- Email: [email protected]
Thermodynamics of {xCdCl2 + (1 − x)CdBr2}(s) investigated by mass spectrometry
M-2244 J. Chem. Thermodynamics 1988,20,
985-988
Thermodynamics of {xCdCI, (1 -x)CdBr2}(s) investigated mass spectrometry KRZYSZTOF SKUDLARSKI, JAN KAPALA
+ by
JERZY DUDEK, and
Institute of Inorganic Chemistry and Metallurgy Technical University of Wrociaw, 50-370 Wroclaw, Poland
of Rare Elements,
(Received 21 December 1987; inJina1 form 1 March
1988)
The mass spectra of vapours over {xCdCl, + (1 -x)CdBr,}(s) have been measured at the temperature 600 K. The ions Cd+, CdW, CdBr’, CdCIi, CdBrt, and CdClBr+ have been found. The excess molar Gibbs free energy has been determined: GE(600 K)/(J .mol-‘) = -(71OOf290)x(l -IX). The mass spectrum of CdClBr(g) and the equilibrium constant of the reaction of formation of CdClBr(g) at 600 K have been calculated.
1. Introduction In a previous paper(l) we described the mass spectra, vapour pressures, enthalpies of sublimation, and entropies of sublimation of cadmium dihalides. Nackenc2) and Ilyasov et al. (3) described the (solid + liquid) phase diagrams. The thermodynamic activities of the liquid mixtures were measured by Greiner and Jelinekc4) by the transpiration method. These authors neglected the presence of the CdClBr(g) molecule; that led to significant systematic errors in their interpretation. Bloom and Anthonyf5) identified the CdClBr+ ion in the mass spectrum of this mixture and calculated the enthalpy of formation of CdClBr(g) from CdCl,(g) and CdBr,(g). This work has been done to complete the thermodynamic description of (xCdC1, + (1 -x)CdBr,}. The method of preparation of salts and of measurements were described in our previous papers. (Lo) The interpretation was made on the basis of the dependence of the measured ion-intensity ratio on mole fraction.c7, *) 2. Results The mass spectra of vapours over the solid mixture exhibit the Cd+, CdCl+, CdBr+, CdCli, CdBrl, and CdClBr+ ions originating from the CdCl,(g), CdBr,(g), and CdClBr(g). The measurements of these mass spectra were made from about 590 to 0021-9614/88/080985 +04 $02.00/O
0 1988 Academic Press Limited
986
K. SKUDLARSKI,
TABLE
1. The measured
X
0.100 0.168 0.215 0.249 0.315 0.405 0.406 0.493 0.573 0.583 0.622 0.702 0.785 0.803 0.906
I(CdC1;) 31.6 104.9 63.6 44.8 195.0 63.0 255.5 484.5 425.4 201.0 373.6 315.2 856.7 151.9 856.7
mass spectrum
J. DUDEK,
AND
J. KAPALA
of vapours over {xCdCl, + (1 -x)CdBr&s) of ions are in arbitrary units
I(CdBr:)
I(CdClBr+)
I(CdC1’)
937.4 2260 1134 775.2 2816 551.7 1926 3087 1888 823.1 1577 891.6 2107 285.2 815.0
191.1 396.7 233.5 93.0 509.3 94.9 519.6 622.1 574.3 185.5 299.8 233.5 396.7 90.3 366.2
11650 5235 2352 7209 1228 3839 5287 2424 910 1500 715.6 946.8 173.0 222.1
at 600 K. Intensities
I(CdBr+) 1708 2376 1216 484.5 1561 260.6 798.8 1265 647.5 199.0 315.2 153.4 265.9 43.5 67.6
Z(Cd+) 634.6 946.8 392.7 101.8 722.8 111.4 546.2 701.4 1067 141.6 384.9 263.2 603.7 90.3 694.4
about 610 K. From the dependences of ln(lT/I”T”) on (l/T) the mean ion intensities at 600 K have been interpolated. These values are shown in table 1. CdClz, CdBri, and CdClBr+ are molecular ions. The origins of the other ions may be described as follows: I(CdC1’)
= I(CdCl+
from CdCl,) +I(CdCl+
from CdClBr),
(1)
I(CdBr+)
= I(CdBr+
from CdBr,) + Z(CdBr+ from CdClBr).
