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IV

Volume - Relation to Pressure

The preceding papers in this series have developed the general characteristics of the liquid state from new fundamental theory and have shown that on this new theoretical basis the volume of a liquid molecule consists of three separate components which respond to changes in temperature in the foil owing manner: the initial component remains constant, the second component varies in direct proportion to the effective temperature, and the third component is generated isothermally at the critical temperature. Because of the distribution of molecular velocities in the liquid aggregate the number of molecules which are individually at or above the critical temperature is a matter of probability and the third volume component of a liquid aggregate therefore followers a probability function which represents the proportion of critical molecules in the total.

This paper will extend the volume relationships to liquids under pressure and will show that in its general aspects the response to variations in pressure is identical with the response to variations in temperature; that is, the initial component remains constant, the second component varies in direct proportion to the reciprocal of the effective pressure, and the third volume component of the aggregate follows a probability function for the same reasons as in the case of temperature variations. Equation (3), the volume-temperature relation previously developed, can therefore be extended to apply to liquids under pressure.

In calculating the volume of a liquid at temperature T and pressure P, we first determine the three volume components at temperature T and saturation pressure in the manner described in paper II. We will call these components VI, VII, and VIII. The initial component, VI, is not affected by either temperature or pressure. The second component, VII, responds to an increase in effective pressure in the same manner as to a decrease in effective temperature. It should be noted, however, that this effective pressure includes the pressure equivalent of the cohesive force between the liquid molecules and an evaluation of this initial pressure, as we will call it, is the first step toward a determination of the second volume component at pressure P.

The unit of pressure corresponding to the 510.2 degree temperature unit is 415.84 atm. or 429.8 kg/cm2, where the initial specific volume, V0, is 1.00. In order to avoid an extended theoretical discussion at this point we will consider this as an empirically determined value for the present, as was done with the temperature unit. For any value of V0 other than unity the pressure unit becomes 415.84./V02/3 atm. This is the pressure exerted against each independent liquid unit within the liquid molecule. The external pressure is exerted against the molecule as a whole rather than against the individual units and where there arc nv units in the liquid molecule, the pressure exerted against each unit is P/nv. For purposes of calculation, however, it will be more convenient to use the external pressure as the reference value and on this basis the external pressure is P and the initial pressure is

P0 = 415.84 nv /V02/3 atm.

(7)


Since the application of pressure is not exactly equivalent to a decrease in thermal energy it is quite possible that the nature of the atomic association that participates in the pressure process may differ from that which participates in the temperature process. The values of nv applicable to equation (7) are therefore not necessarily identical with those, which were arrived at in paper III in connection with the evaluation of V0. Such equality is quite common but there is a tendency to split up into a larger number of units in the pressure process, particularly in the case of the smaller molecules. In the limiting condition each atom is acting independently.

It should also be remembered that the previous determination of nv was concerned only with a ratio: the number of volumetric units corresponding to the mass represented by the formula molecule. The initial pressure calculation, on the other hand, requires a knowledge of the absolute number of individual liquid units in the actual molecule and where the liquid molecule comprises two or more formula molecules the value of nv applicable to equation (7) is the corresponding multiple of the value previously found. The value of nv used in calculating the Cs2 volumes in Table II-3, for instance, is 3, where we now find that the value that must be used in equation (7) is 9. This does not conflict with the previous determination; it merely means that the true liquid molecule is (CS2)3.

Another factor, which enters into the calculation of VII, is that above 510.2 K part of the VII component is subject to only one-sixteenth of the total initial pressure. A complete theoretical explanation of this situation which exists beyond the unit temperature level is not available as yet, but it has been found that the proportion of high temperature volume at any temperature of observation can be computed from the normal probability function using 510.2 K as the base and one-fourth of this value as the probability unit. Up to 2/3 of 510.2 the lower initial pressure is applicable to the full amount thus calculated, beyond 8/9 of 510.2 it is applicable to half of the calculated value, and in between these points the effective proportion decreases linearly.

Turning now to the third component, VIII, we first obtain from our previous calculations the figure representing the number of probability units between temperature T and the critical temperature. Since this quantity will play an important part in the volume determinations it will be desirable to give it a name for convenient reference and we will therefore call it the probability index. To this probability index at saturation pressure we now add the increment corresponding, to the applied pressure, taking the previously established value 415.84 atm. as the probability unit. If the index is above 1.15 at saturation pressure we can proceed directly to a determination of VIII, first obtaining from the probability tables the probability value corresponding to the probability index at each individual pressure and then multiplying each of these probabilities by V3, the third dimensioned value of V0, to obtain VIII.

If the probability index is below 1.15 at saturation pressure the B component of the probability expression (fA + fB) has an appreciable magnitude and this introduces an additional operation into the calculations. The nature of this B component was not indicated very clearly by the way in which it enters into the computation of the saturation volume but its behavior under pressure is more enlightening. We have previously found that the A probability represents the proportion of the total number of molecules which have individually reached the critical temperature and consequently have acquired a volume component in the third dimension. These molecules are still subject to the cohesive forces of the liquid; that is, to the liquid initial pressure. Now we find that as the average temperature of the aggregate approaches closer to the critical temperature and more thermal energy is available some of the molecules escape from the cohesive forces, doubling their volume in the process. The B component of the probability represents the proportion of molecules in this condition and the expression fB V3 is the volume added by this process at saturation pressure. The total volume of these B molecules at saturation is then twice this amount, or 0B V3, and the A portion of the VIII volume, the part still subject to the initial pressure, is (fA + fB) V3. Dividing (fA + fB) by fA gives us the percentage reduction in the A volume due to molecules shifting to the B status.

