Some Thermodynamic Properties of
Nitric Oxide J. B. OPFELL, W. G. SCHLINGER, AND B. H. SAGE California Institute of Technology, Pasadena, Calg.
T
H E thermodynamic properties of nitric oxide have not been determined in detail. Briner and coworkers (3)investigated the volumetric behavior a t pressures from 450 to 2200 pounds per square inch in the temperature interval between - 109' and 48" F. In addition, measurements were recently completed a t pressures up to 2500 pounds per square inch for temperatures between 40' and 220" F. (6). These data were in good agreement with determinations of the second virial coefficient made by Johnston and Weimer (7) a t temperatures between -243" and 70" F.
I
I
I
I
I
I
1
pressure and temperature for which the coefficients were eatablished. In the present instance coefficients of the equation of state were based upon volumetric measurements made by Briner (3) and those recently reported by Golding ( 5 ) . The data of Briner do not agree with the more recent measurements a t temperatures in the neighborhood of 40" F. For this reason the results from the former set of measurements a t temperatures above -40' F. have been omitted. The inclusion of Briner's data above -40" F. would markedly increase the standard deviation of the volumetric data from the equation of state, The elimination of Golding's low temperature data ( 6 ) and the substitution of Briner's values (3) would not yield so small a standard deviation, as the trends of the later data a t temperatures above -40" F. are not compatible with Golding's measurements. The experimental data which were used in evaluating the coefficients have been indicated in Figure 1 together with isotherms from the Benedict equation based upon the coefficients recorded in Table I. A value of the universal gas constant of 10.73147 (cu,feet/lb.mole) (lb./sq. inch)/" R. or 1.98588 (B.t.u./ib. mole)/ R. was employed in the calculations. A series of sets of coefficients, such as that shown in Table I, may be obtained for nitric oxide based upon the data of Figure 1 using different values of y. Values of y between 0 and 10 (cu. feet/lb. mole)2 yield roughly equal deviations from the experimental data (3, 6). This behavior is similar to that found for the lighter hydrocarbons (8). The value of y was taken as 0.5 (cu. feet/lb. mole)* because it gave near the minimum standard error of estimate for values of y between 0 and 10. The coefficients recorded in Table I describe the volumetric behavior of nitric oxide from temperatures of - 100" to 220" F. for pressures up to 3000 pounds per square inch with a standard error of estimate of 0.00458 in the compressibility factor. This measure of disagreement ascribes all the error to the pressure and assumes agreement with respect to volume and temperature. O
Figure 1. Experimental Compressibility Factor for Nitric Oxide
The heat capacity of nitric oxide was calculated by Witmer (11) from spectroscopic measurements of Jenkins, Barton, and Mulliken ( 6 ) . Spencer (IO) proposed an analytical expression for the heat capacity for temperatures above 77" F. His values appear to deviate from Witmer's calculations and for this reason were not used in the present study. The above-mentioned volumetric data served as the basis for the evaluation of the coefficients of the equation of state proposed by Benedict, Webb, and Rubin (1, 2), hereinafter referred to as the Benedict equation. Methods devised by Brough ( 4 )with the modifications suggested by Selleck (9) were employed. These methods involved the application of least squares techniques with automatic digital computing equipment to the estimation of the coefficients yielding the minimum standard error of estimate. Experience has indicated that the Benedict equation, when used with coefficients established by the methods of Brough ( 4 ) and Selleck (9), does not necessarily give a satisfactory description of the volumetric behavior of a pure substance beyond the ranges of
0. h
500
1000 PRESSURE
Figure 2.
189
1500
LB
2000
2500
PER S Q IN.
