- Email: [email protected]
Vib-Vib transitions in mixtures of methane and hydrogen sulfide compared with those in the system methane-water vapour
Physica 47 (1970) 58-63
o North-Hoiland Publishing Co.
VIB-VIB OF METHANE WITH
THOSE H.-J.
TRANSITIONS AND
IN THE
BAUER,
IN MIXTURES
HYDROGEN SYSTEM
SULFIDE
COMPARED
METHANE-WATER
A. C. C. PAPHITIS
VAPOUR
and R. SCHOTTER
I. Physikalisches Institut der Universitiit Stuttgart, Stuttgart, Deutschland Received 21 August 1969
Synopsis The sound absorption in mixtures of CH4 with HsS has been measured from 3 x 1C to 2 x 107 Hz/atm at 25% over the entire composition range. The results are ana lyzed in terms of Vib-Vib transitions. In comparing with the system CH4-HsO it ha been taken into account that the HsS quantum fits better into the lowest, the Ha( quantum into the second excited level of CHa. In the latter case a detailed analysis performed on the measurements of Monkewicz (J. Acoust. Sot. Amer.) yielded th Vib-Vib transition probabilities between those two levels of CH4.
1. Introduction. The efficiency for the transfer of vibrational energy fron one molecule to a different one in a single collision by means of an energ; “flip-flop” process (so-called Vib-Vib transition) can be determined by al investigation of the relaxational behaviour of gaseous mixtures of the twc molecules. The most simple system, namely a mixture of two gases eacl with one excited state only, exhibits two relaxation processes. It has bee] shown theoretically 192~3) that the relation between composition %B and th isothermal relaxation rates l/TpT is quadratic, i.e., if one plots the l/TpT’ vs. the mole-fractions xn one obtains a conic section. Through this thm probabilities of the four Vib-Trans-transitions (Ai or Bi + A or B $ A or Be + A or B) and of the Vib-Vib-exchange (Ai + Bo f Ao + Bi) car be determined. In order to obtain the relaxation rates l/TpT in the total composition range we measure the sound absorption of the mixtures. In principle, eacl relaxation process delivers its absorption maximum though the faste: process may be indetectable experimentally because of a too small relax ation strength (relaxing molar heat capacity SC) 214). The evaluation of the isothermal 1/TpT’s from the positions of the maxim: on the f/+ scale involves some algebra, but can be done straightforwardlyl) If one of the molecules possesses more than one populated excited statt
vm-vm
2295
010
i!y
ooo
TRANSITIONS
IN CH4-HZS MIXTURES
~f!!;:v:;#3
59
2~;~~~~o
t HP Fig.
1.
C",
“2s
mechanisms and reciprocal transition probabilities for the systems and CH4-H20. The unchanged collision partner, if present, is indicated
Reaction
CHrHzS
between parantheses.
two different
cases must be distinguished:
‘1
The close resonance occurs between the lowest excited levels. Then the relaxational behaviour is very similar to the “binary two-level” case, especially if the higher levels contribute only a small amount to the vibrational heat capacity.
2)
The close resonance is into a higher excited level. Then this higher level must be taken into account because the heteromolecular Vib-Vib exchange is then followed by a de-excitation process into the lowest excited level. Both transition probabilities are relevant for the relaxational behaviour. The more complicated theoretical analysis of these systems (their relaxation rates can be calculated only numerically), however, yields more information: it furnishes the transition probability of that second step, which is a Vib-Vib exchange within the same molecule.
The very difference between the systems though similar in many other propertiess), belongs to case 1, the latter to case 2 (cf. fig. ments in the system CHa-HsS are reported ments of Monkewicze) in CHJ-HsO mixtures.
CHd-HsS and CHd-HsO, alis the fact that the former 1). In what follows, measureand compared with measure-
2. Experimental results in CHd-Hz.5 mixtures. The sound absorption per wavelength ,u has been measured in five different mixtures from 3 x 104 to 2 x 107 Hz/atm at 25°C in a parallel-path pulsed apparatus (1 MHz). The HsS was supplied by Gerling, Holz and Co. and purified by fractional distillation. The CH4 has been taken directly from the container with a purity of 99.995%.