We now calculate the total A volume at each pressure by means of the expression f V3 and apply the foregoing reduction factor to arrive at the portion of the volume still remaining in the A condition. The B volume is subject only to the externally applied pressure and it varies in inverse proportion to that pressure. The effective volume at each pressure P is therefore obtained by application of the factor PS/P to fB V3, the B volume at saturation pressure PS.

As can be seen from this description, the whole operation of calculating the liquid volumes under pressure is carried out entirely on the basis of values previously determined in the course of computing the volumes at saturation pressure, with the exception of those cases where nv must be redetermined, either because of an actual difference in the internal behavior of the molecule or because the liquid molecule is composed of more than one formula molecule. There are no "adjustable constants" which can be manipulated to fit the observed values; the volumes under pressure must conform to a fixed pattern in each case, or if there is any element of uncertainty present, must conform to some one of two or three possible alternate patterns. These are very stringent requirements and the degree of correlation between the calculated and observed volumes as shown by the tabulations, which follow, is therefore highly significant as an indication of the validity of the new theoretical principles on which the work is based.

To illustrate the method of calculation let us consider heptane at 30 C. By the methods of paper III we determine that nv for heptane is 9 and the three values of the geometric factor are .9878, .9636, and 1.000. From these figures we obtain V1 = .9346, V2 = .9117, and V3 = .9461. Entering equation (3) with these three values we then calculate the volume components at 30 C and saturation pressure, obtaining VI = .9346, VII = .5417, and VIII = .0038. From our probability tables we find that at 30 C the volume originating above 510.2 K is 5.3 percent of the total VII component, and on this basis we separate VII into two parts: VII(L) = .5130 and VII(H) = .0287. Applying the previously determined values nv = 9 and V0 = .9461 to equation (7) we find that the initial pressure, P0, effective against VII (L) is 3884 atm. The initial pressure effective against VII(H) is then 1/16 x 3884 = 243 atm. To find the VII components at each pressure we now reduce the saturation values of VII(L) and VII(H) by the effective pressure ratios. Pn/(P + P0) and P0/(16P + P0) respectively. The results are shown in columns 2 and 3 of Table IV-1.

Next we evaluate the probability index at 30 C and saturation pressure by the methods of paper II, obtaining the value 2.68. To this we add the increment corresponding to each pressure, which we obtain by dividing the increase in pressure above the saturation level by 415.84 atm. The composite probability indexes thus derived are shown in column 4 of the table. Column 5 gives the values of f corresponding to each index. Multiplying each of these values of f by .9461 we arrive at the VIII component for each pressure as shown in column 6. Column 7 then indicates the total theoretical volume of the liquid aggregate, the sum of VI (constant at .9346), VII(L) from column 2, VII(H) from column 3, and VIII from column 6. Column 8 shows the corresponding measured volumes for comparison.

In order to carry the comparisons into the pressure range above 351 atm., the highest pressure reached in the set of measurements listed in Table IV-1, we now turn to the work of Bridgman who gives us a set of values at 50 C, with the first observation at 1000 kg/cm2 (approximately 1000 atm.) and increasing by steps of 1000 kg/cm2 to a maximum of 10,000 kg/cm2. Bridgman's results are reported as relative volumes based on the volume at 0 C and atmospheric pressure as the reference level. Our first requirement, therefore, is to compute from equation (3) the volume under these reference conditions, which we find to be 1.424 cm3/g. m is value can then be used as a conversion factor to reduce the calculated volume components at 50 C and saturation pressure to Bridgman's relative basis. By this means we arrive at the following volumes: VI = .656, VII(L) = .377, and VII(H) = .029. VIII is negligible in the pressure range of this work and can be disregarded. The volumes under pressure are then calculated in the manner described in the preceding paragraphs. Table IV-2 compares the results with Bridgman's values.

Table IV-3 summarizes the results of a number of similar calculations in the relatively low-pressure field. Since all of these calculations follow the regular pattern without exception, intermediate data such as the probability indexes have been omitted and the table shows only the separate volume components and the tot al calculated and measured volumes. The objective of the comparisons in this table is to show that there is a wide range of temperatures and substances in which the calculated and measured volumes agree within 0.5 percent at all experimental pressures. In some of the other sets of measurements, which have been examined during this investigation, the agreement is less satisfactory in certain portions of the pressure range but the general trend of the values follow the theoretical pattern in all cases.

The preceding papers have stressed the fact that the temperature term in equation (3) refers to the effective temperature: a quantity which is commonly identical with the measured temperature, but not necessarily so. The same is true of the pressure factors with which we are dealing in this paper. We have already seen that the pressure effective against the VII volume component is substantially reduced beyond the unit temperature level (510.2 K). In some substances, chiefly outside the organic division, the pressure applicable to the VIII component is also subject to a reduction from P to P/np and two examples of this kind are included in Table IV-3: H2S (np = 2) and NH3 (np = 3).

Table IV-4 presents some further comparisons with Bridgman's measurements in the range up to 12,000 kg/cm2. Some of his more recent work has extended to considerably higher pressures' reaching a level of 50,000 kg/cm2 in a few instances. At these extreme pressures the transition to the solid state is well under way and the volumes of the liquid aggregates are modified quite substantially by the presence of solid molecules. Consideration of the volume situation in this pressure range will therefore be deferred to the next paper in this series, which will examine the characteristics of the liquid-solid transition. Some of the results at 12,000 kg/ cm2 and below are also subject to this solid state effect and in these cases the tabular comparisons have not been carried beyond the point where the volume decrease due to solid molecules amounts to more than about .002. Double asterisks in the column of observed volumes indicate omissions due to this cause.