Deviation of Predicted Compressibility Factor from Experiment
INDUSTRIAL AND ENGINEERING CHEMISTRY
190
~
~~
TABLE I. COEFFICIENTS OF BENEDICT EQUATION OF STATEFOR VOLUMETRIC BEHAVIOR OF NITRICOXIDE
Coefficient
B
C a
b C
a
X/M
1.81101
TABLE11. ANALYTICALEXPRESSIOKS FOR THERMODYXAMIC PROPERTIES
Units Molal Quantities (Lb./sa. inch) (cu. feet)' Der (lb. mole)' Cu. fee't per lb. mole . . (Lb./sq. inch) (CU.feet)' (" R.)f per (lb. mole) 1 (Lb./sq. inch) (cu. feet)3 per (lb. mol43 (Cu. feet12 per (lb. mole)' (Lh./sq. inch) (cu. feet) O R.)z per (lb. mole)a (Cu. feet)a per (lb. mole;3( (Cu. feet)' per (lb. mole)2
1630.78 0.166389 335.287 X 10' 14188.61 2.21283 915.645 X 106 0,051 2202 0 , 5oooooo
A
Vol. 46, No. 1
~
0.00521158 0.372342 X 101 0.526084 0.00245739 0.033857 1.89553 X 10-6 555.259 X 10-8 0.387620
(g)v =
(BR
+
+ P1 VI - 1
-
+
F)+
1 2c ~3 (bR)- T ~ V(1 ~+
Specific Quantities (Lb./sq. inch) (cu. feet)* per (lb.12 Cu. feet per lb. (Lh./sq. inch) (cu. feet)a ( O R.12 per (lb.)' (Lb./sq. inch) (cu. feet)a per (lb.)3 (Cu. feet)' per (lb.)' (Lb./sq. inch) (cu. feet)a ( " R.)3 per (lb.) 3 (Cu. feet)3 per Ob.)* (Cu. feet)2 per lb.)' (Cu. feet/lb.) &./sq. inch)/" R.
HI = E1
+ PlVl
Inf = I n P *
~
bTi
Figure 3.
Heat Capacity of Nitric Oxide i n the Gas Phase
T h e fractional deviation of the predicted compressibility factor from that determined by experiment is shown in Figure 2. As would be expected from least aquares techniques, the deviations are almost uniformly distributed throughout the field. These coefficients do not describe adequately the behavior of nitric oxide in the heterogeneous or critical regions. At temperatures of 100" and 200' R. marked disagreement from the estimated behavior of this compound results from the use of the coefficients listed in Table I. For convenience the coefficients are expressed on a molal and a specific basis. The expressions for enthalpy, entropy, and fugacity were combined with the relationships for pressure and the isochoric pressure-temperature derivative shown in the first part of Table I1 in order t o obtain the desired expressions for these thermodynamic properties. The iterative solution of these equations was carried out for 29 even values of pressure below 3000 pounds per square inch
a t each of 11 temperatures between -80" and 220' F. The resulting values of volume, enthalpy, entropy, and fugacity which were obtained are recorded in Table 111. The values of enthalpy and entropy have been carried to one more significant figure than is justified by the accuracy of the data, so that the differences between these quantities for adjacent states might be established with reasonable precision. The heat capacity a t infinite attenuation which is shown in Figure 3 was based on the calculations of Witmer (22). ' I n addition, the values of the heat capacity a t higher pressures have been included. The latter data were established by differentiation of the enthalpy function shown in Table I1 a t constant pressure. Figure 4 is an enthalpy-pressure diagram for nitric oxide.
January 1954
INDUSTRIAL AND ENGINEERING CHEMISTRY
Temperature and entropy have been included as parameters. A temperature-entropy diagram is shown in Figure 5 with volume, enthalpy, and pressure as parameters. These two diagrams permit most of the thermodynamic processes of industrial interest to be followed with reasonable accuracy. Figure 6 depicts the compressibility factor as a function of pressure with temperature and entropy as parameters. This diagram, when used with the following expression, allows more accurate estimation of specific volume than is possible from Figures 4 and 5.
