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Foreign gas broadening of difluoromethane by N2, O2 and CO2
J Quonr Spp~lrosc. Rodur. Printed ,n the U.S.A.
Transler Vol. 33, No. 1. pp. 89-91.
1985
0022-4073185 $3.00 + .oO Pergamon Press Ltd
NOTE FOREIGN
GAS BROADENING OF DIFLUOROMETHANE BY NZ, O2 AND CO2
G. K. JOHRI and R. P. RISHLSHVVAR Department of Physics and Electronics, D.A.V. College, Kanpur-208 001, India (Received 30 November 1983)
Abstract-The linewidth parameters of difluoromethane broadened by N,, 0,, and CO, have been measured at microwave frequencies and are compared with calculated values for dipole-quadrupole interactions by using the Murphy-Boggs theory. The observed linewidths yield reasonable values of molecular quadrupole moments. INTRODUCTION
The rotational line shapes at low pressures are of interest in both engineering applications and in physical science. The subject has been reviewed by Rabitz.’ Self-broadening of the slightly asymmetric top molecule difluoromethane (rc = - 0.93) has been studied experimentally.2A We have measured the linewidth parameters of difluoromethane (CH,F,) broadened by N,, O,, and CO2 at 303°K for the transitions JK_ ,,K+, = 51,5+42,2 at 29268.90 MHz and 4,,, -+ 32,2at 31543.75 MHz using a double modulation microwave spectrograph described by Srivastava et aL5 The linewidth parameter has also been calculated for dipole-quadrupole interaction from the Murphy-Boggs6 theory. MEASUREMENTS
AND CALCULATIONS
Difluoromethane was procured from Pierce Chemical Co. and the perturbers N,, O,, and CO, from the Matheson Gas Co. The method of measurement of the linewidth at various pressures has been described by Srivastava et al.’ In the present measurements, the absorber pressure (CH,F,) was fixed at 15 mtorr to obtain a usable shape for the first derivative of the absorption line. The perturber gas was mixed with absorber in the absorption cell by changing the pressure in steps. The change in the linewidth dv, due to the perturber is found from the appropriate difference in measured linewidths. After modulation correction, the linewidth is found to be J(3)dv,/2. The slope of the plot of change in width vs partial pressure of the broadening gas gives the foreign-gas-broadened linewidth parameter and was obtained from a least-squares fit.’
0
10 Partial
20
30
pressure
40 of
50
broodener,p
60
70
(mtorr)
Fig. 1. Foreign broadening of 4,,,-+3z, transition of CH,F, by N,, O,, and CO, at 300°K. 89
; I Y a 0
250.
200-
I 5 3 c s 5 =
Fig. 2. Foreign
150-
loo0-
50-
0
__1_. 20 30 10 Partial pressure
broadening
of 5,.5-+42,2 transition
The linewidth parameter for a rotational final state f is (b/p)
CH2 F2 - N2
n-c CH2Fz - O2 - CO2 a--CH2FZ ._I_..-L.. --.1_ ~_A 40 50 60 70 of broadener,p(mtorr)
of CH,F> by N?, O,, and
CO, at
300°K.
transition involving the initial state i and the
= N c pJz x b db
u),
(1)
$1 - exp ( - P;“r’) + 1 - exp (- Py)].
(2)
J2
s0
x v duF(u)P(b, s0
where P(b, 21)=
Table I.
Measured
and calculated
linewidth
parameters Interaction
Transition
of CHZF, broadened
by N?, 02, and CO>.
