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The concentration dependence of the diffusion coefficient of the system helium - neon at 300 K and one atmosphere pressure
Volume 38A, number 4
THE
P H Y S I C S LE TTE RS
CCNCENTRATION COEFFICIENT AT
300
DEPENDENCE OF
K AND
THE
ONE
SYSTEM
14 February 1972
OF
THE
HELIUM
ATMOSPHERE
DIFFUSION - NEON
PRESSURE
M. A. YABSLEY and P.. J. DUNLOP
Department of Physical and Inorganic Chemistry, University of Adelaide, Adelaide, South Australia 5001 Received 29 Dece~k)er 1971 The concentration dependence of the diffusion coefficient of the system He-Ne has been measured at 300 K and one atmosphere pressure. In agreement with Hogervorst, the data indicate that the results of Van Heijningen et al. may be in error. In the l a s t five y e a r s Van Heijningen et al.[2] and H o g e r v o r s t [1, 3] have r e p o r t e d diffusion data f o r all of the p o s s i b l e b i n a r y m i x t u r e s of the noble g a s e s . Th e f o r m e r w o r k e r s u s e d the t w o - b u l b technique of New and A r m i s t e a d [ 4 ] to obtain data below 400 K, while the l a t t e r r e s e a r c h w o r k e r e m p l o y e d a t e c h n iq u e which he had r e c e n t l y d ev el o p ed to make m e a s u r e m e n t s up to 1400 K. When c o m p a r i n g r e s u l t s with t h o s e of Van Heijningen et at., H o g e r v o r s t noted that his b i nary diffusion c o e f f i c i e n t s f o r the s y s t e m H e - N e w e r e a p p r o x i m a t e l y 3% h i g h e r at 300 K than the c o r r e s p o n d i n g r e s u l t s of the f o r m e r w o r k e r s . A s m a l l e x t r a p o l a t i o n o v e r a five d e g r e e t e m p e r a t u r e i n t e r v a l was n e c e s s a r y to enable a d i r e c t c o m p a r i s o n of the two s e t s of data. TabLe 1 Diffusion coefficients for the system helium-neon at 300 K and 1 atmosphere X~e 0.0969 0.2245 0~376 0.3824 0.4312 0.4530 0.5182 0.6069 0.6710 0.7011 0.7786 0.8078 0.8978 0.9148
Pexp (atm) 1.0003 0.9998 1.0019 1.5464 1.0007 1.5331 0.9999 1.0003 1.4321 0.9998 1.4339 1.0006 1.4338 1.0010
(c/)12)exp (cm2/sec) 1.0949 1A002 1.1034 0.7140 1.1083 0.7231 1.1046 1.1070 0.7759 1.1124 0.7765 1.1158 0.7798 1~186
* XNe is ~he mole fraction of neon.
¢-D12 (cm2/see) 1.0954 1.1000 1.1055 1.1042 1.1091 1.1092 1.1045 1.1073 1.1112 1.1122 1.1134 1.1165 1.1181 1.1197
1.12
I
I 0.2"/,
oO
D12 .1G
1.0e
0'. 2
0~./.