(2)
and I(Cd+) = 1(Cd+ from CdC12)+Z(Cd+
from CdCr,) +Z(Cd+ from CdClBr).
(3)
The molecular-ion intensities may be used for thermodynamic interpretation without additional calculations. The intensities of CdCli and CdBri ions were used for calculation of the excess molar Gibbs free energy Gi as proposed by Neckel and Wagner.@) GE was represented by: G: = x(1-x)XGi(2x-1)‘~‘.
(4)
The calculation formula has the form: RT ln((1 -x)l(CdCl:)/xl(CdBr:)}
= C+Gr(l-2x) +G,(6x(l-x)-l)+
. . .) (5)
where C is a constant, and the Gi are parameters. Equation (5) with one parameter is statistically suitable. By using the least-squares method we obtain a standard deviation of fit equal to 530 J. mol- l, the value of C was (- 110801140) J *mol-l, and the value of G, was (- 7100 + 290) J. mol- I. The integration plot according to equation (5) is shown in figure 1.
THERMODYNAMICS
OF {xCdCl,+(l
-x)CdBr,}(s)
987 ,
l2 +,” u K -tt 2+-A
1 0.5 x FIGURE 1. The dependence of ln[(l-x)I(CdClt/{xI(CdBr~)}] on mole fraction. -, calculation by equation (5); - - - , from calculation by MASFIT procedure. 0
From
The mass spectra of the pure components were used for resolving the mass spectrum of vapours over mixtures. The calculated mass spectra of CdClBr(g) and of the pure components are shown in table 2. From the resolved mass spectrum the standard equilibrium constant of the reaction: CdCl,(g) + CdBr,(g) = 2CdClBr(g),
(6)
K” = {p(CdClBr)}2/(p(CdC12)p(CdBr2)}.
(7)
may be calculated:
From equation (7) and from
~(9 = [VW from W/Y~}I/{~~(O},
(8)
assuming that (o(CdC1Br)}2/(o(CdC12)o(CdBr,)}
= 1,
(9)
TABLE 2. The relative mass spectra of gaseous molecules over (xCdC1, +(l -x)CdBr,}(s). The intensity of respective molecular ions CdCl& CdBrz, or CdClBr+ is equal to one. The energy of ionizing electrons is 8.0 aJ Molecule CdCl+ CdBr+ Cd+
CdCl,“’
CdClBr
CdBr,(‘)
0.221+0.004
o.B3+0.04 0.05 40.04 0.24+0.15
0.2OkO.05 0.02
0.27 +0.03
988
K. SKUDLARSKI,
J. DUDEK,
AND J. KAPALA
we have K” = [Z{I(L
from CdClBr)/y,)]‘/C(l(k
from CdCl,)/y,) x C{Z(k from CdBr,)/y,}*
(10)
where pi is the vapour pressure of the ith gaseous species, s is the sensitivity factor of the mass spectrometer, 0 is the ionization cross section, yk is the electron-multiplier sensitivity factor for the ion k, T is the temperature, and Z(k from i) is the intensity of the ion k originating from the gaseous molecule i. It was assumed that yk is proportional to M; lj2 where Mk is the ion molar mass. The calculated value of K” is (4.1+ 1.1). The value of K” calculated from molecular ions only is (4.2 f 0.9). The same values calculated with assumption of compensation of yk changes are (3.9 + 1.3) and (4.1 kO.8). The value calculated from the paper of Bloom and Anthony (5) from molecular ion intensities is 5.1. 