As mentioned in a previous paper, the scope of this investigation has been so broad that it has been physically impossible to study the "fine structure" of all of the relationships that have been covered, and it is quite possible that there may be factors of this kind which would alter the results slightly. Some additional uncertainty has been introduced by the use of the measured values of the vapor pressure at saturation. Since these uncertainties probably amount to something in the neighborhood of 0.1 percent there is no particular advantage in carrying the calculations to any higher degree of accuracy and it does not appear that such refinements as additional decimal places, fractional values of the probability indexes, etc., are justified at this stage of the project.

TABLE IV - 1
LIQUID COMPRESSION - HEPTANE - 30 C
P0 = 3884 atm. V1 = .9346 V2 = .9117 V3 = .9461 cm3/g
P(atm.) VII(L) VII(H) P.I. f VIII(A) VIII(B) V(calc) V(obs)13
0 .5130 .0287 2.68 .004 .0038   1.480 1.480
7.12 .5121 .0279 2.70 .003 .0028   1.477 1.479
19.08 .5105 .0266 2.73 .003 .0028   1.475 1.476
31.04 .5089 .0254 2.75 .003 .0028   1.475 1.472
43.00 .5074 .0244 2.78 .003 .0028   1.469 1.470
52.31 .5062 .0236 2.81 .002 .0019   1.466 1.467
82.20 .5024 .0214 2.88 .002 .0019   1.460 1.761
112.10 .4986 .0196 2.95 .002 .0019   1.155 1.455
171.09 .4913 .0168 3.09 .001 .0009   1.444 1.444
231.68 .4841 .0147 3.24 - -   1.433 1.433
291.46 .4772 .0130         1.425 1.423
351.25 .4705 .0117         1.417 1.413

TABLE IV - 2
LIQUID COMPRESSION - HEPTANE -50 C
P0 = 4013 kg/cm3 V1 = .656 V2 = .406 (relative)
P VII(L) VII(H) V(calc) V(obs)14 P VII(L) VII(H) V(calc) V(obs)
1000 .302 .006 .964 .958 6000 .151 .001 .808 .815
2000 .252 .003 .911 .908 7000 .137 .001 .794 .800
3000 .261 .002 .874 .875 8000 .126 .001 .783 .7875
4000 .189 .002 .847 .851 9000 .116 .001 .773 .776
5000 .168 .001 .825 .831 10000 .108 .001 .765 .766

TABLE IV - 3
LIQUID COMPRESSION (LOW PRESSURES)
Basic Factors
  V1 V2 V3 Units P0
Propane .8253 .8253 .8436 cu.ft./lb. mole 48860 psi
Butane .017103 .017103 .017419 cu.ft./lb. 52014 psi
Pentane .016116 .016116 .016371 cu.ft,/lb. 54218 psi
Hexane 1.3314 1.3131 1.3498 cu.ft./lb. mole 55839 psi
  83.11 81.97 84.26 cm3/g mole 3800 atm.
Heptane 1.5002 1.4635 1.5187 cu.ft./lb. mole 57077 psi
  .9346 .9117 .9461 cm3/g 3884 atm.
Octane .9120 .8819 .9221 cm3/g 4389 atm.
Nonane 1.8378 1.7640 1.8558 cu.ft./lb. mole 71940 psi
2-Methyl propane .017416 .017416 .018867 cu.ft./lb. 46239 psi
3-Methyl pentane .9512 .9512 .9778 cm3/g 3800 atm.
2,2-Dimethyl butane .9712 .9712 .9778 cm3/g 4222 atm.
2,3-Dimethyl butane .9578 .9512 .9778 cm3/g 3800 atm.
2,2,4-Trimethyl pentane .9221 .9019 .9221 cm3/g 4389 atm.
Propene .018045 .018045 .018045 cu.ft./lb. 50805 psi
1-Butene .9278 .9278 1.0123 cu.ft./lb. mole 71798 psi
1-Pentene .9762 .9762 1.0513 cm3/g 5916 atm.
Benzene .011547 .011547 .012962 cu.ft./lb. 84456 psi
Ammonia .9642 1.0655 1.0823 cm3/g 6312 atm.
Hydrogen Sulfide .4033 .4033 .4217 cu.ft./lb. mole 87102 psi

 

In the second section of this table, which follows, the values of the individual volume components are given in the following units: cm3/g x 104, cu.ft./lb. x 106, cm3/g mole x 102, cu.ft./lb. mole x 104. Total volumes are exnpessed in the units listed above.

Specific Volumes

Propane 100 F (15)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
1000 4660 235 1220 9 1.438 1. 441
2000 4568 186 921 5 1.393 1.394
3000 4479 155 697 3 1.359 1.358
4000 4394 132 514 2 1.330 1.329
5000 1312 115 365 2 1.305 1.307
6000 4234 102 257 2 1.285 1.287
7000 4157 92 174 1 1.268 1.269
8000 4084 83 116 1 1.254 1.254
9000 4013 76 75 1 1.242 1.240
10000 3945 71 50 1 1.232 1.227

Propane 190 F (15)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
1000 5150 556 1172 2302 1.751 1.768
2000 5048 434 991 1191 1.592 1.606
3000 4949 355 819 794 1.517 1.525
4000 4855 301 667 595 1.467 1.471
5000 4764 261 526 476 1.428 1.431
6000 4676 230 411 397 1.397 1.396
7000 4592 206 341 340 1.371 1.371
8000 4510 187 230 298 1.348 1.348
9000 4431 170 169 265 1.329 1.327
10000 4355 157 118 238 1.312 1.308

Butane 100 F (16)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
1000 9641 477 784   .02801 .02808
2000 9163 385 540   .02749 .02755
3000 9290 323 383   .02710 .02714
4000 9124 278 244   .02675 .02679
5000 8964 244 157   .02647 .02649
6000 8810 218 105   .02624 .02621
7000 8660 196 70   .02603 .02597
8000 8516 179 35   .02583 .02575
9000 8376 164 17   .02566 .02553
10000 8241 152 0   .02550 .02534