0a.6
0'.0
X2 Fig.1. Binary diffusion coefficients for the system He-Ne at 300 K and 1 atmosphere: O, present results; [] Van Heijningen et al. [2]; ~, Hogervorst [1]. Using a new method[5] which we have r e c e n t l y d ev el o p ed f o r m e a s u r i n g b i n a r y diffusion c o e f f i c i e n t s in the gas p h a s e , the c o n c e n t r a t i o n dependence of the diffusion c o e f f i c i e n t of the s y s t e m H e - N e was m e a s u r e d at 300 K and 1 a t m o s p h e r e p r e s s u r e . All the e x p e r i m e n t a l d e t a i l s have been g i v en p r e v i o u s l y [5]. The r e s u l t s a r e s u m m a r i s e d in t ab l e 1, and c o m p a r e d with the r e s u l t s of Van Heijningen et at. and of H o g e r v o r s t in r i g A . It i s s e e n that in the r e g i o n w h e r e the m o l e f r a c t i o n of neon a p p r o a c h e s z e r o , the r e s u l t s of H o g e r v o r s t a g r e e with our data within h i s e s t i m a t e d e r r o r of 0.5 to 1%, but that the r e s u l t s of Van Hiejningen et at. a r e 2.5% low. Th e data in table 1 may be r e p r e s e n t e d with an a v e r a g e d ev i at i o n of ±0.14% by the l i n e a r r e l a t i o n q)12 = 1-0944 + 0.02609 x2 w h e r e (D 12 i s the b i n a r y diffusion c o e f f i c i e n t , and 247
Volume 38A, number 4
PHYSICS LETTERS
x 2 is the mole f r a c t i o n of the heavy component. In t h e i r p a p e r Van Heijningen et al. noted that t h e i r e x p e r i m e n t a l c o n c e n t r a t i o n dependences of the diffusion coefficients of those b i n a r y noble gas m i x t u r e s c o n t a i n i n g helium were l a r g e r by a p p r o x i m a t e l y 2% than those p r e d i c t e d f r o m the C h a p m a n - E n s k o g t h e o r y and the L e n n a r d - J o n e s (12,6) potential. The r e s u l t s for He-Ne r e p o r t e d in this note give a c o n c e n t r a t i o n dependence, [(~12(x2 = 1)/O12(x2 = 0)], of 1.024 c o m p a r e d to the t h e o r e t i c a l value of 1.032 c a l c u l a t e d u s i n g
248
14 February 1972
the potential p a r a m e t e r s of H o g e r v o r s t [1].
References [1] w. Hogervorst, Phsyica 51 (1971) 59. [2] R.J.J. Van Heijningen, J.P. Harpe and J.J.M. Beenakker, Physica 38 (1968) 1. [3] W. Hogervorst and J. Freudenthal, Physica 37 (1967) 97. [4] E. P. Ney and F. C. Armistead, Phys. Rev. 71 (1947) 14. [5] P.J. Carson, T. N. Be.. and P. U. Dunlop, J. Chem. Phys. 56 (1972) 531.
THE
P H Y S I C S LE TTE RS
CCNCENTRATION COEFFICIENT AT
300
DEPENDENCE OF
K AND
THE
ONE
SYSTEM
14 February 1972
OF
THE
HELIUM
ATMOSPHERE
DIFFUSION - NEON
PRESSURE
M. A. YABSLEY and P.. J. DUNLOP
Department of Physical and Inorganic Chemistry, University of Adelaide, Adelaide, South Australia 5001 Received 29 Dece~k)er 1971 The concentration dependence of the diffusion coefficient of the system He-Ne has been measured at 300 K and one atmosphere pressure. In agreement with Hogervorst, the data indicate that the results of Van Heijningen et al. may be in error. In the l a s t five y e a r s Van Heijningen et al.[2] and H o g e r v o r s t [1, 3] have r e p o r t e d diffusion data f o r all of the p o s s i b l e b i n a r y m i x t u r e s of the noble g a s e s . Th e f o r m e r w o r k e r s u s e d the t w o - b u l b technique of New and A r m i s t e a d [ 4 ] to obtain data below 400 K, while the l a t t e r r e s e a r c h w o r k e r e m p l o y e d a t e c h n iq u e which he had r e c e n t l y d ev el o p ed to make m e a s u r e m e n t s up to 1400 K. When c o m p a r i n g r e s u l t s with t h o s e of Van Heijningen et at., H o g e r v o r s t noted that his b i nary diffusion c o e f f i c i e n t s f o r the s y s t e m H e - N e w e r e a p p r o x i m a t e l y 3% h i g h e r at 300 K than the c o r r e s p o n d i n g r e s u l t s of the f o r m e r w o r k e r s . A s m a l l e x t r a p o l a t i o n o v e r a five d e g r e e t e m p e r a t u r e i n t e r v a l was n e c e s s a r y to enable a d i r e c t c o m p a r i s o n of the two s e t s of data. TabLe 1 Diffusion coefficients for the system helium-neon at 300 K and 1 atmosphere X~e 0.0969 0.2245 0~376 0.3824 0.4312 0.4530 0.5182 0.6069 0.6710 0.7011 0.7786 0.8078 0.8978 0.9148
Pexp (atm) 1.0003 0.9998 1.0019 1.5464 1.0007 1.5331 0.9999 1.0003 1.4321 0.9998 1.4339 1.0006 1.4338 1.0010
(c/)12)exp (cm2/sec) 1.0949 1A002 1.1034 0.7140 1.1083 0.7231 1.1046 1.1070 0.7759 1.1124 0.7765 1.1158 0.7798 1~186
* XNe is ~he mole fraction of neon.