3. Discussion The analysis of excess molar Gibbs free energies was also made by the MASFIT procedure with five independent coefficients. (9) The result is shown in figure 1. The standard deviation of the fit is 580 J. mol-‘, implying that the difference between the two analyses is insignificant. The parameters Gi from the MASFIT procedure are G, = -7127, G2 = 93, G, = 89, G4 = -636, and G, = -689 J=mol-l. Givan and Loevenschuss’l’) give values of thermodynamic functions of the gaseous phase of the investigated mixture. The values of [@:(600 K) + (Hk(600 K) - Hm(298. 15 K)}] are 284.59, 289.04, and 267.36 J. K- ’ . mol- ’ for CdClBr(g), CdBr,(g), and CdCl,(g), respectively. The corresponding entropy increments at 298.15 K are 244.78, 248.23, and 228.47 J.K-‘ *mol-’ and at 600 K are 346.66, 352.38, and 328.06 J.K-’ mmol-l. The enthalpy of reaction (6) at 298.15 K calculated by the third-law method is (0.6 + 1.4) kJ . mol- ’ for our value of K” = 4.1. The enthalpy calculated from Bloom and Anthony’s results@’ is The molar entropy of reaction (6) at 298.15 K is (-0.5f21) kJ*mol-‘. 12.852 J * K- ’ 9mol-I. Assuming that the enthalpy of reaction (6) is zero we obtain the molar entropy of this reaction at 600 K. This value is (11.7 + 2.3) J. K- ’ . mol-r (calculated by the third-law method this quantity is 12.872 J. K-i . mol- ’ at 600 K). Taking into account the above results it may be assumed that the calculated value of K” is close to that expected. REFERENCES 1987, 1. Skudlarski, K.; Dudek, J.; Kapala, J. J. Chem. Thermodynamics Nacken, R. Zentrallblatt fir Min. Geol. 1907, 301. 3. Ilyasov, I. I.; Rozhkovskaya, L. B.; Bergman, A. G. Zh. Neorg. Khim. 4. Greiner. B.: Jellinek. K. Z. Phvsik. Chem. A 1933. 165, 7. 5. Bloom,‘H.;‘Anthony, R. G. A&t. J. Chem. 1972, !25, 23. 6. Kapala, K.; Skudlarski, K. Int. J. Mass Spectrum. Ion Phys. 1981, 40, 7. Belton, G. R.; Fruehan, R. J. J. Phys. Chem. 1967, 71, 1403. 8. Neckel, A.; Wagner, S. Ber. Bunsenges. Phys. Chem. 1969, 73, 210. 9. Kapala, J.; Skudlarski, K. Int. J. Mass Spectrum. Ion Processes 1987, 10. Givan, A.; Loewenschuss, A. J. Chem. Phys. 1978, 68, 2228.
19. 857.
2.
1957, 2,
255.
77, 13.
2174.
985-988
Thermodynamics of {xCdCI, (1 -x)CdBr2}(s) investigated mass spectrometry KRZYSZTOF SKUDLARSKI, JAN KAPALA
+ by
JERZY DUDEK, and
Institute of Inorganic Chemistry and Metallurgy Technical University of Wrociaw, 50-370 Wroclaw, Poland
of Rare Elements,
(Received 21 December 1987; inJina1 form 1 March
1988)
The mass spectra of vapours over {xCdCl, + (1 -x)CdBr,}(s) have been measured at the temperature 600 K. The ions Cd+, CdW, CdBr’, CdCIi, CdBrt, and CdClBr+ have been found. The excess molar Gibbs free energy has been determined: GE(600 K)/(J .mol-‘) = -(71OOf290)x(l -IX). The mass spectrum of CdClBr(g) and the equilibrium constant of the reaction of formation of CdClBr(g) at 600 K have been calculated.
