Prediction of Vapor Pressure of Parahydrogen from the Tripleto the Critical Point
  

2001, Vol. 45, No. 4

Printed in the Republic of Korea

     

 

  

(2001. 4. 26 )

Prediction of Vapor Pressure of Parahydrogen from the Triple to the Critical Point

Jaygwan G. Chung

Department of Chemical Engineering, Sungkyunkwan University, Suwon 440-746, Korea (Received April 26, 2001)

.         !"# $%&' ()

()*+ ,- ./0 12 3 40 56 7&89 :%&;<:

# =& >?@ ABC D2 !5 E8(T^b= 20.268 K), F(P^c= 1292.81 kPa) G *

+(Tc= 32.976 K)H$I 153J   KLMN O%&' P Q RS TUVW 0.21% ;<.

ABSTRACT. The existing vapor pressure measurements reported in the literature for parahydrogen between the triple point and the critical point have been employed to establish the constants and exponent of the following equation in the form of reduced vapor pressure and reduced temperature:

Only the normal boiling point (Tb= 20.268 K), the critical pressure (Pc= 1292.81 kPa), and the critical tem- perature (Tc= 32.976 K) are necessary to calculate the vapor pressure for an overall average deviation of 0.21

% for 153 experimental vapor pressure data.

 

XY Z[\ ]NX :%^8  C _

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^w Frost- Kalkwarf  x!3¹# yz{&8 

W ^|<.

(1)

3 (1)2 }~ PW q€X  P "# =‚

 ƒ P"# 7& >?@8 \„…V† ?

‡ <. $ˆC ‰U# ƒŠ >?@  P8 * + ‹$€X D'P/T² Œ DTⁿ# :%‚  q

I,² DTⁿ# 3 (1) O%& 3 (2)$ <.

(2) lnP_r 2.64 2.75

T_r

--- 1.48129lnT+ _r+0.11T_r⁵ –

=

lnP_r 2.64 2.75 T_r

--- 1.48129lnT+ _r+0.11T_r⁵ –

=

lnP A' B'

---- C'lnT D'T P T² ---

+ + +

=

lnP A' B'

---- C'lnT D'TT ⁿ

+ + +

=

l@  &'     

 !" R7 O%Ž  q8 4 n "#

.‡ <. 3 (2)6   q8  

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. >&' ’’ “”OX !  KL"

# :%&' • z{&;I^3-9–C 1993— Pavese W 3# ITS-90X TWC D# ˜%&;<.¹⁰

   

P = PcPr T = T^cTr# 3 (2) ™& ./0 1<.

(3)

'@

$<. 3 (3)#  O%& <š 1$<.

A =−B−D (4)

›s Plank-Riedel œ^11,12 lž 3 (3)X ‘

Ÿ 3 (5)6  b<.

(5)

5 œ2 Goodwin  ¡?¹³08 5$&<. ¢ˆ

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(6)

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 !" §(P^r1, Tr1)# O%C<. §

# 3 (6) ™&' !¨& 3 (7)$ ^I

(7) '@

(8)

(9) lnP_r A B

T_r

--- ClnT_r DT_rⁿ

+ + +

=

A=A' lnP– _c+C'lnT_c

B B' T_c ---

=

C=C'

D D'Tc

= n

B=–Dn²

lnP_r ClnT_r D T( _rⁿ–1) n² 1 1 T_r ---

 – 

 

+ +

=

Y=C DX+

X

T_rⁿ–T_r1ⁿ ( ) n² 1

T_r --- 1

T_r1 ---

 – 

 

–

ln T_r T_r1 ---

   ---

=

Y P_r P_r1 ---

 

  ln

T_r T_r1 ---

   ln ---

=

Table 1. Moduli X and Y for the typical vapor pressure data of Weber et al.⁹(n=5)

Temp. [K] Vapor pressure

X Y

[atm] [kPa]

20.2680 22.0000 23.0000 25.0000 26.0000 27.0000 28.0000 29.0000 30.0000 30.5000 31.0000 31.5000 32.0000 32.5000 32.6000 32.7000 32.8000 32.9000

1.0000 1.6124 2.0688 3.2462 3.9826 4.8285 5.7920 6.8863 8.1162 8.7886 9.5003 10.25250 11.05160 11.89890 12.07510 12.25360 12.43520 12.61830

