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3.5 Critical constants and second virial coefficients of gases
The critical pressure pc, critical
molar volume Vcm, and critical temperature
Tc, are the values of the pressure p, molar volume
Vm, and thermodynamic temperature T, at which the
densities of coexisting liquid and gaseous phases become identical. At the
critical point:
|
(∂p/∂V)T=Tc
= 0
(∂2p/∂V2)T=Tc
= 0 |
(1) |
At temperatures above the critical temperature a gas
cannot be liquefied.
The state of a gas can be accurately expressed by an
equation of the form:
|
Z = pVm/RT= 1 +
B/Vm +C/V2m +
... |
(2) |
where R is the gas constant: R = (8.314
510 ± 0.000 070) J K−1 mol−1;
B,C,..., are the second, third,..., virial coefficients which for a
given substance are functions of temperature only; and Z is called the
compression factor. As a rough rule, neglect of the third and higher virial
coefficients in equation (2) leads to percentage errors 102
|δZ/Z| <x provided that
p/pc < 0.2x1/2 at
T/Tc = 0.6; or
p/pc < 0.6x1/2
at T/Tc = 1; or
p/pc < 1.3x1/2 at
T/Tc = 2; or
p/pc < 3x1/2 at
T/Tc = 4.
The second virial coefficient B of a gas can be
fitted, usually within experimental errors over the range of temperatures at
which measurements have been made, by an equation of the form:
|
B/(cm3 mol−1) = a
− b exp{c(K/T)}. |
(3) |
Values of a, b, and c are given, where
possible, for the range of temperatures from TL to
TU.
For Ar, Kr, Xe,
CH4, N2, O2, and CO accurately, and with
useful but lower accuracy for other substances, the critical compression factor
Zc = 0.29, and B is given by
|
Bpc/RTc = 0.599 − 0.467
exp(0.694Tc/T). |
(4) |
An estimate of B for a substance with a value of
Zc appreciably different from 0.29 can be obtained by the
method described in The Properties of Gases and Liquids by Reid,
Prausnitz, and Sherwood, 3rd edn, 1977, p. 53 (McGraw-Hill, New York).
Experimental values of B can be found in The Virial Coefficients of
Pure Gases and Mixtures, by Dymond and Smith, 2nd edn, 1980 (Clarendon
Press, Oxford).
Elements and inorganic
compounds
|
Element or Compound
|
|
|
|
|
|
Coefficients |
|
|
of |
|
|
equations (3) |
|
a |
b |
c |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Ammonia . . . . .
|
11.35 |
72.5 |
405.5 |
0.244 |
44.3 |
23.6 |
766.6 |
273 |
573 |
|
Argon . . . . . .
|
4.90 |
74.6 |
150.9 |
0.291 |
154.2 |
119.3 |
105.1 |
80 |
1024 |
|
Bromine . . . . .
|
10.3 |
127 |
588 |
0.268 |
— |
— |
— |
— |
— |
|
Carbon
dioxide . .
|
7.38 |
94.0 |
304.1 |
0.274 |
137.6 |
87.7 |
325.7 |
220 |
1100 |
|
Carbon disulphide . .
|
7.9 |
173 |
552 |
0.298 |
211.0 |
167.1 |
538.7 |
280 |
430 |
|
Carbon monoxide . .
|
3.50 |
93.1 |
132.9 |
0.295 |
202.6 |
154.2 |
94.2 |
90 |
573 |
|
Carbonyl chloride . .
|
|
|
|
|
|
|
|
|
|
|
|
(phosgene) . . . |
5.67 |
190 |
455 |
0.285 |
— |
— |
— |
— |
— |
|
Chlorine
. . . . .
|
7.98 |
124 |
416.9 |
0.285 |
201.9 |
131.8 |
409.9 |
360 |
700 |
|
Cyanogen
. . . .
|
6.0 |
— |
400 |
— |
746.9 |
508.2 |
238.0 |
308 |
423 |
|
Deuterium . . . .
|
1.65 |
60 |
38.2 |
0.312 |
155.1 |
132.5 |
18.9 |
18 |
423 |
|
Deuterium
oxide . . |
21.67 |
56.3 |
643.9 |
0.228 |
−16.8 |
3.37 |
1928.2 |
423 |
773 |
|
Dinitrogen
oxide . . |
7.25 |
97.4 |
309.6 |
0.274 |
180.7 |
114.8 |
305.4 |
200 |
423 |
|
Fluorine . . . . .