1. Introduction In a previous paper(l) we described the mass spectra, vapour pressures, enthalpies of sublimation, and entropies of sublimation of cadmium dihalides. Nackenc2) and Ilyasov et al. (3) described the (solid + liquid) phase diagrams. The thermodynamic activities of the liquid mixtures were measured by Greiner and Jelinekc4) by the transpiration method. These authors neglected the presence of the CdClBr(g) molecule; that led to significant systematic errors in their interpretation. Bloom and Anthonyf5) identified the CdClBr+ ion in the mass spectrum of this mixture and calculated the enthalpy of formation of CdClBr(g) from CdCl,(g) and CdBr,(g). This work has been done to complete the thermodynamic description of (xCdC1, + (1 -x)CdBr,}. The method of preparation of salts and of measurements were described in our previous papers. (Lo) The interpretation was made on the basis of the dependence of the measured ion-intensity ratio on mole fraction.c7, *) 2. Results The mass spectra of vapours over the solid mixture exhibit the Cd+, CdCl+, CdBr+, CdCli, CdBrl, and CdClBr+ ions originating from the CdCl,(g), CdBr,(g), and CdClBr(g). The measurements of these mass spectra were made from about 590 to 0021-9614/88/080985 +04 $02.00/O
0 1988 Academic Press Limited
986
K. SKUDLARSKI,
TABLE
1. The measured
X
0.100 0.168 0.215 0.249 0.315 0.405 0.406 0.493 0.573 0.583 0.622 0.702 0.785 0.803 0.906
I(CdC1;) 31.6 104.9 63.6 44.8 195.0 63.0 255.5 484.5 425.4 201.0 373.6 315.2 856.7 151.9 856.7
mass spectrum
J. DUDEK,
AND
J. KAPALA
of vapours over {xCdCl, + (1 -x)CdBr&s) of ions are in arbitrary units
I(CdBr:)
I(CdClBr+)
I(CdC1’)
937.4 2260 1134 775.2 2816 551.7 1926 3087 1888 823.1 1577 891.6 2107 285.2 815.0
191.1 396.7 233.5 93.0 509.3 94.9 519.6 622.1 574.3 185.5 299.8 233.5 396.7 90.3 366.2
11650 5235 2352 7209 1228 3839 5287 2424 910 1500 715.6 946.8 173.0 222.1
at 600 K. Intensities
I(CdBr+) 1708 2376 1216 484.5 1561 260.6 798.8 1265 647.5 199.0 315.2 153.4 265.9 43.5 67.6
Z(Cd+) 634.6 946.8 392.7 101.8 722.8 111.4 546.2 701.4 1067 141.6 384.9 263.2 603.7 90.3 694.4
about 610 K. From the dependences of ln(lT/I”T”) on (l/T) the mean ion intensities at 600 K have been interpolated. These values are shown in table 1. CdClz, CdBri, and CdClBr+ are molecular ions. The origins of the other ions may be described as follows: I(CdC1’)
= I(CdCl+
from CdCl,) +I(CdCl+
from CdClBr),
(1)
I(CdBr+)
= I(CdBr+
from CdBr,) + Z(CdBr+ from CdClBr).
(2)
and I(Cd+) = 1(Cd+ from CdC12)+Z(Cd+
from CdCr,) +Z(Cd+ from CdClBr).
(3)
The molecular-ion intensities may be used for thermodynamic interpretation without additional calculations. The intensities of CdCli and CdBri ions were used for calculation of the excess molar Gibbs free energy Gi as proposed by Neckel and Wagner.@) GE was represented by: G: = x(1-x)XGi(2x-1)‘~‘.
(4)
The calculation formula has the form: RT ln((1 -x)l(CdCl:)/xl(CdBr:)}
= C+Gr(l-2x) +G,(6x(l-x)-l)+
. . .) (5)
where C is a constant, and the Gi are parameters. Equation (5) with one parameter is statistically suitable. By using the least-squares method we obtain a standard deviation of fit equal to 530 J. mol- l, the value of C was (- 110801140) J *mol-l, and the value of G, was (- 7100 + 290) J. mol- I. The integration plot according to equation (5) is shown in figure 1.
THERMODYNAMICS
OF {xCdCl,+(l
-x)CdBr,}(s)
987 ,
l2 +,” u K -tt 2+-A
1 0.5 x FIGURE 1. The dependence of ln[(l-x)I(CdClt/{xI(CdBr~)}] on mole fraction. -, calculation by equation (5); - - - , from calculation by MASFIT procedure. 0
From
The mass spectra of the pure components were used for resolving the mass spectrum of vapours over mixtures. The calculated mass spectra of CdClBr(g) and of the pure components are shown in table 2. From the resolved mass spectrum the standard equilibrium constant of the reaction: CdCl,(g) + CdBr,(g) = 2CdClBr(g),
(6)
K” = {p(CdClBr)}2/(p(CdC12)p(CdBr2)}.