101.33 163.38 209.62 328.92 403.54 489.25 586.87 697.75 822.37 890.51 962.62 1038.830 1119.800 1205.660 1223.510 1241.600 1260.000 1278.550

41.1134 39.5941 38.8200 37.4665 36.8767 36.3394 35.8513 35.4099 35.0128 34.8304 34.6585 34.4968 34.3453 34.2039 34.1768 34.1501 34.1238 34.0979

20.21920 5.8260 5.7490 5.6115 5.5488 5.4901 5.4353 5.3860 5.3394 5.3182 5.2979 5.2785 5.2608 5.2445 5.2415 5.2387 5.2360 5.2333

$<. §X@8 ©#›C !"$ wª C  KL"+ :% W«&4›  :% U


` !5 E8 (normal boiling point, T^b

= 20.268 K)# temperature modulus X0 vapor pressure modulus Y6 =&89 :%&;<. JJ 

!" &' Y "# =&;£ X "# =

& >?@8 n "# .‡ <. l@ n "

# W!&' X6 =&;I 3 (7)$
”Ž `¬

4 X" &' Y"# +\(plotting)&;<. n=5

&' X0 Y ­ W
”^|I =rX

® Weber ¯⁹  MN0 = X0 Y "

# Table 1 °\&;<. CU 5$C MN± C

?e Q8 Fig. 1 °\^w q<.  §

(X²41.0) ¦³@ Y"$ 5´k µw[ D# p  q89 $D2 §$ ‰]¶$ ^8 D# °

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(10)

n=50 §X ­·C !5 E8 (T^b=

20.268 K) T^r1=0.61463 &' ¢ C¸8 X

= 41.11$ <. Fig. 1@ °\ 8

Y = 1.48129 + 0.11X (11)

X@ C = 1.48129, D = 0.11$ <. CU 3 (5)0 3 (4)X‘Ÿ B0 A6 7& B = -2.75, A = 2.64 W

<.

d dT_r

--- T( _rⁿ–T_r1ⁿ) n² 1 T_r --- 1

T_r1 ---

 – 

 

–

d dT_r --- ln T_r

T_r1 ---

  

--- nT_rⁿ n² T_r --- +

=

Fig. 1. Relationship between X and Y for the vapor pressure data of parahydrogen (n=5). Ref. 1. Ancsin³, 2. Barber and Horsford⁴, 3. Hoge and Arnold⁵, 4. Keesom et al.⁶, 5. Roder et al.⁷, 6. Van Itterbeek et al.⁸, 7. Weber et al.⁹.

Table 2. Experimental and calculated vapor pressures for parahydrogen

Temp. [K] Vapor pressure [kPa]

Source Exptl. Calc. Dev.(%)

c13.8030^a

c13.8030^a 16.2885 16.9652 17.1980 17.3890 17.8194 18.5712 18.7960 19.0503 20.0301

c20.2680^b 20.3969 20.5067 20.8555 21.1946 21.6773 22.2504 22.5692 22.7720 22.8958 23.0000 23.6341 24.6800 31.3921 31.5000 31.8810 32.0000 32.1292 32.2760 32.3753 32.5000 32.6000 32.6357 32.7000 32.8000 32.8833 32.9000

c32.9760^c

117.035 117.039 124.401 32.41 35.59 38.37 45.12 58.94 63.66 69.27 94.35 101.331 105.271 108.681 120.081 131.961 1150.281 1174.441 1188.801 1198.421 1204.64 1 1209.621 1243.591 1306.871 1021.301 1038.8 01 1100.601 1119.801 1140.901 1166.901 1183.201 1205.701 1223.501 1229.20 1 1241.601 1260.001 1275.401 1278.501 1292.801

17.001 17.001 24.430 32.420 35.570 38.330 45.100 58.980 63.680 69.310 194.420 101.390 105.310 108.740 120.160 132.050 150.400 174.440 188.930 198.570 204.620 209.820 243.460 306.970 1021.4001 1038.3001 1099.9001 1119.7001 1141.500v 1166.7001 1184.0001 1206.0001 1223.8001 1230.2001 1241.9001 1260.1001 1275.5001 1278.6001 1292.8001

