JERRY A. ACClARRl and RICHARD H. GERLACH Continental Oil Co., Ponca City, Okla.
Automatic Computation of Antoine Equation Constants tert-Butyl alcohol is used as an example to show application of procedure
THIS
article describes an automatic computer procedure for obtaining .4ntoine equation constants. using an IBhl Type 650 magnetic drum data-processing machine. T h e program is written in the Bell floating-decimal interpretive system ( 3 ) and allows Taylor's method (1)to be carried out Lvith great facility for any substance for \vhich vapor pressure-temperature data are available. A discussion of the method \vas published in I, E C in 1957 ( 7 ) . Approximately 1 minute of computer time is required to obtain Antoine equation constants giving the best possible fit to a group of experimental vapor pressure points. Card punching requires approximately 10 minutes. and testing and checking can be done in less than 20 minutes. Standard l y p e 533 read-punch unit \\iring is used (.?). This procedure processes a minimum of three and u p to a maximum of 49 experimental vapor pressure-temperature data points. After the best values of the Antoine equation constant3 are determined. equilibrium tt-mperatures are calculated for 50 integral values of vapor pressure. ranging from 2 to 800 mm. of mercury. Taylor's method requires an initial rough estimate for three constantsa,, bo> and L . ~ . From these better estimates (a. h: and c) of these same constants are obtained. The latter may then be used to obtain still better estimates! which are used to calculate the conventional .4ntoine constants of Equation l .
Loglo P
=
.'I- B / ( t
+ C)
(1)
Essentially the same procedure is used herein. with modifications made possible by machine computation. T h e procedure of this article requires a choice of three vapor pressure-temperature data points: one each at a loxv.; intermediate. and high pressure. These are substituted in the following modified form of the Antoine equation: ai
+ b + c log," P - I l0%1,, P
=
0 (2)
irhere a = -4;
b = (AC - B ) ; andc = -C
(3)
This gives three simultaneous equations in a. 6, and c. The computer then calculates approximate values of constants a. b , and c. designated as oo. 6,. and c,. T h e vapor pressureetemperaLure data are then entered into the computer on standard IBhf cards to carry out the calculation for the least squares curve fitting. In principle. these repeated trials are not necessary. as the Taylor equations can be solved explicitly for the desired constants, if a large enough number of significant figures are retained in all the steps of the calculations. In practice it is more efficient to use fewer significant figures and repeated trials. T h e weighting factors of Taylor's method have not been included in the present application, in the sense that a weight of unity is given to each dat2 point. In general. the effect of these Ireighting factors on the results is
Thirty minutes-all the time required for obtaining Antoine equation constants with an automatic computer
small: and in some cases questions can be raised as to the property of the assigned factors. Nomenclature
.I R C
constant in Antoine equation constant in Antoine equation constant in Antoine equation defined by Equation 3 defined by Equation 3 defined by Equation 3 first approximation of a first approximation of b first approximation of c logarithm to the base 10 experimental vapor pressure. mm.
P
= = = = = = = = = = =
1
= experimental temperatures. "C.
a
b c a,
6, co
log
Hg
Available for Sixty Cents Complete table of nomenclature, block diagram for IBM 650 computation of Antoine equation constants, detailed explanation of calculations and sequence, programming chart, and complete card listing for program constants to b e loaded into computer, plus seven tables using tert-butyl alcohol as an example. Address: Editor, I/EC, 1 155 Sixteenth St., N.W., Washington, D. C., sending cash, money order, or check payable to American Chemical Society.
Literature Cited (1) Rose, A r t h u r , Acciarri? J. A , , Johnsun, R . C., Sanders, W. W.? IND.E N G .CHEM. 49, 104 ( 1 9 5 7 ) . (2) Willingham, C. B., Taylor, W. .J., Pignocco, J. M., Rossini, F. D., J . Research .Vat[. B u r . Standards 35, 219 (1945). (3) Wolontis, V. M., 1RM Technical .\ite~[etter, No. 11 (March 1 9 5 6 ) . VOL. 51, NO. 3
MARCH 1959
239