60
H.-J.
BAUER,
A.
C. C. PAPHITIS
AND
R.
SCHOTTER
10.9% H,S 26.3 *I~ 42.57%
Fig. 2. Sound
absorption
per wavelength
in CH4-HsS
mixtures
at 25°C
i
-
b C’+L
d.5
XHZS
A.;
I
Fig. 4. Relaxing molar heat capacity of the CH4-HsS mixtures. total vibrational heat capacity of the mixtures.
VIB-VIB
1
TRANSITIONS
I
IN CH4-H&
I
I
MIXTURES
61
I
0.3 0.5 0.7 0.9 Fig, 3. Isothermal relaxation rates in CH4-HzS mixtures. 0.1
Fig. 2 shows the results. The solid lines are least squares fits of a single Debye absorption curve plus an absorption proportional to f/fi due to viscothermal loss and rotational relaxation. From the (f/fi)max and pmax values the isothermal relaxation rates l/TPT and the relaxing molar heat capacities SC have been calculated as usual (figs. 3 and 4). From fig. 4 we gather that approximately the total vibrational heat capacity Cvib of the mixtures (solid line) relaxes in the single process found experimentally. The second, faster process, expected from the theory, therefore has too small a relaxation strength to be detected. However, the nonlinear dependence of l/TpT on the composition supplies enough information to construct the entire conic section.
H.-J.
62
BAUER,
A.
C. C. PAPHITIS
AND
R.
SCHOTTER
3. Disctission. 3.1. CHd-H&S system. In using the conic section equation of the binary two-level model we neglect all higher excited levels, especially the twofold state CH4 (0100). The better resonance to the threefold CH4 (0001) level justifies that neglection. Moreover, a strict calculation including both the (0100) and the (0001) levels with a high transition probability in between (as resulting from an analysis of Monkewicz’s data in CHb--HsO, see below) needs nearly the same transition probabilities as the binary two-level approximation to explain the experimental result. Fig. 1 contains the reciprocal transition probabilities; for Vib-Trans transitions the collision partner is shown between parantheses. The fastest reaction is, as expected, the Vib-Vib process, where only 50 collisions in the mean transfer one HsS (010) quantum onto the methane molecule. Furthermore, HsS is a ten-fold more effective collision partner for the Vib-Trans deexcitation of methane than methane itself. The Vib-Trans efficiency of CHJ for the de-excitation of HsS could not be determined since the relaxational behaviour of the mixtures is (within the experimental accuracy) not sensitive on that parameter. 3.2. CH4-HsO system. Fig. 5 shows Monkewicz’s6) results in CH4-Hz0 mixtures. They have been analyzed by Monkewicz himself by the use of the Tuesday-Boudart approach which is an approximate theory even in the binary two-level case. A strict binary two-level analysis by one of us7) yielded different transition probabilities. The details of the Vib-Vib transfer, however, were suppressed by the fact that the excited levels of CH4 have been substituted by a five-fold mean level. A better analysis must consider the CH4 (0001) and CH4 (0100) levels separately, as is done in fig. 1 and the following reaction scheme : la, b:
HsO (010)
+ (Hz0 or CH4) $ Hz0 (000)
2a, b:
CH4 (0001) + (Hz0 or CH4) + CHJ (0000) + (Hz0 or CH4) ;
3:
HZ0 (0 10)
4a, b:
CH4 (0100) + (Hz0 or CH4) f
+ CH4 (0000)
$ HZ0 (000)
+ (Hz0 or CH4);
+ CH4 (0100) ;
CH4 (0001) + (Hz0 or CH4).