|
5.22 |
66 |
144.3 |
0.288 |
71.4 |
48.0 |
165.0 |
80 |
300 |
|
Helium . . . . .
|
0.227 |
57.2 |
5.19 |
0.301 |
114.1 |
98.7 |
3.245
|
7 |
150 |
|
Hydrogen . . . .
|
1.297 |
65.0 |
33.2 |
0.306 |
315.0 |
289.7 |
9.47 |
14 |
400 |
|
Hydrogen bromide . |
8.55 |
— |
363.2 |
— |
— |
— |
— |
— |
— |
|
Hydrogen chloride . |
8.31 |
81 |
324.7 |
0.249 |
57.7 |
37.8 |
495.9 |
190 |
480 |
|
Hydrogen cyanide . |
5.39 |
139 |
456.7 |
0.197 |
— |
— |
— |
— |
— |
|
Hydrogen deuteride |
1.48 |
63 |
36.0 |
0.312 |
— |
— |
— |
— |
— |
|
Hydrogen fluoride . |
6.48 |
69 |
461 |
0.117 |
— |
— |
— |
— |
— |
|
Hydrogen iodide . |
8.31 |
— |
424 |
— |
— |
— |
— |
— |
— |
|
Hydrogen sulphide |
8.94 |
98.5 |
373.2 |
0.284 |
47.7 |
30.3 |
632.9 |
278 |
493 |
|
Iodine . . . . .
|
— |
155 |
819 |
— |
— |
— |
— |
— |
— |
|
Krypton . . . .
|
5.50 |
91.2 |
209.4 |
0.288 |
189.6 |
148.0 |
145.3 |
110 |
700 |
|
Mercury . . . .
|
172 |
42.7 |
1750 |
0.505 |
— |
— |
— |
— |
— |
|
Neon . . . . .
|
2.76 |
41.7 |
44.4 |
0.311 |
81.0 |
63.6 |
30.7 |
44 |
973 |
|
Nitrogen . . . .
|
3.39 |
89.5 |
126.2 |
0.289 |
185.4 |
141.8 |
88.7 |
75 |
700 |
|
Nitrogen
dioxide . |
10.1 |
84 |
431 |
0.240 |
— |
— |
— |
— |
— |
|
Nitrogen
oxide . . |
6.48 |
57.7 |
180 |
0.250 |
15.9 |
11.0 |
372.3 |
122 |
311 |
|
Oxygen . . . . .
|
5.04 |
73.4 |
154.6 |
0.288 |
152.8 |
117.0 |
108.8 |
90 |
400 |
|
Ozone . . . . .
|
5.57 |
88.9 |
261.1 |
0.228 |
— |
— |
— |
— |
— |
|
Phosphine . . . .
|
6.5 |
— |
324.5 |
— |
248.6 |
164.9 |
276.4 |
190 |
297 |
|
Radon . . . . .
|
6.3 |
— |
377 |
— |
— |
— |
— |
— |
— |
|
Silane . . . . . .
|
4.84 |
— |
269.7 |
— |
— |
— |
— |
— |
— |
|
Silicon tetrachloride . |
3.59 |
326 |
508.1 |
0.277 |
— |
— |
— |
— |
— |
|
Silicon tetrafluoride . |
3.72 |
— |
259.0 |
— |
346.7 |
257.2 |
185.5 |
206 |
475 |
|
Sulphur . . . . .
|
20.7 |
— |
1314 |
— |
— |
— |
— |
— |
— |
|
Sulphur
dioxide . . |
7.88 |
122 |
430.8 |
0.269 |
134.4 |
72.5 |
606.5 |
265 |
473 |
|
Sulphur hexafluoride |
3.77 |
199 |
318.7 |
0.283 |
422.1 |
281.3 |
273.5 |
200 |
525 |
|
Sulphur
trioxide . . |
8.20 |
127 |
491.0 |
0.255 |
— |
— |
— |
— |
— |
|
Tin (IV)
chloride . . |
3.75 |
351 |
591.9 |
0.267 |
— |
— |
— |
— |
— |
|
Uranium hexafluoride |
4.66 |
250 |
505.8 |
0.277 |
540.5 |
380.9 |
445.0 |
321 |
469 |
|
Water . . . . . .
|
22.06 |
56.0 |
647.1 |
0.229 |
33.0 |
15.2 |
1300.7 |
293 |
1248 |
|
Xenon . . . . . .