¢-D12 (cm2/see) 1.0954 1.1000 1.1055 1.1042 1.1091 1.1092 1.1045 1.1073 1.1112 1.1122 1.1134 1.1165 1.1181 1.1197
1.12
I
I 0.2"/,
oO
D12 .1G
1.0e
0'. 2
0~./.
0a.6
0'.0
X2 Fig.1. Binary diffusion coefficients for the system He-Ne at 300 K and 1 atmosphere: O, present results; [] Van Heijningen et al. [2]; ~, Hogervorst [1]. Using a new method[5] which we have r e c e n t l y d ev el o p ed f o r m e a s u r i n g b i n a r y diffusion c o e f f i c i e n t s in the gas p h a s e , the c o n c e n t r a t i o n dependence of the diffusion c o e f f i c i e n t of the s y s t e m H e - N e was m e a s u r e d at 300 K and 1 a t m o s p h e r e p r e s s u r e . All the e x p e r i m e n t a l d e t a i l s have been g i v en p r e v i o u s l y [5]. The r e s u l t s a r e s u m m a r i s e d in t ab l e 1, and c o m p a r e d with the r e s u l t s of Van Heijningen et at. and of H o g e r v o r s t in r i g A . It i s s e e n that in the r e g i o n w h e r e the m o l e f r a c t i o n of neon a p p r o a c h e s z e r o , the r e s u l t s of H o g e r v o r s t a g r e e with our data within h i s e s t i m a t e d e r r o r of 0.5 to 1%, but that the r e s u l t s of Van Hiejningen et at. a r e 2.5% low. Th e data in table 1 may be r e p r e s e n t e d with an a v e r a g e d ev i at i o n of ±0.14% by the l i n e a r r e l a t i o n q)12 = 1-0944 + 0.02609 x2 w h e r e (D 12 i s the b i n a r y diffusion c o e f f i c i e n t , and 247
Volume 38A, number 4
PHYSICS LETTERS
x 2 is the mole f r a c t i o n of the heavy component. In t h e i r p a p e r Van Heijningen et al. noted that t h e i r e x p e r i m e n t a l c o n c e n t r a t i o n dependences of the diffusion coefficients of those b i n a r y noble gas m i x t u r e s c o n t a i n i n g helium were l a r g e r by a p p r o x i m a t e l y 2% than those p r e d i c t e d f r o m the C h a p m a n - E n s k o g t h e o r y and the L e n n a r d - J o n e s (12,6) potential. The r e s u l t s for He-Ne r e p o r t e d in this note give a c o n c e n t r a t i o n dependence, [(~12(x2 = 1)/O12(x2 = 0)], of 1.024 c o m p a r e d to the t h e o r e t i c a l value of 1.032 c a l c u l a t e d u s i n g
248
14 February 1972
the potential p a r a m e t e r s of H o g e r v o r s t [1].
References [1] w. Hogervorst, Phsyica 51 (1971) 59. [2] R.J.J. Van Heijningen, J.P. Harpe and J.J.M. Beenakker, Physica 38 (1968) 1. [3] W. Hogervorst and J. Freudenthal, Physica 37 (1967) 97. [4] E. P. Ney and F. C. Armistead, Phys. Rev. 71 (1947) 14. [5] P.J. Carson, T. N. Be.. and P. U. Dunlop, J. Chem. Phys. 56 (1972) 531.