Reactions 1 and 2 describe the de-excitation of the HsO and the CH4 molecule, respectively, in collisions of the Vib-Trans type, whereas reactions 3 and 4 pay regard to the Vib-Vib step process, causing de-excitation of the Hz0 molecule onto the lowest excited mode of CH4. Two of the seven transition probabilities (1 at, 2b) were considered fixed since they result from the measurements in the pure components. The other five have been determined by a least squares fit to the data of Monkewicz. They are shown in fig. 1. Again one sees the high efficiency of the heterot We selected in pure water
PI,
=
vapours.9)
l/87)
instead
but causes
of l/87 a much
which worse
value
results
fit to the data.
from
measurements
VIB-VIB
TRANSITIONS
0.1
IN CH4-H&S MIXTURES
0.2
Fig. 5. Isothermal relaxation rates in CH4-He0
63
0.3 mixtures (Monkewicz, ref. 6).
molecular Vib-Vib transition (3). In addition, the Vib-Vib process (0100) f (0001) within the methane is very fast too, a fact which is responsible for the single relaxation of pure methane due to a close thermodynamic coupling of those two levels. The transition probabilities of both processes agree rough1Y with the results of the binary two-level analysis (1 /P M 8, ref. 7). REFERENCES
1) Bauer, H.-J., Physical Acoustics, W. P. Mason ed., Vol. IIA, pp. 47-131, Acad. 4 3) 4) 5) 6) 7) 8) 9)
Press (New York, 1965). Bauer, H.-J. and Roesler, H., 2. Naturforsch. 19 (1964) 656. Bauer, H.-J. and Schotter, R., J. them. Phys. 51 ( 1969) 326 1. Bauer, H.-J. and Roesler, H., Molecular Relaxation Processes, The Chemical Society Special Publication 20 (1966) 245. Bauer, H.-J., Paphitis, A. C. C. and Schotter, R., Physica 47 (1970) 109. Monkewicz, A. A., J. Acoust. Sot. Amer. 42 (1967) 258. Bauer, H.-J., J. Acoust. Sot. Amer. 44 (1968) 255. Roesler, H. and Sahm, K. F., J. Acoust. Sot. Amer. 37 (1965) 386. Yamada, K. and Fujii, Y., J. Acoust. Sot. Amer. 39 (1966) 250.
o North-Hoiland Publishing Co.
VIB-VIB OF METHANE WITH
THOSE H.-J.
TRANSITIONS AND
IN THE
BAUER,
IN MIXTURES
HYDROGEN SYSTEM
SULFIDE
COMPARED
METHANE-WATER
A. C. C. PAPHITIS
VAPOUR
and R. SCHOTTER
I. Physikalisches Institut der Universitiit Stuttgart, Stuttgart, Deutschland Received 21 August 1969
Synopsis The sound absorption in mixtures of CH4 with HsS has been measured from 3 x 1C to 2 x 107 Hz/atm at 25% over the entire composition range. The results are ana lyzed in terms of Vib-Vib transitions. In comparing with the system CH4-HsO it ha been taken into account that the HsS quantum fits better into the lowest, the Ha( quantum into the second excited level of CHa. In the latter case a detailed analysis performed on the measurements of Monkewicz (J. Acoust. Sot. Amer.) yielded th Vib-Vib transition probabilities between those two levels of CH4.
1. Introduction. The efficiency for the transfer of vibrational energy fron one molecule to a different one in a single collision by means of an energ; “flip-flop” process (so-called Vib-Vib transition) can be determined by al investigation of the relaxational behaviour of gaseous mixtures of the twc molecules. The most simple system, namely a mixture of two gases eacl with one excited state only, exhibits two relaxation processes. It has bee] shown theoretically 192~3) that the relation between composition %B and th isothermal relaxation rates l/TpT is quadratic, i.e., if one plots the l/TpT’ vs. the mole-fractions xn one obtains a conic section. Through this thm probabilities of the four Vib-Trans-transitions (Ai or Bi + A or B $ A or Be + A or B) and of the Vib-Vib-exchange (Ai + Bo f Ao + Bi) car be determined. In order to obtain the relaxation rates l/TpT in the total composition range we measure the sound absorption of the mixtures. In principle, eacl relaxation process delivers its absorption maximum though the faste: process may be indetectable experimentally because of a too small relax ation strength (relaxing molar heat capacity SC) 214). The evaluation of the isothermal 1/TpT’s from the positions of the maxim: on the f/+ scale involves some algebra, but can be done straightforwardlyl) If one of the molecules possesses more than one populated excited statt
vm-vm
2295
010
i!y
ooo
TRANSITIONS
IN CH4-HZS MIXTURES
~f!!;:v:;#3
59
2~;~~~~o
t HP Fig.