(7)
may be calculated:
From equation (7) and from
~(9 = [VW from W/Y~}I/{~~(O},
(8)
assuming that (o(CdC1Br)}2/(o(CdC12)o(CdBr,)}
= 1,
(9)
TABLE 2. The relative mass spectra of gaseous molecules over (xCdC1, +(l -x)CdBr,}(s). The intensity of respective molecular ions CdCl& CdBrz, or CdClBr+ is equal to one. The energy of ionizing electrons is 8.0 aJ Molecule CdCl+ CdBr+ Cd+
CdCl,“’
CdClBr
CdBr,(‘)
0.221+0.004
o.B3+0.04 0.05 40.04 0.24+0.15
0.2OkO.05 0.02
0.27 +0.03
988
K. SKUDLARSKI,
J. DUDEK,
AND J. KAPALA
we have K” = [Z{I(L
from CdClBr)/y,)]‘/C(l(k
from CdCl,)/y,) x C{Z(k from CdBr,)/y,}*
(10)
where pi is the vapour pressure of the ith gaseous species, s is the sensitivity factor of the mass spectrometer, 0 is the ionization cross section, yk is the electron-multiplier sensitivity factor for the ion k, T is the temperature, and Z(k from i) is the intensity of the ion k originating from the gaseous molecule i. It was assumed that yk is proportional to M; lj2 where Mk is the ion molar mass. The calculated value of K” is (4.1+ 1.1). The value of K” calculated from molecular ions only is (4.2 f 0.9). The same values calculated with assumption of compensation of yk changes are (3.9 + 1.3) and (4.1 kO.8). The value calculated from the paper of Bloom and Anthony (5) from molecular ion intensities is 5.1. 3. Discussion The analysis of excess molar Gibbs free energies was also made by the MASFIT procedure with five independent coefficients. (9) The result is shown in figure 1. The standard deviation of the fit is 580 J. mol-‘, implying that the difference between the two analyses is insignificant. The parameters Gi from the MASFIT procedure are G, = -7127, G2 = 93, G, = 89, G4 = -636, and G, = -689 J=mol-l. Givan and Loevenschuss’l’) give values of thermodynamic functions of the gaseous phase of the investigated mixture. The values of [@:(600 K) + (Hk(600 K) - Hm(298. 15 K)}] are 284.59, 289.04, and 267.36 J. K- ’ . mol- ’ for CdClBr(g), CdBr,(g), and CdCl,(g), respectively. The corresponding entropy increments at 298.15 K are 244.78, 248.23, and 228.47 J.K-‘ *mol-’ and at 600 K are 346.66, 352.38, and 328.06 J.K-’ mmol-l. The enthalpy of reaction (6) at 298.15 K calculated by the third-law method is (0.6 + 1.4) kJ . mol- ’ for our value of K” = 4.1. The enthalpy calculated from Bloom and Anthony’s results@’ is The molar entropy of reaction (6) at 298.15 K is (-0.5f21) kJ*mol-‘. 12.852 J * K- ’ 9mol-I. Assuming that the enthalpy of reaction (6) is zero we obtain the molar entropy of this reaction at 600 K. This value is (11.7 + 2.3) J. K- ’ . mol-r (calculated by the third-law method this quantity is 12.872 J. K-i . mol- ’ at 600 K). Taking into account the above results it may be assumed that the calculated value of K” is close to that expected. REFERENCES 1987, 1. Skudlarski, K.; Dudek, J.; Kapala, J. J. Chem. Thermodynamics Nacken, R. Zentrallblatt fir Min. Geol. 1907, 301. 3. Ilyasov, I. I.; Rozhkovskaya, L. B.; Bergman, A. G. Zh. Neorg. Khim. 4. Greiner. B.: Jellinek. K. Z. Phvsik. Chem. A 1933. 165, 7. 5. Bloom,‘H.;‘Anthony, R. G. A&t. J. Chem. 1972, !25, 23. 6. Kapala, K.; Skudlarski, K. Int. J. Mass Spectrum. Ion Phys. 1981, 40, 7. Belton, G. R.; Fruehan, R. J. J. Phys. Chem. 1967, 71, 1403. 8. Neckel, A.; Wagner, S. Ber. Bunsenges. Phys. Chem. 1969, 73, 210. 9. Kapala, J.; Skudlarski, K. Int. J. Mass Spectrum. Ion Processes 1987, 10. Givan, A.; Loewenschuss, A. J. Chem. Phys. 1978, 68, 2228.
19. 857.
2.
1957, 2,
255.
77, 13.
2174.