|
5.84 |
118 |
289.7 |
0.287 |
245.6 |
190.9 |
200.2 |
160 |
650 |
|
|
|
|
|
|
|
|
|
|
|
|
Organic compounds |
|
|
|
|
|
|
|
|
|
|
Acetaldehyde . . .
|
— |
— |
461 |
— |
−71.8 |
12.3 |
1351 |
288 |
476 |
|
Acetic
acid . . .
|
5.79 |
171 |
592.7 |
0.201 |
—
|
— |
— |
— |
— |
|
Acetone . . . . .
|
4.70 |
209 |
508.1 |
0.232 |
—
|
— |
— |
— |
— |
|
Acetonitrile . . . .
|
4.85 |
173 |
545.5 |
0.185 |
—
|
— |
— |
— |
— |
|
Acetylene . . . .
|
6.14 |
113 |
308.3 |
0.270 |
49.2 |
42.9 |
354.9 |
200 |
273 |
|
Aniline . . . . . .
|
5.31 |
287 |
699 |
0.262 |
— |
— |
— |
— |
— |
|
Benzene . . . . .
|
4.90 |
256 |
562.0 |
0.268 |
571.4 |
348.4 |
526.6 |
290 |
600 |
|
Bromobenzene . . .
|
4.52 |
324 |
670 |
0.263 |
— |
— |
— |
— |
— |
|
Bromoethane . . . .
|
6.23 |
215 |
503.9 |
0.320 |
— |
— |
— |
— |
— |
|
Bromomethane . . .
|
— |
— |
464 |
— |
51.1 |
42.4 |
792.2 |
244 |
383 |
| Bromotrifluoromethane |
|
|
|
|
|
|
|
|
|
|
(R13B1)
. . . . |
3.97 |
196 |
340.2 |
0.275 |
— |
— |
— |
— |
— |
|
Buta-1,3-diene . . .
|
4.33 |
221 |
425 |
0.270 |
— |
— |
— |
— |
— |
|
Butane
. . . . .
|
3.80 |
255 |
425.1 |
0.274 |
165.4 |
135.4 |
555 |
250 |
400 |
|
Butanone . . . . .
|
4.21 |
267 |
536.8 |
0.252 |
948.6 |
314.6 |
702.4 |
315 |
371 |
|
But-1-ene . . . .
|
4.02 |
240 |
419.6 |
0.277 |
522.9 |
289.6 |
421.2 |
243 |
420 |
|
cis-But-2-ene . . .
|
4.20 |
234 |
435.6 |
0.271 |
1369.5 |
778.2 |
297.4 |
251 |
343 |
|
trans-But-2-ene
. |
3.98 |
238 |
428.6 |
0.266 |
1245.0 |
763.3 |
284.3 |
243 |
333 |
|
Carbon tetrachloride |
4.56 |
276 |
556.4 |
0.272 |
607.6 |
463.0 |
461.0 |
316 |
419 |
|
Carbon tetrafluoride |
|
|
|
|
|
|
|
|
|
|
(R14). . . . .
|
3.74 |
140 |
227.6 |
0.276 |
256.32 |
172.80 |
206.0 |
|
625 |
|
Chlorobenzene . .
|
4.52 |
308 |
632.4 |
0.265 |
— |
— |
— |
— |
— |
|
Chlorodifluoromethane |
|
|
|
|
|
|
|
|
|
|
(R22) . . . . .
|
4.99 |
169 |
369.3 |
0.274 |
374.7 |
270.2 |
287.8 |
298 |
473 |
|
Chloroethane . . .
|
5.30 |
— |
460.4 |
— |
182.4 |
88.4 |
717.9 |
273 |
605 |
|
Chloroform . . . .
|
5.47 |
239 |
536.4 |
0.293 |
485.7 |
272.5 |
542.7 |
316 |
400 |
|
Chloromethane
. . . |
6.68 |
139 |
416.2 |
0.268 |
396.7 |
259.2 |
337.3 |
280 |
600 |
|
Chlorotrifluoromethane |
|
|
|
|
|
|
|
|
|
|
(R13) . . . . .
|
3.87 |
180 |
302.0 |
0.278 |
388.6 |
282.9 |
229.5 |
192 |
533 |
|
Cyclohexane
. . . |
4.07 |
308 |
553.5 |
0.273 |
677.3 |
393.2 |
531.4 |
300 |
560 |
|
Cyclopentane . . .
|
4.51 |
260 |
511.7 |
0.275 |
— |
— |
— |
— |
— |
|
Cyclopropane . . .