1.
C",
“2s
mechanisms and reciprocal transition probabilities for the systems and CH4-H20. The unchanged collision partner, if present, is indicated
Reaction
CHrHzS
between parantheses.
two different
cases must be distinguished:
‘1
The close resonance occurs between the lowest excited levels. Then the relaxational behaviour is very similar to the “binary two-level” case, especially if the higher levels contribute only a small amount to the vibrational heat capacity.
2)
The close resonance is into a higher excited level. Then this higher level must be taken into account because the heteromolecular Vib-Vib exchange is then followed by a de-excitation process into the lowest excited level. Both transition probabilities are relevant for the relaxational behaviour. The more complicated theoretical analysis of these systems (their relaxation rates can be calculated only numerically), however, yields more information: it furnishes the transition probability of that second step, which is a Vib-Vib exchange within the same molecule.
The very difference between the systems though similar in many other propertiess), belongs to case 1, the latter to case 2 (cf. fig. ments in the system CHa-HsS are reported ments of Monkewicze) in CHJ-HsO mixtures.
CHd-HsS and CHd-HsO, alis the fact that the former 1). In what follows, measureand compared with measure-
2. Experimental results in CHd-Hz.5 mixtures. The sound absorption per wavelength ,u has been measured in five different mixtures from 3 x 104 to 2 x 107 Hz/atm at 25°C in a parallel-path pulsed apparatus (1 MHz). The HsS was supplied by Gerling, Holz and Co. and purified by fractional distillation. The CH4 has been taken directly from the container with a purity of 99.995%.
60
H.-J.
BAUER,
A.
C. C. PAPHITIS
AND
R.
SCHOTTER
10.9% H,S 26.3 *I~ 42.57%
Fig. 2. Sound
absorption
per wavelength
in CH4-HsS
mixtures
at 25°C
i
-
b C’+L
d.5
XHZS
A.;
I
Fig. 4. Relaxing molar heat capacity of the CH4-HsS mixtures. total vibrational heat capacity of the mixtures.
VIB-VIB
1
TRANSITIONS
I
IN CH4-H&
I
I
MIXTURES
61
I
0.3 0.5 0.7 0.9 Fig, 3. Isothermal relaxation rates in CH4-HzS mixtures. 0.1
Fig. 2 shows the results. The solid lines are least squares fits of a single Debye absorption curve plus an absorption proportional to f/fi due to viscothermal loss and rotational relaxation. From the (f/fi)max and pmax values the isothermal relaxation rates l/TPT and the relaxing molar heat capacities SC have been calculated as usual (figs. 3 and 4). From fig. 4 we gather that approximately the total vibrational heat capacity Cvib of the mixtures (solid line) relaxes in the single process found experimentally. The second, faster process, expected from the theory, therefore has too small a relaxation strength to be detected. However, the nonlinear dependence of l/TpT on the composition supplies enough information to construct the entire conic section.
H.-J.
62
BAUER,
A.
C. C. PAPHITIS
AND
R.