191
However, it is not possible to follow isochoric processes directly upon Figure 6. The data of Table 111 and Figures 4,5, and 6 were based on a reference state of zero for the enthalpy and entropy a t a temperature of absolute zero and a pressure of 1 atmosphere for the ideal gas state. This basis corresponds to the convention adopted by Rossini (8)and affords a convenient reference for the enthalpy and entropy. Any uncertainties in the changes in enthalpy and entropy between absolute zero and the lowest temperature in the tables do not introduce errors in the use of the tabular information, since the reference states may be chosen arbitrarily. I t is believed that the values of pressure, volume, enthalpy, entropy, and fugacity are self-consistent with a standard deviation of not more than 0.1 %. However, values of the enthalpy, entropy, and specific volume as a function of state may involve a standard deviation as large as 0.6% as a result of uncertainties in the experimental values of the heat capacity and specific volume,
~
~~~
TABLE 111. THERMODYNAMIC PROPERTIES OF NITRICOXIDE Pressure, Lb./Sq. Inch Absolute
Volume Cu. Feet) Lb.
Enthalpy, B.t.u./ Lb.
Entrop B.t.u.7' (Lb.) ("
R.)
Fugacity,
Lb./Sq. Inch
-80' F. 10 14.696 20 30 40 50 60
80 100 125 150 200 250 300 400 5 00
Figure 5. Temperature-Entropy Diagram for Nitric Oxide
600
800 1000 1250 1500 1750 2000 2250 10 14.696 20 30 40 50 60 80 1OD 123
150 200 250 300 400 500 600 800
1000 1250 1500 1750 2000 2250 10 14.696 20 30 40
Figure 6. Pressure-Compressibility Factor Diagram for Nitric Oxide
13.55 9.21 6.76 4.50 3.37 2.687 2.235 1.670 1.330 1.059 0.8777 0.6511 0.5151 0,4245 0.3110 0,2427 0.1970 0.1395 0.1046 0.0761 0.0567 0.0435 0.0353 0.0306 14.63 9.95 7.30 4.86 3.64 2.909 2,420 1.809 1.448 1.150 0.9543 0,7099 0.5633 0.4656 0.3433 0.2698 0.2208 0.1594 0.1223 0.0825 0.0725 0.0584 0,0482 0.0409 15.70 10.68 7.84 5.22 3.91
93.71 93.63 93.53 93.34 93.16 92.98 92.80 92.43 92.07 91.60 91.14 90.11 89.23 88.26 86.27 84.22 82.09 77.60 72.73 65,99 58,49 50.78 44.32 39.88 -50' F. 100.97 100.90 100.82 100.68 100.53 100.381 100.23 99.92 99.62 99.24 98.86 98.09 97.31 96.52 94.92 93.27 91.58 88,06 84,33 79.34 73.95 68.24 62.44 57.00 -20' F. 108.19 108.13 108.06 107.94 107.81
I . 6197
1.5941 1.5735 1 ,5463 1.5270 1.6118 1 ,4094 1 ,4797 1 ,4642 1.4486 1 ,4356 1.4148 1.3981 1.3842 1.3613 1.3425 1 ,3263 1 ,2983 1 ,2737 1 ,2451 1.2173 1,1910 1.1692 1.1535
9.980 14.652 19.919 29 .a19 39.679 49,499 69.280 78.722 98.007 121.89 145.52 192,06 237.63 282.22 368.53 451.04 529.77 676.09 807.76 952.11 1074.8 1177.7 1265.3 1343.0
1 ,6381 1.6125 1 ,5920 1.5650 1 ,5456 1.5306 1.5183 1.4987 1 ,4834 1 ,4679 1.4552 1 ,4348 1.4186 1.4051 1 ,3832 1.3655 1.3503 1.3248 1.3031 1.2789 1.2566 1 ,2353 1.2151 1.1968
9.985 14.663 19.939 29.864 39.758 49.621 59,455 79.030 98.486 122.64 146.60 193.96 240.59 286.47 376.04 462 .68 546.48 705.52 853,46 1023.2 1176.7 1314.9 1439 3 1552.3
1 ,6553 9.989 1 ,6296 14.671 1.6091 19 954 20.895 1,5821 39.814 1.5628 (Continued on next page)
INDUSTRIAL AND ENGINEERING CHEMISTRY
192
Vol. 46, No. 1
TABLE 111. THERMODYNAMIC PROPERTIES OF NITRIC OXIDE(Continued) Pressure, Lb / 8q
. .
