fT.) log (ps/p)l
(5)
which is equation 2 in another form. Equation (2) can be derived in other ways from equation 3 , hut the above derivation is briefest. By noting the relationship between equation (3) and the integrated form of the Clapeyron-Clausius equation, Ts = T ( l - n log pat,.) = T [ 1 + n(2.8808 - log p,,.)] ( 2 ) it is seen that fT,/T, = AHv,./2.303RTb. (This expression appears in some textbooks; e. g., S. Glasstone, where n = "Textbook of Physical Chemistry," D. Van Nostrand ( T . - Ts)/T. log pa,,. = 2.303RTs/AH,,. = 1750C Co., New York, 1946, p. 457.) The other expression, is more accurate than Crafts's rule. Comparison of jT,/Tb = [T,/(T, - T b ) ]log p,,., is readily derived equations 1 and 2 shows that Crafts's rule is an approxi- from the van der Waals vapor pressure equation. Note that equation 2 is equivalent to that of Wrede, mation of this formula. I t will be derived below,= as will another useful formula. The constant n has the logp = A - B / T (6) value 0.21 for substances that obey Trouton's rule. which is generally quite accurate for organic' liquids, Values of n for water and various common types of and even solids, over a pressure range of several hundred organic compounds are given in the table." When van der Waals's vapor pressure equation millimeters.6 (Because of this equivalence, values of n in the accompanying table can be used, if desired, to 10s( P ~ P =) f(T=/T - 1) ( 3 ) determine the vapor pressure-temperature behavior of (wheref is theoretically a universal constant but varies pure organic substances over a fair range of pressure with the nature of the substance and even somewhat centering around one atmosphere; A = l / n if p is l / n if p is in mm. of with temperature) is set up for a given substance a t its measured in atm. 01 = 2.8808 normal boiling point and one other temperature, and mercury, and B = T p / nin either case.) There is an especial paucity of adequate data in the ' C u m , J. M., Bw., 20, 709 (1887); Compt. rend., 157, 1403 literature on even common compounds of the following (1913). types: aldehydes, acyl halides and anhydrides, alkyl 2 It is related in form to several other equations, all of which we somewhat more complex. The closest relative is that of C. S. fluorides (data for the other alkyl halides are freC~GOE I.,C. T., 3 , 246 (1928). Another near relative is T o = quently inconsistent, particularly in the case of the T ( l - m In pa*.)'/*, where m = 3To/ln AH,., which wsa deduced by 0. PILUNG,PhySik. Z., 10, 162 (1909), from known bromides), lactones, amines and sulfur compounds relationships, assuming in addition a continuous change of (the available data in these classes are few and highly inconsistent), arnides, silicon compounds, compounds density between liquid and vapor. Though there are tables of Crafts's constant in the literature, containing the CF, group, terpenes, heterocycles, and they were assembled using older data than were used in compiling aromatics other than hydrocarbons, as well as phosthis table. It is s. great pleasure to acknowledge the invaluable assistance of J. TIMMERMANS, "Physico-chemical Constants of phorus compounds. It is amarent from the a c c o m ~ that Pure Orzanic Comoounds." Elsevier Puhl. Co.. New York. 1950. . ~ a"u v-i ntable which was used as' a son& of data as mueh'as poesible.' he l / n M , which is proportional to the entropy of vaporiaageneral agreement between the various methods of calculation tion per gram a t the boiling point, is, as a rule, related
+
and between the valuelues for adjacent members of homologous series was such that it is unwarranted to given to more than two aignihant figures. In calculating n, less reliance was placed on ( T o - To)/T, log p, .tm. than on 2.303RTa/AH,, and 1750(dt/ dp,, )a/Ta, because of the generally lesser reliability of critical data.-The author wishes that a work similar to Timermans' w-ould Boon become available for inorganic compounds. This would be a profitable area for international cooperation which is so sorely needed nowadays.
'This equation is, of course, also applicable to volatile inorganic materials; e. g., it holds so well for NI (and CH,) all the way from its triple point to ita critical point and for 01over an even wider range that a four-constant equation fits the data only slightly better P do no^, B. F., nNn H. N. Dnms,J. Am. C h a . Soc. 49, 610 (1927)). E. g., see GERMANN, F. E. E.,AND 0.S. KNIGAT,Znd. Eng. Chem., 26,467 (1934).