SCHOTTER
3. Disctission. 3.1. CHd-H&S system. In using the conic section equation of the binary two-level model we neglect all higher excited levels, especially the twofold state CH4 (0100). The better resonance to the threefold CH4 (0001) level justifies that neglection. Moreover, a strict calculation including both the (0100) and the (0001) levels with a high transition probability in between (as resulting from an analysis of Monkewicz’s data in CHb--HsO, see below) needs nearly the same transition probabilities as the binary two-level approximation to explain the experimental result. Fig. 1 contains the reciprocal transition probabilities; for Vib-Trans transitions the collision partner is shown between parantheses. The fastest reaction is, as expected, the Vib-Vib process, where only 50 collisions in the mean transfer one HsS (010) quantum onto the methane molecule. Furthermore, HsS is a ten-fold more effective collision partner for the Vib-Trans deexcitation of methane than methane itself. The Vib-Trans efficiency of CHJ for the de-excitation of HsS could not be determined since the relaxational behaviour of the mixtures is (within the experimental accuracy) not sensitive on that parameter. 3.2. CH4-HsO system. Fig. 5 shows Monkewicz’s6) results in CH4-Hz0 mixtures. They have been analyzed by Monkewicz himself by the use of the Tuesday-Boudart approach which is an approximate theory even in the binary two-level case. A strict binary two-level analysis by one of us7) yielded different transition probabilities. The details of the Vib-Vib transfer, however, were suppressed by the fact that the excited levels of CH4 have been substituted by a five-fold mean level. A better analysis must consider the CH4 (0001) and CH4 (0100) levels separately, as is done in fig. 1 and the following reaction scheme : la, b:
HsO (010)
+ (Hz0 or CH4) $ Hz0 (000)
2a, b:
CH4 (0001) + (Hz0 or CH4) + CHJ (0000) + (Hz0 or CH4) ;
3:
HZ0 (0 10)
4a, b:
CH4 (0100) + (Hz0 or CH4) f
+ CH4 (0000)
$ HZ0 (000)
+ (Hz0 or CH4);
+ CH4 (0100) ;
CH4 (0001) + (Hz0 or CH4).
Reactions 1 and 2 describe the de-excitation of the HsO and the CH4 molecule, respectively, in collisions of the Vib-Trans type, whereas reactions 3 and 4 pay regard to the Vib-Vib step process, causing de-excitation of the Hz0 molecule onto the lowest excited mode of CH4. Two of the seven transition probabilities (1 at, 2b) were considered fixed since they result from the measurements in the pure components. The other five have been determined by a least squares fit to the data of Monkewicz. They are shown in fig. 1. Again one sees the high efficiency of the heterot We selected in pure water
PI,
=
vapours.9)
l/87)
instead
but causes
of l/87 a much
which worse
value
results
fit to the data.
from
measurements
VIB-VIB
TRANSITIONS
0.1
IN CH4-H&S MIXTURES
0.2
Fig. 5. Isothermal relaxation rates in CH4-He0
63
0.3 mixtures (Monkewicz, ref. 6).
molecular Vib-Vib transition (3). In addition, the Vib-Vib process (0100) f (0001) within the methane is very fast too, a fact which is responsible for the single relaxation of pure methane due to a close thermodynamic coupling of those two levels. The transition probabilities of both processes agree rough1Y with the results of the binary two-level analysis (1 /P M 8, ref. 7). REFERENCES
1) Bauer, H.-J., Physical Acoustics, W. P. Mason ed., Vol. IIA, pp. 47-131, Acad. 4 3) 4) 5) 6) 7) 8) 9)
Press (New York, 1965). Bauer, H.-J. and Roesler, H., 2. Naturforsch. 19 (1964) 656. Bauer, H.-J. and Schotter, R., J. them. Phys. 51 ( 1969) 326 1. Bauer, H.-J. and Roesler, H., Molecular Relaxation Processes, The Chemical Society Special Publication 20 (1966) 245. Bauer, H.-J., Paphitis, A. C. C. and Schotter, R., Physica 47 (1970) 109. Monkewicz, A. A., J. Acoust. Sot. Amer. 42 (1967) 258. Bauer, H.-J., J. Acoust. Sot. Amer. 44 (1968) 255. Roesler, H. and Sahm, K. F., J. Acoust. Sot. Amer. 37 (1965) 386. Yamada, K. and Fujii, Y., J. Acoust. Sot. Amer. 39 (1966) 250.