Inoh
Absolute
Volume Cu. Lb.
Enthalp
Feci/
B.t.u.7' Lb.
-20' 50 60 80 100 125 150 200 260 300 400 500 600
800 lo00 1250 1500 1750 2000 2250
3.13 2.601 1.947 1.554 1.239 1.030 0.7675 0.6102 0.5054 0.3743 0,2956 0.2431 0.1775 0.1380 0.1065 0.0855 0,0706 0.0597 0.0515
Entropy, B.t.u./ LLb.) (
R.)
Fugacity, Lb./Sq. Inch
16.78 11.41 8.38 5.68 4.18 3.34 2.784 2.084 1.664 1.328 1.104 0,8843 0.6563 0.5443 0.4043 0.3204 0.2644 0.1945 0.1526 0.1191 0.0969 0.0812 0.0697 0.0608
10 14.696 20 30 40 50 60 80 100 125 150 200 250 300 400 500 600 800 1000 1250 1500 1760 2000 2250 10 14.696 20 30 40 50 60 80 100 125 160 200 250 300 400 500 600 800 1000 1250
Volume, Cu. Feet/ Lb.
F. ( C o d . ) 107.69 107.56 107.31 107.06 106.75 106.43 105.79 105.15 104.50 103.17 101.82 100.44 97,58 94.60 90.68 86.55 82.23 77.81 73.40
1,5479 1.5356 1.5161 1.5010 1,4857 1.4731 1 .4530 1.4371 1.4240 1.4027 1 ,3857 1.3713 1 .3473 1.3274 1.3057 1.2863 1.2683 1.2514 1.2356
49,708 59.579 79.251 98.830 123.17 147.37 195.33 242.71 289.52 381.45 471.12 558.57 726.96 886.84 1075.2 1251.2 1415.6 1569.5 1714.1
loo F. 10 14.696 20 30 40 50 60 80 100 125 150 200 250 300 400 500 600, 800 1000 1250 1500 1750 2000 2250
Pressure, Lh./Sq. Inch Absolute
1.6709 1.6455 1.6249 1.5980 1.6788 1 .5639 1.5517 1.6323 1.5172 1 .5020 1.4895 1.4696 1 .4640 1.4411 1 ,4203 1.4037 1.3898 1.3670 1 .3482 1.3282 1.3106 1 .2946 1,2799 1,2659
9.991 14,677 19.964 29.918 39.853 49.770 59.669 79.411 99.081 123.56 147.93 196.32 244.27 291 -77 385.42 477.33 567.50 742.83 911.58 1113.8 1306.7 1491.0 1667.4 1836.8
17.85 12.14 8.92 5.94 4.46 3.56 2.965 2.220 1.774 1.416 1.178 0.8804 0.7017 0.5826 0.4338 0.3445 0.2850 0.2107 0.1662 0.1308 0.1073 0.0907 0.0784 0,0690
115.38 115.32 115.27 115.16 115.06 114.96 114.85 114.64 114.42 114.16 113.89 113.35 112.81 112.26 111.15 110.01 108.86 106.49 104.04 100.85 97.55 94.14 90.71 87.17 40' F. 122.54 122.50 122.45 122.36 122,27 122.18 122.09 121.91 121.73 121.50 121.27 120.82 120.35 119.88 118.93 117.97 116.99 115.00 112.94 110.29 107.57 104.79 101.98 99.15
1.6857 1.6604 1.6398 1.6129 1.5937 1.5788 1.5666 1.5473 1.5323 1.5172 1.5048 1.4851 1.4696 1.4569 1,4364 1.4202 1 .4067 1 .3846 1.3666 1.3477 1.3313 1.3166 1.3032 1.2907
9.993 14.680 19.971 29.934 39.883 49.816 59.735 79.530 99.265 123.85 148.35 197.07 245.44 293.44 388.41 482.02 574.25 764.83 930.32 1143.1 1348.9 1548.3 1742.1 1930.7
18.93 12.88 9.46 6.30 4.73 3.78 3.15 2.357 1.883 1.504 1.252 0.9361 0.7467 0.6205 0.4626 0.3681 0.3051 0.2264 0.1793 0.1418
70' F. 129.70 129.66 129.62 129.55 129.47 129.32 129.32 129.15 128.98 128.80 128.60 128.20 127.80 127.40 126.58 125.75 124.91 123.21 121.46 119.23
1.6998 1 ,6742 1.6539 1.6268 1.6078 1.5929 1.5807 1.5614 1.5464 1.5314 1.5191 1.4995 1.4841 1.4715 1.4513 1.4353 1.4221 1.4005 1.3832 1.3651
9.994 14.683 19.977 29.947 39.905 49,852 59.786 79,620 99.408 124.07 148.67 197.64 246.33 294.73 390.72 485.60 579.44 764.06 944.82 1165.7
1500 1750 2000 2250 2500 2750 3000
0.1170 0.0995 0.0864 0.0765 0.0686 0.0623 0.0572
Enthalpy, B.t.u./ Lb. 70° F. (Contd.) 116.95 114.64 112.30 109.97 107.66 105.38 103.17
Entropy, B.t.u./ (Lb.)