Butane 280 F (16)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
1000 11591 1762 2519 3873 .03685 .03719
2000 11375 1396 2112 1937 .03392 .03414
3000 11167 1156 1739 1291 .03246 .03252
4000 10966 987 1399 968 .03142 .03146
5000 10772 860 1113 775 .03062 .03066
6000 10585 763 860 646 .02996 .03000
7000 10401 685 660 554 .02941 .02943
8000 10229 622 480 484 .02892 .02895
9000 10061 569 353 430 .02852 .02854
10000 9897 525 247 387 .02816 .02815

Heptane 200 C (13)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
52.6 6749 1389 1754 40 1.928 1.926
112.4 6648 1148 1403 19 1.856 1.846
172.1 6550 979 1125 12 1.801 1.793
231.9 6454 853 882 9 1.754 1.751
291.7 6362 756 675 7 1.715 1.718
351.5 6272 678 513 6 1.682 1.690

0ctane 100 C (27)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
50 5606 660 111   1.550 1.547
100 5544 571 83   1.532 1.530
150 5483 504 55   1.516 1.514
200 5423 451 46   1.504 1.501
250 5364 408 28   1.492 1.489
300 5307 372 18   1.482 1.477

0ctane 125 C (27)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
50 5855 818 221   1.601 1.602
100 5789 708 166   1.578 1.580
150 5726 624 129   1.560 1.560
200 5663 558 92   1.543 1.544
250 5602 505 65   1.529 1.529
300 5542 461 46   1.517 1.516

0ctane 150 C (27)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
50 6100 977 406   1.660 1.662
100 6032 846 314   1.631 1.634
150 5966 745 240   1.607 1.610
200 5901 666 175   1.586 1.589
250 5837 603 129   1.569 1.571
300 5775 550 92   1.554 1.554

Pendane 100 F (17)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
1000 9086 449 262   .02591 .02598
2000 8924 366 180   .02559 .02564
3000 8768 308 115   .02531 .02534
4000 8618 267 65   .02507 .02505
5000 8472 235 49   .02487 .02481
6000 8331 210 33   .02468 .02460
7000 8195 189 16   .02452 .02442
8000 8064 173 0   .02435 .02424
9000 7936 159     .02421 .02407
10000 7812 147     .02408 .02394

Pentane 340 F (17)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
1000 11605 1910 3058 1735 .03442 .03480
2000 11398 1532 2520 867 .03243 .03256
3000 11197 1280 2057 578 .03123 .03120
4000 11004 1098 1631 434 .03028 .03026
5000 10817 962 1279 147 .02952 .02950
6000 10636 856 964 289 .02886 .02886
7000 10462 771 723 248 .02832 .02831
8000 10293 701 519 217 .02785 .02786
9000 10129 643 371 193 .02745 .02750
10000 9971 594 259 174 .02711 .02721

Hexane 160 F (18)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
1000 7862 657 243   2.210 2.219
2000 7746 537 162   2.176 2.187
3000 7614 454 112   2.149 2.159
4000 7487 393 70   2.126 2.133
5000 7364 347 42   2.107 2.110
6000 7245 310 28   2.090 2.089
7000 7129 281 14   2.074 2.071
8000 7018 256 0   2.059 2.054
9000 6909 236     2.046 2.039
10000 6804 218     2.034 2.025

Octane 175 C (27)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
50 6415 1078 719   1.733 1.732
100 6344 933 572   1.697 1.697
150 6274 822 443   1.666 1.664
200 6205 735 350   1.641 1.638
250 6139 664 258   1.618 1.616
300 6073 606 203   1.600 1.596

Octane 200 C (27)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
50 6533 1356 1145 2 1.816 1.808
100 6460 1172 934 1 1.769 1.760
150 6389 1033 751 1 1.729 1.721
200 6319 922 605 0 1.697 1.689
250 6251 834 476   1.668 1.663
300 6184 760 366   1.643 1.640

3-Methyl Pentane 150 C (28)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
49.0 6584 1058 1420 7 1.858 1.847
101.5 6496 891 1169 3 1.807 1.794
154.1 6409 769 937 2 1.763 1.755
206.7 6325 676 734 2 1.725 1.723
259.4 6243 603 589 1 1.695 1.696
311.8 6163 545 444 1 1.667 1.673

2,2-Dimettyl Butane 100 C (29)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
50 6182 731 655   1.728 1.730
100 6111 630 518   1.697 1.696
150 6041 553 401   1.671 1.670
200 5972 493 303   1.648 1.667
250 5906 445 235   1.630 1.627
300 5840 405 176   1.613 1.606

2,3-Dimethyl Butane 100 C (30)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
48.9 6040 706 508   1.683 1.686
101.5 5959 596 381   1.651 1.658
154.1 5879 515 293   1.627 1.635
206.7 5802 454 215   1.605 1.613
252.4 5737 411 166   1.589 1.595
311.8 5654 366 117   1.572 1.570

Hexane 400 F (18)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
1000 9707 2037 2584 1073 2.072 2.886
2000 9539 1646 2136 537 2.717 2.705
3000 9376 1381 1728 358 2.616 2.596
4000 9219 1189 1361 268 2.535 2.519
5000 9066 1045 1052 215 2.469 2.458
6000 8919 931 807 179 2.415 2.408
7000 8776 840 567 153 2.367 2.368
8000 8630 765 432 134 2.328 2.333
9000 8505 702 310 119 2.295 2.301
10000 8375 649 212 107 2.266 2.272