tie
sured ZLQ/p). in AHi/torr
Calculated b3/p) in MHz/torr
j.2320.09
5.60
Cti2F2-N2 collision 41,3-32,2
29268.90
(4.10 ox)* 51,5-42,2
31543.75
1*89+0.05
5.50 (4.10 D?d8
Gi2F2-02 collision 41,3-32,2
29268.90
4*03+0.04
4.55 (2.06 L&9
51,5-42,2
31543.75
3*89+0.06
4.55 (2.06 D%)9
CH2F2-CO2 collision 41,3-32,2
29268.90
6*99+0.05
31543.75
6.13+0.14
8.70 (8.60 D%)l'
51,5-42,2
8.70 (8.60 D?,)l"
--
Note
91
In Eqs. (1) and (2), N is the total number of colliding molecules, p,, the fraction of the colliding molecules in state J2, b the impact parameter, u the relative velocity, F(v) the Maxwellian distribution function, and P,MB(a= i,fl the probability of leaving the initial state i or final state J The method of calculation of P,“” is described elsewhere.6 DISCUSSION
OF
RESULTS
The plots of corrected linewidths dv (in KHz) vs partial pressure p (mtorr) of N,, 02, and CO, are shown in Figs. 1 and 2. Measured linewidth parameters (MHz/torr) are given in Table 1. The uncertainties shown with the measured values are standard deviations.7 The Murphy-Boggs6 theory was used to calculate the linewidth parameters for the dominant dipole-quadrupole interaction. Calculated linewidth parameters are also given in Table 1. Table 1 shows that the Murphy-Boggs theory accounts for the observed parameters satisfactorily. The molecular quadrupole moments are evaluated by fitting the measured parameters to calculated values. The quadrupole moments of N,, O,, and CO* are 3.53 + 0.15, 1.83 + 0.07 and 5.43 + 0.28 DA respectively. .4cknon,/edgements_The authors thank G. P. Srivastava for providing experimental facilities and encouragement. We also thank S. C. Mehrotra for help, with the calculations and the University Grants Commission, India, for financial support.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. IO.
H. Rabitz, Ann. Rev. Phys. Chem. 25, 155 (1974). P. C. Pandey and S. L. Srivastava, J. Phys. B 5, 1427 (1972) G. K. Johri, J. Phys. B 10, 1859 (1977). G. K. Johri, Indian J. Pure Appl. Phys. 16, 546 (1978). G. P. Srivastava, H. 0. Gautam, and A. Kumar, J. Phys. B 6, 743 (1973). J. S. Murphy and J. E. Boggs, J. Chem. Phys. 43, 691 (1967). P. C. Pandey, K. K. Kirty, and S. L. Srivastava, J. Phys. B 4, 786 (1971). T. H. Spurling and E. A. Mason, J. Chem. Phys. 46, 322 (1967). M. Kontani, Y. Mizuno, and K. Kayama, J. Phys. Sot. Jap. 12, 707 (1957). A. D. Buckingham and R. L. Disch, Proc. Roy. Sot. Lond. A 273, 275 (1963).
Transler Vol. 33, No. 1. pp. 89-91.
1985
0022-4073185 $3.00 + .oO Pergamon Press Ltd
NOTE FOREIGN
GAS BROADENING OF DIFLUOROMETHANE BY NZ, O2 AND CO2
G. K. JOHRI and R. P. RISHLSHVVAR Department of Physics and Electronics, D.A.V. College, Kanpur-208 001, India (Received 30 November 1983)
Abstract-The linewidth parameters of difluoromethane broadened by N,, 0,, and CO, have been measured at microwave frequencies and are compared with calculated values for dipole-quadrupole interactions by using the Murphy-Boggs theory. The observed linewidths yield reasonable values of molecular quadrupole moments. INTRODUCTION
The rotational line shapes at low pressures are of interest in both engineering applications and in physical science. The subject has been reviewed by Rabitz.’ Self-broadening of the slightly asymmetric top molecule difluoromethane (rc = - 0.93) has been studied experimentally.2A We have measured the linewidth parameters of difluoromethane (CH,F,) broadened by N,, O,, and CO2 at 303°K for the transitions JK_ ,,K+, = 51,5+42,2 at 29268.90 MHz and 4,,, -+ 32,2at 31543.75 MHz using a double modulation microwave spectrograph described by Srivastava et aL5 The linewidth parameter has also been calculated for dipole-quadrupole interaction from the Murphy-Boggs6 theory. MEASUREMENTS
AND CALCULATIONS
Difluoromethane was procured from Pierce Chemical Co. and the perturbers N,, O,, and CO, from the Matheson Gas Co. The method of measurement of the linewidth at various pressures has been described by Srivastava et al.’ In the present measurements, the absorber pressure (CH,F,) was fixed at 15 mtorr to obtain a usable shape for the first derivative of the absorption line. The perturber gas was mixed with absorber in the absorption cell by changing the pressure in steps. The change in the linewidth dv, due to the perturber is found from the appropriate difference in measured linewidths. After modulation correction, the linewidth is found to be J(3)dv,/2. The slope of the plot of change in width vs partial pressure of the broadening gas gives the foreign-gas-broadened linewidth parameter and was obtained from a least-squares fit.’