Fugacity, Lb./Sq.
R.)
Inch
1.3595 1.3358 1.3233 1.3118 1.3011 1.2911 1.2817
1381.5 1592.6 1799.8 2003.5 2204.4 2403.1 2600.0
1.7127 1 ,6873 1.6670 1.6401 1.6209 1.6061 1.5939 1.5747 1.5597 1 .5447 1 ,5324 1.5129 1 ,4977 1 ,4852 1 ,4652 1.4494 1.4363 1.4152 1 ,3984 1 .3808 1.3659 1,3528 1.3410 1 ,3302 1.3202 1.3109 1.3021
9.995 14.686 19.981 29.958 39.923 49.881 59.828 79.693 99.520 124.25 148.92 198.09 247.03 295.74 392.51 488.40 583.46 771.25 956.02 1183.3 1406.8 1627.2 1844.9 2060.4 2274.4 2487.3 2699.5
1.7253 1,6999 1.6794 1 ,6524 1.6334 1.6185 1.6064 1 .5872 1 ,5723 1.5573 1 ,5450 1.5256 1.6104 1.4980 1.4781 1.4625 1 .4496 1,4289 1.4123 1.3953 1.3809 1.3682 1,3569 1.3467 1.3372 1.3284 1.3202
9.996 14.688 19.985 29.965 3Y. 937 49,902 59,858 79.748 99.606 124.39 149.12 198.44 247.57 296.53 393.90 490.60 586.65 776,88 964.88 1197.2 1426.9 1654.5 1880.4 2105.4 2329.7 2553.8 2778.3
("
looo F. 10 14.696 20 30 40 50 60 80 100 125 150 200 250 300 400 500 600 800 1000 1250 1500 1750 2000 2250 2500 2750 3000
20.01 13.61 10.00 6.66 5.00 3.99 3.33 2.492 1.992 1.591 1.325 0.9912 0.7912 0.6578 0.4912 0.3913 0.3247 0.2417 0.1920 0.1524 0.1263 0.1077 0.0940 0.0834 0.0751 0.0684 0.0629
10 14.696 20 30 40 50 60 80 100 125 150 200 250 300 400 500 600 800 1000 1250 1500 1750 2000 2250 2500 2750 3000
21.08 14.34 10.54 7.02 5.26 4.21 3.51 2.628 2.101 1.679 1.398 1.046 0.8355 0.6950 0.5195 0.4142 0.3441 0.2566 0.2043 0.1627 0.1351 0.1156 0.1011 0.0900 0.0812 0.0741 0.0682
10 14.696 20 30 40 50 60 80 100 126 150 200 250 300 400 500 600 800 1000 1250 1500 1750 2000 2250 2500
23.23 15.80 11.61 7.74 5.80 4.64 3.87 2.898 2.317 1.852 1.543 1.156 0.9236 0.7687 0.5754 0.4595 0.3822 0.2859 0.2283 0.1824 0.1520 0.1305 0.1145 0.1022 0.0925
136.84 136.81 136.78 136.72 136.55 136.58 136.51 136.37 136.23 136.05 135.89 135.53 135.18 134.83 134.13 133.41 132.68 131.21 129.72 127.81 125.87 123.92 121.96 120.01 118.07 116.17 114.31 130° F. 143.99 143.96 143.93 143.87 143.81 143.75 143.69 143.57 143.45 143.30 143.15 142.84 142.53 142.22 141.60 140.98 140.34 139.06 137.77 136.12 134.47 132.80 131.14 129.49 127.85 126.25 124.68 190° F. 158.27 158.25 158.23 158.18 158.13 158.08 158.03 157.94 157.84 157.72 167.60 157.37 157.13 156.88 156.40 155.92 155.42 154.44 153.45 152.21 150.97 149.73 148.51 147.30 146.12
1 ,7483 1.7225 1.7021 1.6752 1.6562 1.6413 1.6292 1.6100 1 ,5952 1 .5802 1.5680 1.5487 1.5337 1. a 1 3 1.5017 1.4863 1.4737 1.4534 1.4373 1.4209 1.4072 1.3952 1 ,3847 1.3751 1.3664
9.998 14.691 19.990 29.976 39.957 49.933 59.904 79.828 99.733 124.58 149.40 198.95 248.37 297.67 395.95 493.78 591.23 785.05 977.71 1217.2 1455.7 1693.7 1931.5 2169.8 2408.9 (Concluded on next page)