Heptane 40 F (19)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
1000 7558 212 15   2.278 2.284
2000 7430 174 0   2.261 2.266
3000 7306 147     2.246 2.250
4000 7186 128     2.232 2.234
5000 7071 113     2.219 2.220
6000 6959 101     2.206 2.207
7000 6850 91     2.194 2.195
8000 6745 84     2.183 2.184
9000 6643 77     2.172 2.172
10000 6544 71     2.162 2.160

Heptane 100 F (19)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
1000 8256 412 46   2.372 2.373
2000 8116 338 30   2.349 2.352
3000 7981 286 15   2.328 2.333
4000 7850 248 0   2.310 2.315
5000 7724 219     2.295 2.298
6000 7601 197     2.280 2.282
7000 7483 178     2.266 2.267
8000 7368 163     2.253 2.252
9000 7256 150     2.241 2.236
10000 7148 139     2.229 2.222

Nonane 220 F (20)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
1000 11281 1325 130   3.111 3.12
2000 11128 1321 23   3.072 3.08
3000 10960 972 56   3.039 3.04
4000 10835 857 37   3.011 3.01
5000 10694 767 19   2.986 2.980
6000 10557 694 0   2.963 2.956
7000 10423 633     2.943 2.935
8000 10293 583     2.925 2.916
9000 10166 540     2.908 2.895
10000 10042 502     2.892 2.872

2,3-Dimethyl Butane 125 C (30)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
48.9 6316 878 880   1.765 1.763
101.5 6231 740 704   1.725 1.726
154.1 6148 639 548   1.691 1.696
206.7 6067 563 430   1.664 1.666
259.4 5988 503 323   1.639 1.645
311.8 5912 454 235   1.618 1.623

2,2,4-Trimethyl Pentane 100 C (31)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
50 5739 678 184   1.582 1.582
100 5675 587 138   1.562 1.563
150 5612 518 101   1.545 1.545
200 5551 463 74   1.531 1.530
250 5491 419 55   1.519 1.515
300 5433 382 37   1.507 1.502

2,2,4-Trimethy1 Pentane 125 C (31)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
50 5993 839 360   1.641 1.639
100 5926 726 277   1.615 1.614
150 5860 640 212   1.593 1.593
200 5797 572 157   1.575 1.573
250 5734 518 120   1.559 1.556
300 5673 472 83   1.545 1.541

1-Pentene 80 C (32)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
49.0 6000 632 673   1.707 1.717
101.5 5948 561 536   1.681 1.687
154.1 5896 504 399   1.656 1.662
206.7 5846 458 305   1.637 1.640
259.4 5796 419 231   1.621 1.621
311.8 5747 387 168   1.606 1.605

1-Pentene 100 C (32)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
49.0 6237 776 1093   1.787 1.789
101.5 6182 689 862   1.750 1.749
154.1 6129 619 694   1.720 1.716
206.7 6076 562 536   1.694 1.689
259.4 6024 514 399   1.670 1.666
311.8 5973 474 305   1.651 1.647

Nonane 400 F (20)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
1000 13033 2726 1559   3.570 3.56
2000 12857 2303 1151   3.469 3.46
3000 12685 1993 835   3.389 3.38
4000 12518 1757 575   3.323 3.32
5000 12355 1571 390   3.269 3.27
6000 12196 1421 260   3.226 3.22
7000 12042 1297 167   3.188 3.18
8000 11891 1193 111   3.157 3.15
9000 11744 1104 74   3.130 3.12
10000 11601 1027 37   3.104 3.09

2-Methyl Propane 160 F (21)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
500 10562 997 3003 24 .03200 .03215
1000 10449 866 2648 12 .03139 .03139
1500 10340 763 2331 8 .03086 .03079
2000 10232 683 1996 6 .03033 .03027
2500 10127 617 1734 5 .02990 .02986
3000 10024 563 1511 4 .02952 .02944

Propene 70 F (22)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
1000 9778 369 2133 5 .03033 .03026
2000 9592 296 1613 3 .02955 .02943
3000 9413 247 1183 2 .02889 .02883
4000 9241 212 842 1 .02834 .02832
5000 9075 185 609 1 .02792 .02790
6000 8915 165 412 1 .02754 .02755
7000 8760 148 269 1 .02722 .02725
8000 8611 135 179 1 .02697 .02696
9000 8467 124 108 1 .02675 .02670
10000 8327 114 72 1 .02656 .02645

Ammonia 30 C (33)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
100 5911 273 747   1.657 1.658
200 5820 227 639   1.633 1.637
300 5732 193 552   1.612 1.608
400 5646 169 465   1.592 1.593
500 5563 150 390   1.575 1.577
600 5482 134 325   1.558 1.558
700 5404 122 271   1.544 1.543
800 5328 112 227   3.531 1.530
900 5254 103 184   1.518 1.519
1000 5182 96 152   1.507 1.511
1100 5112 89 119   1.496 1.503

Ammonia 110 C (33)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
100 6935 978 2198 2679 2.243 2.235
200 6827 790 2017 1340 2.062 2.080
300 6722 663 1848 893 1.977 1.903
400 6621 571 1680 670 1.918 1.918
500 6523 501 1523 536 1.873 1.868
600 6427 447 1373 447 1.834 1.830
700 6335 403 1228 383 1.799 1.793
800 6245 367 1096 335 1.769 1.763
900 6157 337 975 298 1.741 1.733
1000 6072 311 855 268 1.715 1.710
1100 5989 289 753 244 1.692 1.688

Hydrogen Sulfide 40 F (25)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
1000 2099 65 304  . 650 .652
2000 2075 56 261   .643 .643
3000 2052 49 224   .636 .635
4000 2030 44 190   .630 .627
5000 2008 40 156   .624 .621
6000 1986 36 131   .619 .614
7000 1965 33 110   .614 .6085
8000 1944 31 89   .610 .604
9000 1924 29 72   .606 .600
10000 1904 27 59   .602 .598