|
5.58 |
162 |
398.3 |
0.274 |
355.7 |
255.2 |
316.7 |
303 |
403 |
|
Dichlorodifluoromethane |
|
|
|
|
|
|
|
|
|
|
(R12) . . . . .
|
4.14 |
217 |
385.0 |
0.280 |
463.1 |
341.7 |
291.2 |
239 |
478 |
|
Dichlorofluoromethane |
|
|
|
|
|
|
|
|
|
|
(R21) . . . . .
|
5.18 |
196 |
451.6 |
0.271 |
435.0 |
401.9 |
266.7 |
239 |
450 |
|
1,2-Dichlorotetra- |
|
|
|
|
|
|
|
|
|
|
fluoroethane (R114)
|
3.25 |
297 |
418.8 |
0.277 |
639.9 |
431.5 |
361.3 |
296 |
504 |
|
Diethylamine
. . . |
3.71 |
301 |
496.6 |
0.270 |
673.0 |
378.0 |
517.7 |
314 |
405 |
|
Diethyl ether
. . . |
3.64 |
280 |
466.7 |
0.262 |
968.3 |
346.6 |
552.3 |
280 |
400 |
|
Dimethylamine . . .
|
5.34 |
— |
437.2 |
— |
407.7 |
234.2 |
456.0 |
312 |
405 |
|
Dimethyl ether
. . |
5.37 |
190 |
400.0 |
0.307 |
371.0 |
267.4 |
351.3 |
273 |
328 |
|
2,2-Dimethylpropane |
3.20 |
311 |
433.8 |
0.276 |
407.0 |
281.0 |
450 |
250 |
440 |
|
1,4-Dioxan . . .
|
5.21 |
238 |
587 |
0.254 |
— |
— |
— |
— |
— |
|
Ethane . . . . .
|
4.87 |
146 |
305.3 |
0.279 |
267.3 |
191.5 |
256 |
210 |
500 |
|
Ethanol . . . . .
|
6.14 |
168 |
514.0 |
0.241 |
864.6 |
45.4 |
1345 |
313 |
399 |
|
Ethyl
acetate . . .
|
3.83 |
286 |
523.2 |
0.252 |
982.9 |
407.5 |
598.1 |
330 |
399 |
|
Ethylamine . . . .
|
5.62 |
182 |
456 |
0.270 |
533.6 |
289.0 |
452.3 |
293 |
405 |
|
Ethylene
. . . . .
|
5.03 |
130 |
282.3 |
0.280 |
278.9 |
193.5 |
231.2 |
181 |
448 |
|
Ethyl formate
. . . |
4.74 |
229 |
508.5 |
0.257 |
763.9 |
341.0 |
542.6 |
323 |
395 |
|
Ethyl methyl ether
. |
4.40 |
221 |
437.8 |
0.267 |
— |
— |
— |
— |
— |
|
Fluorobenzene . .
|
4.55 |
269 |
560.1 |
0.263 |
613.0 |
360.0 |
555.4 |
318 |
623 |
|
Fluoromethane . .
|
5.88 |
113 |
317.8 |
0.252 |
269.2 |
172.8 |
303.0 |
273 |
423 |
|
Heptane
. . . . .
|
2.74 |
428 |
540.2 |
0.261 |
982.0 |
523.9 |
582.3 |
300 |
700 |
|
Hept-1-ene . . . .
|
— |
— |
537.3 |
— |
1245.0 |
635.1 |
530.9 |
334 |
411 |
|
Hexane . . . . . .
|
3.02 |
368 |
507.6 |
0.264 |
839.6 |
404.1 |
572.6 |
300 |
450 |
|
Hex-1-ene . . . .
|
— |
— |
504.0 |
— |
836.6 |
460.4 |
507.1 |
313 |
410 |
|
Iodobenzene . . . .
|
4.52 |
351 |
721 |
0.265 |
— |
— |
— |
— |
— |
|
Iodomethane . . .
|
— |
— |
528 |
— |
459.8 |
248.0 |
476.0 |
313 |
383 |
|
Isobutane . . . .
|
3.64 |
259 |
407.8 |
0.278 |
270.3 |
192.1 |
460 |
250 |
440 |
|
Methane . . . . .
|
4.60 |
98.6 |
190.6 |
0.286 |
206.4 |
159.5 |
133.0 |
110 |
600 |
|
Methanol . . . .
|
8.08 |
117 |
512.5 |
0.223 |
14 |
3.958 |
1840 |
280 |
400 |
|
Methyl acetate
. . |
4.69 |
228 |
506.8 |
0.254 |
762.9 |
336.7 |
577.9 |
323 |
391 |
|
Methylamine . . .