INDUSTRIAL AND ENGINEERING CHEMISTRY
January 1954
TABLE 111. THERMODYNAMIC PROPERTIES OF NITRICOXIDE (Concluded)
Pressure, Lb./Sq. Inch Ab8o1ute
Volume
Enthalpy, B.t.u./ Lb.
Cu. Fee$ Lb.
Entropy, B.t.u./ (Lb.) (O
R.)
Fugacity, Lb./Sq. Inoh
0.0846 0.0781
190° F. (Contd.) 144.96 143.82
1.3E83 1 ,3508
2649.4 2891.4
10 14.696 20 30 40 50 60 80 100 125 150 200 250 3 00 400 500 600 800 1000 1250 1500 1750 2000 2250 2500 2750 3000
22.16 15.07 11 .@7 7.38 5.53 4.43 3.69 2.763 2.209 1.766 1.470 1.101 0.8795 0.7318 0 5475 0.4369 0.3632 0.2713 0.2164 0.1727 0.1437 0,1232 0.1079 0.0962 0,0869 0.0794 0.0733
160° F. 151.13 151.11 151.08 151.03 150.98 150.92 150.87 150.76 150.65 160.52 150.38 150.11 149.84 149.56 149.02 148.47 147.92 146.80 145.67 144.24 142.81 141.38 139.96 138.55 137.16 135.80 134.47
1 ,7372 1.7115 1.6911 1 .6641 1.6451 1,6302 1.6181 1,5989 1,5840 1,5691 1.5569 1,5375 1.5224 1.5100 1,4903 1.4748 1 .4620 1.4416 1,4253 1 .4086 1.3945 1.3823 1.3714 1.3615 1,3525 1.3441 1.3362
9.997 14.689 19.987 29.971 39.948 49.918 59.882 79.790 99.674 124.49 149.27 198.72 248.01 297.16 395.02 492.34 589.17 781.37 972.01 1208.3 1442.8 1676.2 1908.7 2141.1 2373.6 2606.8 2841.1
10 14.696 20 30 40 50 60
24.30 16.53 12,15 8.10 6.07 4.85 4.05 3.03 2,425 1.939 1.615 1.210 0.9672 0.8053 0.6030 0.4818 0.4010 0.3002 0.2400 0.1920 0.1602 0.1377 0.1210 0.1080 0.0978 0.0896 0.0828
220° F. 165.42 165.39 165.37 165.32 165.28 164.24 165.20 165.11 165.03 164.92 164.81 164.60 164.39 164.17 163.74 163.31 162.88 162.01 161.13 160.05 158.97 157.90 156.84 155.81 154.80 153.80 152.84
1.7586 1,7329 1.7127 1.6857 1.6666 1.6519 1.6397 1,6206 1.6057 1,5908 1.5786 1.5594 1.5443 1.5320 1.5125 1.4972 1.4846 1.4645 1.4486 1.4325 1,4189 1.4073 1,3969 1.3877 1,3792 1.3713 1.3641
9.998 14.691 19.991 29.979 39.963 49.942 69.918 79.855 99.776 124.65 149.501 199.12 248.64 298. OS 396.67 494.93 592.87 787.96 982.32 1224.3 1466.0 1707.7 1949.8 2192.9 2437.3 2683.4 2931.8
2750 3000
80 100
125 150 200 250 300 400 500 600 800 1000 1250 1500 1750 2000 2250 2500 2750 3000
I
4- VdP
Temperature,
F. - 80
-
50 -20 10 40 70 100 ' 130 160 190 220
,5
- H1 - HZ - (S1- SI) fz - T ~
Enthalpy, B.t.u./Lb. 93.90 101.12 108.32 115.49 122,64 129.77 136.91 144.05 161.18 148.32 165.46
THE
Entropy5 B.t.u./Lb: ("
R.)
1.5946 1.6129 1,6299 1.6457 1 ,6605 1.6744 1 ,6875 1.6999 1.7116 1.7226 1.7331
Values of entropy apply t o a pressure of 14.696lb. per sq. inch,
ACKNOWLEDGMENT