1-Butene 160 F (23)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
1000 5601 500 1237 3 1.662 1.676
2000 5525 421 935 1 1.616 1.625
3000 5451 364 684 1 1.578 1.585
4000 5379 320 503 1 1.548 1.555
5000 5309 286 342 1 1.522 1.530
6000 5240 258 241 0 1.502 1.509
7000 5174 235 161   1.485 1.490
8000 5109 216 101   1.470 1.473
9000 5046 200 70   1.459 1.458
10000 4984 186 40   1.449 1.444

1-Butene 220 F (23)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
1000 5956 734 2102 246 1.832 1.852
2000 5875 615 1682 123 1.757 1.759
3000 5796 530 1321 82 1.701 1.695
4000 5719 465 1021 62 1.655 1.650
5000 5644 415 764 49 1,615 1.616
6000 5571 374 566 41 1.583 1.589
7000 5500 341 403 35 1.556 1.565
8000 5431 313 283 31 1.534 1.542
9000 5364 289 197 27 1.516 1.522
10000 5298 269 129 25 1.500 1.504

Benzene 100 F (24)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
1000 6550 350 26   .01847 .01849
2000 6475 302 13   .01835 .01836
3000 6401 265 0   .01821 .01823
4000 6328 237     .01811 .01810
5000 6258 214     .01802 .01799
6000 6188 195     .01793 .01790
7000 6121 179     .01785 .01783
8000 6054 165     .01777 .01776
9000 5990 154     .01769 .01767
10000 5926 144     .01762 .01758

Benzene 220 F (24)
P VII VIII Total V
  (L) (H) (A) (B) calc. obs.
1000 7400 895 181   .02002 .02003
2000 7314 772 117   .01975 .01981
3000 7231 678 78   .01953 .01961
4000 7149 605 39   .01934 .01942
5000 7069 546 26   .01919 .01923
6000 6991 497 13   .01905 .01907
7000 6914 457 0   .01892 .01895
8000 6839 422     .01881 .01882
9000 6766 393     .01871 .01869
10000 6695 367     .01861 .01856

Table IV - 4
LIQUID COMPRESSION
(HIGH PRESSURE)
Octane 50 C
VI = .656 P0 = 4535 Kg/cm2
P VII(L) VII(H) calc. obs.
0 .373 .029    
1000 .306 .006 .968 .965
2000 .259 .004 .919 .920
3000 .224 .003 .883 .888
4000 .198 .002 .856 .864
5000 .177 .002 .837 .843
6000 .161 .001 .818 .825
7000 .147 .001 .804 .810

Decane 95 C
VI = .653 P0 = 5580 Kg/cm2
P VII(L) VII(H) calc. obs.
0 .399 .053    
1000 .338 .014 1.005 .995
2000 .294 .008 .955 .946
3000 .259 .006 .918 .915
4000 .232 .004 .889 .888
5000 .210 .003 .866 .868
6000 .192 .003 .848 .848
7000 .177 .003 .033 .834
8000 .164 .002 .819 .822

Hexane 50 C
VI = .653 P0 = 3926 kg/cm2
P VII(L) VII(H) calc. obs.
0 .379 0029    
1000 .302 .006 .961 .957
2000 .251 .003 .907 .905
3000 .215 .002 .870 .872
4000 .188 .002 .843 .847
5000 .167 .001 .821 .826
6000 .150 .001 .804 .809
7000 .136 .001 .790 .794
8000 .125 .001 .779 .782
9000 .115 .001 .769 .771
10000 .107 .001 .761 .7615
11000 .100 .001 .754 .754

2-Metlyl Butane 0 C
VI = .647 P0 = 3388 kg/cm2
P VII(L) VII(H) calc. obs.
0 .336 .011    
1000 .259 .002 .908 .903
2000 .211 .001 .859 .857
3000 .178 .001 .826 .826
4000 .154 .001 .802 .8025
5000 .136   .783 .783
6000 .121   .768 .767
7000 .110   .757 .753

2,3-Dimethyl Butane 95 C
VI = .652 Po = 3926 kg/cm2
P VII(L) VII(H) calc. obs.
0 .412 .055    
1000 .328 .011 .991 .988
2000 .273 .006 .931 0920
3000 .234 .004 .890 .884
4000 .204 .003 .859 .856
5000 .181 .003 .036 .834
6000 .163 .002 .817 .816
7000 .148 .002 .802 .801
8000 .136 .002 .790 .787
9000 .125 .001 .778 .776
10000 .116 .001 .769 .76115
11000 .108 .001 .761 .755

Hexane 95 C
VI = .653 P0 = 3926 kg/cm2
P VII(L) VII(H) calc. obs.
0 .141 .054    
1000 .328 .011 .992  
2000 .272 .006 .931 .930
3000 .233 .004 .890 .891
4000 .204 .003 .860 .863
5000 .181 .003 .837 .870
6000 .163 .002 .818 .8225
7000 .148 .002 .803 .807
8000 .135 .002 .790 .794
9000 .125 .001 .779 .782
10000 .116 .001 .770 .772
11000 .108 .001 .762 .763

2-14ethyl Butane 95 C
VI = .653 P0 = 5580 kg/cm2
P VII(L) VII(H) calc. obs.
0 .412 .055    
1000 .318 .010 .975 .981
2000 .259 .005 .911 .912
3000 .219 .004 .870 .871
4000 .189 .003 .839 .840
5000 .166 .002 .815 .818
6000 .149 .002 .798 ,800
7000 .134 .002 .783 .786
8000 .123 .001 .771 .771

