A NOMOGRAPH FOR CORRECTION OF BOILING POINTS R. THOMAS MYERS' Kent State University, Kent, Ohio F O R laboratories which are located at any appreciable elevation above sea level the correction of boiling points because of decreased atmospheric pressure is frequently a bot,hersome chore. As an example, most organic chemistry laboratory manuals are written for lowlanders, and the cuts to be taken during fractionation of a sample at high altitudes are not those given in the laboratory manuals. There are rather complex functions and nomographs available for the correction of boiling points, such as that of Hass and Newton,%hut for most purposes the correction is not needed to an extreme degree of arcuracy. Further, the data for normal boiling points are usually not sufficiently reliable to make highly accurate corrections advisable. A. suitable beginning for the correction is the Clapeyron equation in its differential form, where AH is the heat of vaporization of tlie liquid at its normal boiling point To, and R the gas constant.
dP dT
AHP
=
RTaP
(1)
Pnsented the of Chemioal Education at the 129th Meeting of the Amerioan Chemical Society, April, 1956. HGS, H. B., AND R. F . NEWTON,"Handbook of Chemistry and Physics," 36th ed., Chemical Rubber Publishing Ca., Clewland, 1954, p. 2119.-
If the equation is assumed t,o hold for finite changes, then RT: Ap AT = AHP.
If Trouton's rule hold% then C' = equat,iO1l~ gives
(2) AH/Tb
in the above
When the temperature is expressed in degrees absolute Kelvin and P in mm. of Hg., then C is 0.00012 for normal nonassociated liquids (Trouton's constant 21 cal./ mole/'K.), and 0.0010 for associated liquids (Trouton's constant 25 c a I . / m ~ l e / ~ K . ) .hsociated ~ liquids are those like water, alcohols, and organic acids, which contain groups which are capable of hydrogen bonding. Usually the temperature is expressed in centigrade degrees and the change in pressure in mm. of Hg. At = C(273 f t)(760 - P )
(4)
The range of variables to be chosen depends on the location and needs of the user. For our illustration 17-e have chosen t between 30' and 230°C. and P betmeeu GLASSTONE, s., "Textbook of Physical Chemistry," 2nd ed., D. Van Nostrand Co., Inc., New York, 1946, p. 458. J
JOURNAL OF CHEMICAL EDUCATION
760 mm. and 600 mm. This range of temperatures includes the great majority of compounds which can be distilled without decomposition, and the pressure range includes locations up to one mile, or slightly higher. Using variables betreen these limits a nomograph can be constructed by standard method^.^ The temperature change axis At will have two scales, since there are two values for the constant C . I t is of course not true that equation (4) will hold for such low pressures as Tye have assumed, and so the temperature corrections calculated by equation (1)!dl be incorrect at the lowest pressures. To get around this difficulty we proceed empirically. The actual boiling poiuts of about ten each of associated and normal liquids were compared with the boiling points determined by use of the nomograph. (In a few cases the boiline ~ o i n t were s calculated bv use
' LEHOCZKY, P. N., "Alignment charts, their construction and use," Ohio State Univ., Engr. Expt. Station, Circular No. 34, rev. ed., (1947).
of t'he integrated Clausius-Clapeyron equation, using the actual value for heat of vaporization instead of the value assumed by Trouton's rule.) It is now possible to make a graph of the actual boiling-point corrections against the figures obtained from the nomograph. Now the calibrations on the t scale are erased and the average actual values substituted instead. The result is shown in Figure 1. The use of the nomograph is illustrated by the two examples. The corrections are accurate to abont *0.3" at the lower pressures. A useful variation of the nomograph is possible v-hen it is to be used a t constant pressure. For example, at Golden, Colorado, the pressure is almost always ~vithin 5 mm. of 617 mm. Figure 2 shows the boiling-point. corrections a t 617 mm., obtained from the nomograph. To use the chart one need only connect the normal boiling point (on the two outside vertical lines) to obtain the boiling-point correction for associated and normal liquids on the two vertical lines in the middle of the figure.
-
--200 -210
-
p-cymene a t 6 7 3 m m : 175-5 = 170°C
-190
-180
64.7-4.7 = 60°C
650
-120
--110
-
-100
-
60
Figur. 1.
Nomowaph for Boiling-Point Correction to 760 mm.
VOLUME 34, NO. 2, FEBRUARY, 1957
Cornaction of Boilin. Points at 817 to 760 rnm