This work was supported by the Office of Naval Research. The assistance of W. R. Connell in carrying out the computation8 with a commercial punched card calculator is acknowledged. Virginia Berry prepared the large scale pressure-enthalpy and temperature-entropy diagrams. W. N. Lacey reviewed the manuscript. NOMENCLATURE
Coefficients in Benedict equation of state C C J
b
specific gas constant heat capacity a t constant pressure, B.t.u./(lb.) ( 'R,) = differential operator = base of Naperian logarithm = internal energy. B.t.u. per Ib. = fugacity, Ib. per sq. inch = enthalpy, B.t.u. per Ib. = natural logarithm = molecular weight = absolute pressure, lb. per sq. inch = universal gas constant = entropy, B.t.u./(lb.) (",R.) = absolute temperature, R. = molal volume. cu. feet aer Ib. mole = specific volume, cu. fee6 per Ib. = compressibility factor, PV or PV RT hT .. = partial differential operator =
C p =
d e
E f
'H In M P R
(2)
The relationship of fugacity to enthalpy and entropy was checked from the following thermodynamic rela tion, which iu applicable to an isothermal change of state: b l n f1-
the thermodynamic properties of nitric oxide a t pressures up to 3000 pounds per square inch in the temperature interval between -80" and 220" F. It is again emphasized that the extension of the Benedict equation, based upon the coefficients recorded in Table I, to states beyond those covered by the dat)a employed in this study may result in calculated values which deviate markedly from the actual behavior of this compound.
TABLE IV. EKTHALPY AND ENTROPY FOR NITRICOXIDEIN IDEAL GASSTATE
For the convenience of readers particularly interested in the properties of nitric oxide in the ideal gas state, values of the enthalpy and entropy of this compound a t a pressure of 1 atmosphere and in the ideal gas state are recorded in Table IV. As indicated earlier, these data are based upon the heat capacities calculated by Witmer (11). The self-consistency of the data was established by application of the following expression to a series of random polytropic paths:
dH = TdS
193
S T V V
2
b
SUBSCRIPTS 0 = reference state I, 2 = particular states of system SUPERSCRIPT * = value of property a t state of infinite attenuation LITERATURE CITED
(3)
The statistical estimatea of consistency given above were based upon these checks. The information of Table I11 together with the graphical presentation in Figures 4 and 5 suffices to establish
(1) Benedict, M., Webb, G. B., and Rubin, L. C..J . Chem. Phys., 8, 334 (1940). (2) Ibid., 10, 747 (1942). (3) Briner, E., Biedermann, H., and Rothen, A., Helv. Chim. Acta. 8, 923 (1925);