2-Methyl Pentane 95 C
VI = .651 P0 = 3926 kg/cm2
P VII(L) VII(H) calc. obs.
0 .42 .055    
1000 .328 .011 .990 .985
2000 .273 .006 .930 .923
3000 .234 .004 .889 .883
4000 .204 .003 .858 .855
5000 .181 .003 .835 .834
6000 .163 .002 .816 .818
7000 .148 .002 .801 .802
8000 .136 .002 .789 .787
9000 .125 .001 .777 .776
10000 .116 .001 .768 .766

2,3-Dimethyl Butane 0 C
VI = .652 P0 = 3926 kg/cm2
P VII(L) VII(H) calc. obs.
0 .335 .011    
1000 .267 .002 .921 .915
2000 .222 .001 .875 .870
3000 .190 .001 .843 .8395
4000 .166 .001 .819 .818
5000 .147 .001 .800 .800
6000 .133   .785 .7855

Propyl Alcohol 60 C
VI = .720 P0 = 4356 kg/cm2
P VII(L) VII(H) calc. obs.
0 .312 .028    
1000 .254 .006 .980 .978
2000 .214 .003 .937 .934
3000 .185 .002 .907 .906
4000 .163 .002 .885 .885
5000 .145 .001 .866 .867
6000 .131 .001 .852 .852
7000 .120 .001 .841 .839
8000 .110 .001 .831 .828
**

Anyl Alcohol 80 C
VI = .699 P0 = 4828 kg/cm2
P VII(L) VII(H) calc. obs.
0 .347 .041    
1000 .287 .009 .995 .914
2000 .245 .005 .949 .945
3000 .214 .004 .917 .914
4000 .190 .003 .892 .890
5000 .170 .002 .871 .871
6000 .155 .002 .856 .856
7000 .142 .002 .843 .842
8000 .131 .001 .831 .830
9000 .121 .001 .821 .819
10000 .113 .001 .813 .809
11000 .106 .001 .806 .800
12000 .103 .001 .800 .793

2-Methyl Pentane, 0 C
VI = .651 P0 = 3926 kg/cm2
P VII(L) VII(H) calc. obs.
0 .335 .011    
1000 .267 .002 .920 .913
2000 .222 .001 .874 .871
3000 .190 .001 .842 .842
4000 .165 .001 .818 .819
5000 .147 .001 .799 .801
6000 .133   .784 .784

Butyl Alcohol 50 C
VI = .708 P0 = 4857 kg/cm2
P VII(L) VII(H) calc. obs.
0 .320 .025    
1000 .265 .006 .979 .978
2000 .227 .003 .938 .937
3000 .198 .002 .908 .909
4000 .175 .002 .885 .887
5000 .158 .001 .867 .868
6000 .143 .001 .852 .853
7000 .131 .001 .840 .839
8000 .121 .001 .830 .827
**

Acetone 60 C
VI = .647 P0 = 5045 kg/cm2
P VII(L) VII(H) calc. obs.
0 .393 .035    
1000 .328 .008 .983 .992
2000 .281 .005 .933 .937
3000 .246 .003 .896 .900
4000 .220 .003 .870 .8725
5000 .197 .002 .846 .851
6000 .180 .002 .829 .834
7000 .165 .002 .814 .818
8003 .152 .001 .000 .804
9000 .141 .001 .789 .791
10000 .132 .001 .780 .780
11000 .124 .001 .772 .770
12000 .116 .001 .764 .761

Ethyl Chloride 20 C
VI = .653 P0 = 3167 kg/cm2
P VII(L) VII(H) calc. obs.
0 .329 .015    
1000 .250 .003 .926 .928
2000 .202 .001 .876 .877
3000 .169 .001 .843 .844
4000 .145 .001 .819 .820
5000 .128 .001 .802 .799
**

Ethyl Bromide 20 C
VI = .650 P0 = 4884 kg/cm2
P VII(L) VII(H) calc. obs.
0 .357 .017    
1000 .296 .004 .950 .948
2000 .253 .002 .905 .904
3000 .223 .002 .873 .878
4000 .196 .001 .847 .8505
5000 .176 .001 .827 .832
6000 .160 .001 .811 .816
7000 .147 .001 .798 .802
8000 .135 .001 .786 .790
9000 .126 .001 .777 .779
10000 .117 .001 .768 .769
11000 .110   .760 .760
12000 .103   .753 .752

Butyl Bromide 0 C
VI = .651 P0 = 5846 kg/cm2
P VII(L) VII(H) calc. obs.
0 .338 .011    
1000 .289 .003 .943 .938
2000 .252 .002 .905 .9025
3000 .223 .001 .875 .874
4000 .201 .001 .853 .853
5000 .182 .001 .834 .836
6000 .167 .001 .819 .821
7000 .154 .001 .806 .808
8000 .143   .794 .797
9000 .133   .784 .786
10000 .125   .776 .777
11000 .117   .768 .768
12000 .111   .762 .761

Propyl Chloride 0 C
VI = .675 P0 = 3684 kg/cm2
P VII(L) VII(H) calc. obs.
0 .313 .010    
1000 .246 .002 . 923 .926
2000 .203 .001 .879 .888
3000 .173 .001 .849 .854
4000 .150 .001 .826 .832
5000 .133   .808 .814
6000 .119   .794 .799
7000 .108   .783 .785
8000 .099   .774 .773
9000 .091   .766 .7625
**

Propyl Bromide 0 C
VI = .651 P0 = 5358 kg/cm2
P VII(L) VII(H) calc. obs.
0 .338 .011    
1000 .285 .003 .939 .936
2000 .246 .002 .899 .897
3000 .217 .001 .869 .8695
4000 .194 .001 .846 .848
5000 .175 .001 .827 .829
6000 .159 .001 .811 .813
7000 .147 .001 .7/9 .800
8000 .136   .786 .789
9000 .126   .777 .778
10000 .118   .769 .769
11000 .111   .762 .7595
12000 .104   .755 .7515

