# 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 ½(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 ½fB 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 ½(fA + fB) V3. Dividing ½(fA + fB) by ½fA 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 ½ 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 ½f corresponding to each index. Multiplying each of these values of ½f 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. ½f 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.