J. Chim. Phys., 23, 157 (1926).
INDUSTRIAL AND ENGINEERING CHEMISTRY
194
Brough, H. W., Schlinger, W, G., and Sage, B. H., IND.ENG. CHBIM., 43, 2442 (1951). (5) Golding, B. H.,and Sage, B H. Ibid., 43,160 (1951) (6)Jenkins, F. A., Barton, H. A,, and Mulliken, R. S., Phys. Rev., (4)
30, 150 (1927). (7)Johnston, H.L,,and Weimer, H. R., J. Am. C h m . Soc., 56, 625 (1934). (8) Rossini, F. D., “Chemioal Thermodynamics,” p 191,New York, John Wiley & Sons, 1950.
Vol. 46*No. k
(9)Selleck, F. T.,Opfell, J. B., and Sage, B H., IND.EXG.CHEM., 45, 1350 (1953). (10)Spencer, H.M., Ibid., 40, 2152 (1948). (11) Witmer, E.E.,J . Am. Chem. Soc., 56, 2229 (1934). RECEIVED for review December 22, 1952.
~ 4 c C E P r E pJuly 27, 1953. Copies of Figures 4 and 5, with a more detailed coordinate aystem approximately W/Z by 11 inches, may be obtained from the authom far the aaat a i duplication.
Thermodynamic Correlation of
Vapor-Liquid Equilibria PREDICTION OF MULTICOMPONENT SYSTEMS BERNARD S. EDWARDS’, FRANK HASHMALL2, ROGER GILMONT3, AND DONALD F. OTHMER The Polytechnic Institute of Brooklyn, Brooklyn, N . Y .
A
NEW method of predicting the equilibrium conditions of
multicomponent systems from binary data has been developed. Parameters determined from relative volatility data of the binaries are extended by thermodynamic principles to cover multicomponent systems. The equations for determining the parameters are generalized for use under constant-pressure as well as constanttemperature conditions. -4 correlation which would permit the prediction of vaporliquid equilibria of multicomponent systems from experimental binary data would be a valuable aid in the chemical field. A method based on thermodynamic, rather than empirical, considerations, which is applicable to both constant-pressure and constanbtemperature systems, and which would require relatively simple mathematical manipulation would be the most ideal correlation. Considerable work has been done in this field by both the thermodynamic and the empirical approach. For the most part, the work in binary (1, 8, 11, 18, 16, 19) and ternary systems (8,9,18, II,22) was primarily correlation methods which expressed data in the form of equations. The prime purposes of these equations are twofold: to determine internal inconsistency, and, where necessary, to smooth existing data. These correlations may also be considered prediction correlations only in so far as they permit interpolations betxeen experimental points, or neglect multicomponent effects. Gilmont et al. ( 4 ) have correlated binary mixtures by plotting the relative volatilities and obtaining a series of parameters which determine an analytical expression for the activity coefficient. The purpose of this paper is to develop a set of equations which may extend these parameters to predict multicomponent systems without recourse to multicomponent data.
+ or
in which log y i j represents the value of log pressed as a function of q. By defining
yi
in a binary i-j ex-
(3) and taking into consideration the Gibbs-Duhem equation %,d(g,) i
=
0
(4)
it may be shoa-n that, by operating on Equation 1
(5)
DERlVATION OF PREDICTION EQUATIONS
The total molal free energy of a multicomponent system, divided by 2.303RT, can be expressed as
or
9 = z1 log
Y1
+
22
log
YZ
+ z3 log + Y3
For an ideal binary mixture
For a nonideal binary with an ideal vapor phase
Sssuming that the excess chemical potential of a multicomponent 1 2
3
Present address, E. I. du Pont de Nemours 8: Co., Ino., Buffalo, N. Y . Present address, M. W. Kellogs, Co., New York. N. Y. Present address, The Emil Greiner Co., Xew York, N. Y .
Therefore
y1/y2
is the deviation from ideality for the relative
