182
INDUSTRIAL AND ENGINEERING CHEMISTRY
mould have been found nhen using a value of the hypothetic normal boiling point of T , = 186.07' K. instead of 185.31 K. o r a value AT,' = 27.95 0.8976 instead of 27.95i0.55. It m a y be pointed out that the calculated \-alues of p , Trary only slightly over the different ranges although the values C' and AT, vary considerably. This may he due partly to the fact that the tabulated data are not the original values measured by experiment but are calculated from empirical equations n hich closely agree n i t h the expeiimental results. When, therefore, a different Equation 9 is used for calculating the ~ a l u e sC' and AT, from the tabulated data, t h e resulting values may not be found constant over the whole range. However, the variation of one value should be compensated by the variation of the other value in such a v a y that interpolated and extrapolated data can be found by using constant values calculated for a m a l l range or as averages for LL wider range. The pressure a t the limit temperature of 0.85 T, = 258.52' K. = - 14.64" C. follows froin O
log
p2jg.j
p,,,
= 0.01420 =
(258.52 - 18t5.31) + 4.2737258.52 = 1.3717 - 27.99
23.53 kg./sq. cm.
The modified values of ATO' and To' entering into Equation 16 for the straight line between 0.85 T , and T , are found from Equations 17 and 18 to be 39.50' and 189.07' K., respectively. Instead of 0.85, the value of 0.8976, found to be more consistent for calculating the critical pressure, was used. Pressures calculated from Equation 16 follow, together with Plank's values: C. Pressure, kg./sq. Equation 16 Plank Deriation, yo Temp.
31
30
20
73.17 73.34 0.18
58.94
46.44
58.46: 0.82
45.95 1.07
10
0
- 10
35.86 35.54 0.90
37.05 26.99
CIIL
7.5.02
74.96 0.08
0.22
Thus, an error up to about 1 per cent occurs when a straight chart for carbon line is assumed between 0.55 T , and T,. dioxide is given in Figure 7 .
Oxygen Figure 8, a chart for oxygen, illustrates the applicability of the proposed method. Consistent data for oxygen were published by Henning ( 3 ) . They were used for calculating average values C' = 3.5245 and AT, = 5.963" C. from pressures of 25.17 and 629.13 mm. of mercury at 66.69' and 88.42' K., respectively. The pressure at the triple point, T,, = 54.33' K., calculated from these values is I .I1 nim. compared to a true value of 1.2 mm. The critical presure at I', = 154.36' K. is found to be46.4atmospheres compared to the true value of p , = 49.7 atmospheres. The result is satisfactory as far as the triple point is concerned and not inconsistent for the critical point, considering the critical piessure lying far beyond the range for which the values of C" and AT , had been calculated. The discussion of the proposed chart has been limited to characteristic examples which may encourage investigators to compare measured data m-ith values found from the chart and to discuss its practicability more definitely than this first study can do. For similar reasons the modified Trouton's constant has not been considered further. Future investigations may find it to be a true constant which then could be used for calculating the latent heat of vaporization or a consistent value of AT, for vapors for which the latent heat of vaporization is known. The examples indicate that if the values of C' and AT, vary, the increase or decrease of C' is compensated b y a de-
Vol. 34, No. 2
crease and increase of A T,, respectively. Consistent results are thus obtained when using constant values of C' and ATb over a range n-hich differs from the range over which those d u e s had been found. For beat results C' and ATb should be determined from data as near the range of application as possible. Though no precise results can be expected when using an arbitrary value of C' considerably lower or higher than the true value, such variation may sometimes be suitable for comparing different vapors. One system of coordinates using one arbitrary value of C' may thus be utilized for representing pressure-temperature relations for a series of vapors of similar chemical constitution.
Universal Chart Such a chart is given by Figure 9. It goes a step farther b y dealing with vapors of different chemical constitution. The arbitrary value of C' = 4.2 has been assumed. KO consistency may be expected for ammonia which has a true value of C'considerably higher than 4.2. Following a straight line down to the triple point, the change of slope occurs a t a temperature of about 30" C. which is considerably lower than 0.85 To. Although certain limitations are given for using such a universal chart, it is suitable for solving general problems where exact data are missing such as: 1. Flnding the approximate normal boiling point of iin unknown vaDor. 2. Staiing approximate pressure-temperature relations for a vapor the pressure of which is known only at one temperature, 3. Identifying a vapor by its approximate normal boiling point if its pressure has been meas-14'61 ured at onlv one temDerature. 23.40 A verticd line passing through the reference point ... represents the approximate relation for those three . .. cases in which data are known only for one point. If, in case 2, data are given for two points, a line with a fixed slope results and greater precision is attained. It will often be possible to presume the slope in case 3 and to foretell somewhat the probable constitution of the vapor. Interpolating data between twn points. /?. D. Extrapolating data beyond the measured range. For cases 4 and 5 individual charts are preferable and may give some help even for scientific purposes such as precise interpolation over a sniall range or extrapolation beyond the critical point in order to find the partial pressure of vapors dissolved in liquids at temperatures higher t'han the critical temperature.
Literature Cited (1) Bur. of Standards. Circ. 142 (1923). ( 2 ) Cox, E. R., IND. E N G .CHEX, 28, 613 (1936). (3) Henning, F., and Otto, J., PTGC.7th Intern. Congr.. R ~ f r i g . , The Hague-Amsterdam,, 1936,I, No. 3, 174 (1939).
(4) Kay, W. B., IND. ENG.CHEM.,32,358 (1940). (5) Mehl, W., Bull. Intern. Inst. R e f r i g . , 15, 33-4lh (1934). Stand(6) Osborne, N. S., and Myers, C. H., J . Recezrch Natl. BZLT. ards, 13, 1-20 (1934) (Research Paper 691). (7) Plank, R., and Kambeits, J., 2. ge3. Ktilte-lnd., 43,203 (1936). (8) Pl.ank, R., and Kuprianoff, J., 2 . ges. Kd(te-Industrie, 1, l(1929). (9) Riedel, L., Bull. Intern. Inst. R e f T i o . , 20, No. 4, Annex No. 5 , B1-10 (1939). (10) Smith, E. R., J . Research S a t l . B I W .Standards, 24, 229 (1940). (11) Tanner, H. G., Bonning, A. F., and Mathewson, W. F.. IND. ENO.C H E M .31, , 575 (1030).
Citrus Pectates-Correction An errnr has just come to our attention in this article in the March, 1941, issue. On Figure 4, page 291, the original latex should contain 35%, not 25%, rubber. Vir. E. BAIER