Amyl Bromide 0 C
VI = .664 P0 = 5708 kg/cm2
P VII(L) VII(H) calc. obs.
0 .326 .010    
1000 .277 .003 .944 .943
2000 .241 .002 .907 .907
3000 .214 .001 .879 .881
4000 .192 .001 .857 .860
5000 .174 .001 .839 .843
6000 .159 .001 .824 .828
7000 .146   .810 .815
8000 .136   .800 .804
9000 .127   .791 .793

Ethyl Ether 20 C
VI = .657 P0 = 5738 kg/cm2
P VII(L) VII(H) calc. obs.
0 .333 .016    
1000 .261 .003 .934 .936
2000 .215 .002 .887 .887
3000 .182 .001 .853 .853
4000 .158 .001 .829 .8275
5000 .140 .001 .811 .807
6000 .125 .001 .796 .792
**

Butal Iodide 50 C
VI = .653 P0 = 5580 kg/cm2
P VII(L) VII(H) calc. obs.
0 .368 .028    
1000 .312 .007 .984 .9785
2000 .270 .004 .939 .936
3000 .239 .003 .907 .907
4000 .214 .002 .881 .883
5000 .193 .002 .859 .864
6000 .177 .002 .844 .847
7000 .162 .001 .828 .833
8000 .150 .001 .816 .821
9000 .140 .001 .806 .810
10000 .131 .001 .798 .7995
11000 .123 .001 .789 .7905
12000 .116 .001 .782 .782

Phosphorus Trichloride 80 C
VI = .651 P0 = 6113 kg/cm2
P VII(L) VII(H) calc. obs.
0 .403 .047    
1000 .346 .013 1,010 1.0065
2000 .304 .008 .963 .956
3000 .270 .005 .926 .922
4000 .241 .004 .899 .896
5000 .222 .003 .876 .876
6000 .203 .003 .857 .860
7000 .188 .002 .841 .8115
8000 .115 .002 .828 .832
9000 .163 .002 .816 .821
10000 .153 .002 .806 .811
11000 .144 .002 .797 .801
12000 .136 .001 .788 .793

Benzene 95 C
VI = .649 P0 = 5938 kg/cm2
P VII(L) VII(H) calc. obs.
0 .413 .055    
1000 .353 .015 1.017 1.020
1500 .330 .011 .990 .992
2000 .309 .009 .967 .968
2500 .291 .007 .947 .949
3000 .274 .006 .929 .932
3500 .260 .005 .914 .918

Carbon Disulfide 20 C
VI = .657 P0 = 5738 kg/cm2
P VII(L) VII(H) calc. obs.
0 .350 .017    
1000 .298 .005 .960 .959
2000 .260 .003 .920 .917
3000 .230 .002 .888 .888
4000 .206 .001 .864 .865
5000 .187 .001 .845 .845
6000 .171 .001 .829 .8295
7000 .158 .001 .816 .815
8000 .146 .001 .804 .802
9000 .136 .001 .794 .792
10000 .128 .001 .786 .7805
11000 .120 .001 .778 .7715
12000 .113   .770 .766

Carbon Disulfide 80 C
VI = .657 P0 = 5738 kg/cm2
P VII(L) VII(H) calc. obs.
0 .395 .046    
1000 .336 .012 1.005 1,008
2000 .293 .007 .957 .955
3000 .259 .005 .921 .9185
4000 .233 .004 .894 .890
5000 .211 .003 .871 .868
6000 .193 .003 .853 .850
7000 .178 .002 .837 .835
8000 .165 .002 .824 .822
9000 .154 .002 .813 .811
10000 .144 .002 .803 .900
11000 .135 .001 .793 .789
12000 .128 .001 .786 .7795

REFERENCES

13. Smith, L. Be, Beattie, J. A*, and Kay, W. C., J. Am. Chem. Soc., 59-1587.

14. For a bibliography of Bridgman's reports see his book “The Physics of High Pressure.” G. Bell & Sons'. Ltd., London, 1958.

15. Reamer, H. H., Sage, B. H., and Lacey., W. N., Ind, Eng. Chem. 41-482.

16. Olds, R. H., Reamer, H. H., Sage B. H., and Lacey., W. M. Ibid., 36-282.

17. Sage, B. H., and Lacey., W. N., Ibid., 34-732.

18. Stewart, D. E., Sage, B. H., and Lacey., W. N. Ibid., 46-2529.

19. Nichols, W. B., Reamer, H. H., and Sage., B. H. Ibid., 47-2219.

20. Carmichael, L. T., and Sage, B. H., Ibid., 45-2697.

21. Sage., B. H., and Lacey., W. N., Ibid., 30-673.

22. Farrington., P. S., and Sage,, B. H., Ibid., 41-1734.

23. Olds., R. H., Sage. B. H., and Lacey., W. N., Ibid., 38-301

24. Glanville, J. W., and Sage, B. H., Ibid. 41-1272.

25. Reamer., H. H., Sage., B. H., and Lacey, W. N., Ibid., 42-140.

26. Kelso E. A., and Felsing, W. A.,, J. Am. Chem. Sec., 62-3132.

27. Felsing, W. A., and Watson., G. M., Ibid., 64-1822.

28. Day, H. 0., and Felsing, W. A., Ibid., 74-1952.

29, Felsing, W. A., and Watson., G. M., Ibid., 65-1889.

20. Kelso, E. A., and Felsing, W. A., Ind. Eng. Chem., 34-161.

31. Felsing, W. A., and Watson, G. M., J. Am. Chem. soc., 65-780.

32. Day, H. O., and Felsing, W. A., Ibid., 73-4839.

33. Keyes, Frederick G., Ibid., 53-967.


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