|
7.61 |
— |
430.7 |
— |
85.3 |
57.1 |
685.9 |
293 |
550 |
|
2-Methylbutane . . |
3.38 |
306 |
460.4 |
0.270 |
952.1 |
620.4 |
355.8 |
|
450 |
|
Methylcyclohexane . |
3.47 |
368 |
572.2 |
0.268 |
— |
— |
— |
— |
— |
|
Methylcyclopentane |
3.78 |
319 |
532.7 |
0.272 |
— |
— |
— |
— |
— |
|
Methyl
formate . . |
6.00 |
172 |
487.2 |
0.255 |
581.0 |
269.3 |
525.5 |
319 |
397 |
|
2-Methylpentane .
|
3.04 |
368 |
497.7 |
0.270 |
— |
— |
— |
— |
— |
|
2-Methylpropene .
|
4.00 |
239 |
417.9 |
0.275 |
722.1 |
354.4 |
405.8 |
243 |
333 |
|
Naphthalene . . .
|
4.05 |
407 |
748.5 |
0.269 |
— |
— |
— |
— |
— |
|
Octafluorocyclobutane |
2.78 |
324 |
388.5 |
0.279 |
895.7 |
616.4 |
285.6 |
373 |
623 |
|
Octane. . . . . .
|
2.49 |
492 |
568.7 |
0.259 |
1138.0 |
536.1 |
672.5 |
300 |
700 |
|
Oct-1-ene . . . .
|
— |
— |
566.7 |
— |
1328.0 |
631.5 |
614.2 |
359 |
412 |
|
Pentane . . . . .
|
3.37 |
311 |
469.7 |
0.268 |
377.9 |
237.6 |
560 |
270 |
500 |
|
Pent-1-ene . . . .
|
3.53 |
— |
464.8 |
— |
655.7 |
344.2 |
499.9 |
294 |
410 |
|
Phenol . . . . . .
|
6.1 |
— |
694.2 |
— |
— |
— |
— |
— |
— |
|
Propadiene . . . .
|
— |
— |
393 |
— |
391.4 |
272.0 |
310.5 |
223 |
353 |
|
Propane . . . . .
|
4.25 |
200 |
369.8 |
0.281 |
322.8 |
220.3 |
350 |
240 |
330 |
|
Propan-1-ol . . . .
|
5.17 |
218 |
536.8 |
0.252 |
861.9 |
297.3 |
669.2 |
378 |
423 |
|
Propene . . . . .
|
4.60 |
181 |
364.8 |
0.274 |
286.6 |
197.0 |
349 |
220 |
400 |
|
Propyne . . . . .
|
5.63 |
164 |
402.4 |
0.275 |
444.6 |
314.6 |
292.2 |
348 |
473 |
|
Pyridine . . . . .
|
5.63 |
254 |
620.0 |
0.277 |
796.1 |
398.8 |
576.3 |
347 |
438 |
|
Tetramethylsilane . |
2.82 |
362 |
448.6 |
0.273 |
792.2 |
502.2 |
403.4 |
295 |
539 |
|
Toluene . . . . .
|
4.11 |
316 |
591.8 |
0.264 |
719.1 |
373.3 |
646.4 |
341 |
583 |
|
Trichlorofluoromethane |
|
|
|
|
|
|
|
|
|
|
(R11) . . .
. . |
4.41 |
248 |
471.2 |
0.279 |
532.1 |
394.6 |
351.2 |
239 |
478 |
|
Triethylamine . . .
|
3.03 |
389 |
535.6 |
0.265 |
1261.6 |
739.1 |
442.1 |
323 |
405 |
|
Trimethylamine . .
|
4.09 |
254 |
432.8 |
0.288 |
747.0 |
466.5 |
347.3 |
298 |
375 |
|
2,2,4-Trimethylpentane |
2.57 |
468 |
544.0 |
0.266 |
— |
— |
— |
— |
— |
|
m-Xylene . . . .
|
3.54 |
375 |
617.0 |
0.259 |
— |
— |
— |
— |
— |
|
o-Xylene . . . .
|
3.73 |
370 |
630.3 |
0.263 |
— |
— |
— |
— |
— |
|
p-Xylene . . . .
|
3.51 |
378 |
616.2 |
0.259 |
— |
— |
— |
— |
— |
|
|
|
|
|
|
|
|
|
|
|
|
D.Ambrose
M.B.Ewing
M.L.McGlashan
|
|