0
10 Partial
20
30
pressure
40 of
50
broodener,p
60
70
(mtorr)
Fig. 1. Foreign broadening of 4,,,-+3z, transition of CH,F, by N,, O,, and CO, at 300°K. 89
; I Y a 0
250.
200-
I 5 3 c s 5 =
Fig. 2. Foreign
150-
loo0-
50-
0
__1_. 20 30 10 Partial pressure
broadening
of 5,.5-+42,2 transition
The linewidth parameter for a rotational final state f is (b/p)
CH2 F2 - N2
n-c CH2Fz - O2 - CO2 a--CH2FZ ._I_..-L.. --.1_ ~_A 40 50 60 70 of broadener,p(mtorr)
of CH,F> by N?, O,, and
CO, at
300°K.
transition involving the initial state i and the
= N c pJz x b db
u),
(1)
$1 - exp ( - P;“r’) + 1 - exp (- Py)].
(2)
J2
s0
x v duF(u)P(b, s0
where P(b, 21)=
Table I.
Measured
and calculated
linewidth
parameters Interaction
Transition
of CHZF, broadened
by N?, 02, and CO>.
tie
sured ZLQ/p). in AHi/torr
Calculated b3/p) in MHz/torr
j.2320.09
5.60
Cti2F2-N2 collision 41,3-32,2
29268.90
(4.10 ox)* 51,5-42,2
31543.75
1*89+0.05
5.50 (4.10 D?d8
Gi2F2-02 collision 41,3-32,2
29268.90
4*03+0.04
4.55 (2.06 L&9
51,5-42,2
31543.75
3*89+0.06
4.55 (2.06 D%)9
CH2F2-CO2 collision 41,3-32,2
29268.90
6*99+0.05
31543.75
6.13+0.14
8.70 (8.60 D%)l'
51,5-42,2
8.70 (8.60 D?,)l"
--
Note
91
In Eqs. (1) and (2), N is the total number of colliding molecules, p,, the fraction of the colliding molecules in state J2, b the impact parameter, u the relative velocity, F(v) the Maxwellian distribution function, and P,MB(a= i,fl the probability of leaving the initial state i or final state J The method of calculation of P,“” is described elsewhere.6 DISCUSSION
OF
RESULTS
The plots of corrected linewidths dv (in KHz) vs partial pressure p (mtorr) of N,, 02, and CO, are shown in Figs. 1 and 2. Measured linewidth parameters (MHz/torr) are given in Table 1. The uncertainties shown with the measured values are standard deviations.7 The Murphy-Boggs6 theory was used to calculate the linewidth parameters for the dominant dipole-quadrupole interaction. Calculated linewidth parameters are also given in Table 1. Table 1 shows that the Murphy-Boggs theory accounts for the observed parameters satisfactorily. The molecular quadrupole moments are evaluated by fitting the measured parameters to calculated values. The quadrupole moments of N,, O,, and CO* are 3.53 + 0.15, 1.83 + 0.07 and 5.43 + 0.28 DA respectively. .4cknon,/edgements_The authors thank G. P. Srivastava for providing experimental facilities and encouragement. We also thank S. C. Mehrotra for help, with the calculations and the University Grants Commission, India, for financial support.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. IO.
H. Rabitz, Ann. Rev. Phys. Chem. 25, 155 (1974). P. C. Pandey and S. L. Srivastava, J. Phys. B 5, 1427 (1972) G. K. Johri, J. Phys. B 10, 1859 (1977). G. K. Johri, Indian J. Pure Appl. Phys. 16, 546 (1978). G. P. Srivastava, H. 0. Gautam, and A. Kumar, J. Phys. B 6, 743 (1973). J. S. Murphy and J. E. Boggs, J. Chem. Phys. 43, 691 (1967). P. C. Pandey, K. K. Kirty, and S. L. Srivastava, J. Phys. B 4, 786 (1971). T. H. Spurling and E. A. Mason, J. Chem. Phys. 46, 322 (1967). M. Kontani, Y. Mizuno, and K. Kayama, J. Phys. Sot. Jap. 12, 707 (1957). A. D. Buckingham and R. L. Disch, Proc. Roy. Sot. Lond. A 273, 275 (1963).