−0.48

−0.54

−0.10

−0.03

−0.05

−0.11

−0.04

−0.07

−0.03

−0.07

−0.08

−0.06

−0.04

−0.05

−0.06

−0.07

−0.08

−0.00

−0.07

−0.07

−0.01

−0.10

−0.05

−0.03

−0.01

−0.05

−0.60

−0.01

−0.05

−0.01

−0.06

−0.03

−0.03

−0.09

−0.02

−0.01

−0.01

−0.01 0.00

3 5 4 5 6 6 5 5 6 4 5 5 5 5 5 5 5 5 5 7 5 8 5 7 5 8 5 8 5 7 5 8 8 5 8 8 5 8 7

aTriple point, ^bNormal boiling point, ^cCritical point

  

5 A, B, C G D0 4 n" Œ¹
2 P ]7

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TUV σ8 3 (12)0 1$ 7ÁI ’ MN±  X TUV6 =&;<.

(12)

7J MN± C 153J  !" &' () ()*+ ,-  x!3# O%

? P Q RSTUV8 0.21%;<.

4 n = 5 "$ ¾´C46 af& >?@ 5$

C n " &' 5C x†# ÃÄ O%&;I ’

’ n " l <Å A, B, C G D"$ Q!^|<.

n = 3, 4, 5, 6, 7  C TUVW Fig. 2 °\^

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!"# :%&' () ()*+ ,- 

 x!3 50 46 7&;I Q! 32 <

š 1<.

# =& >?@ ABC D2 !5 E8  (Tb= 20.268 K), F(P^c= 1292.81 kPa) *+

(Tc= 32.976 K)H$I 153J   !

" O%C Q 0.21% RSTUV6  |<.



A, B, C, D : constants, Eq. (3) [-]

A', B', C', D' : constants, Eq. (1) [-]

n : exponent, Eq. (2) [-]

P : vapor pressure [kPa]

Pr : reduced vapor pressure, P/Pc [-]

T : absolute temperature [K]

Tr : reduced temperature, T/Tc [-]

X : temperature modulus, Eq. (8) [-]

Y : vapor pressure modulus, Eq. (9) [-]



1 : reference point

b : normal boiling point

c : critical point

r : reduced value

   

1. Frost, A. A.; Kalkwarf, D. R. J. Chem. Phys. 1953, 21, 264.

σ 1 N----

= P_exp–P_calc P_exp

--- 100×

 

 

i 1= i

∑

lnP_r 2.64 2.75 T_r

--- 1.48129lnT+ _r+0.11T_r⁵ –

= Table 3. Average deviations between experimental and calcu-

lated vapor pressures of parahydrogen

Source No. of points Average

deviation(%) Ancsin³

Barber and Horsford⁴ Hoge and Arnold⁵ Keesom et al.⁶ Roder et al.⁷ Van Itterbeek et al.⁸ Weber et al.⁹

11 10 48 12 11 41 40

0.48 0.16 0.14 0.32 0.00 0.38 0.09

7 sources 1531 0.21

Fig. 2. Relationship between n and average devitation for parahydrogen.

2. Chung, J. G.; Thodos, G. Chem. Eng. J. (Netherlands) 1976, 12, 219.

3. Ancsin, J. Metrologia 1977, 13, 79.

4. Barber, C. R.; Horsford, A. Brit. J. Appl. Phys. 1963, 14, 920.

5. Hoge, H. J.; Arnold, R. D. J. Res. Natl. Bur. Stds. 1951, 47, 63.

6. Keesom, W. H.; Bijl, A.; van der Horst, H. Comm. No.

217a, Leiden. Proc. Acad. Sci. Amsterdam. 1931, 34, 1223.

7. Roder, H. M.; Diller, D. E.; Weber, L. A.; Goodwin, R. D.

Cryogenics 1963, 3, 16.

8. Van Itterbeek, A.; Verbeke, O.; Theewes, F.; Staes, K.;

De Boelpaep, J. Physica 1964, 30, 1238.

9. Weber, L. A.; Diller, D. E.; Roder, H. M.; Goodwin, R. D.

Cryogenics, 1962, 2, 236.

10. Pavese, F. J. Chem. Thermodynamics 1993, 25, 1351.

11. Plank, R.; Riedel, L. Ing. Arch. 1948, 16, 255.

12. idem.: Tex. J. Sci. 1949, 1, 86.

13. Goodwin, R. D. J. Res. Natl. Bur. Stand., Sect. A 1969, 73A, 487.