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The Journal of Physical Chemistry, Vol. 82, No. 13, 1978
W. H. Breckenridge and A. M. Renlund (42) A. C. Vikis and H. C. Moser, J . Chem. fhys., 53, 2333 (1970). (43) H. E. Gunning, J. M. Campbell, H. S. Sandhu, and 0. P. Strausz, J . Am. Chem. Soc., 95, 746 (1973). (44) G. C. Marconi, G. Orlandi, and G. Poggi, Chem. fhys. Left., 40, 88 (1976). (45) R. A. Holroyd and T. E. Pierce, J . fhys. Chem., 68, 1392 (1964). (46) A. B. Callear and J. C. McGurk, J . Chem. SOC.,Faraday Trans. 2, 68, 289 (1972). (47) H. Hunziker, private communication. (48) A. C. Vikis and D. J. LeRoy, Can. J . Chem., 51, 1207 (1973). (49) B. L. Earl and R. Herm, Chem. fhys. Lett., 22, 95 (1973). (50) J. T. Waber and D. T. Comer, J. Chem. fhys., 42, 4116 (1965). (51) J. C. Slater, J. Chem. fhys., 41, 3199 (1964). (52) J. 0. Hirschfelder, C. F. Curtiss, and R. B. Blrd, "Molecular Theory of Gases and Liquids", Wlley, New York, N.Y., 1964. (53) SF,: R. N. Compton and C. D. Cooper, J . Chem. Phys., 59, 4140 (1973); M. M. Hubers and J. Los, Chem. fhys., 10, 235 (1975). COP: R. N. Compton, P. W. Reinhardt, and C. D. Cooper, J . Chem. Phys., 63, 3821 (1975). NO: P. D. Burrow, Chem. fhys. Lett., 26, 265 (1974). N:, D. Mathur and J. B. Hasted, J. fhys. 6,10, L265 (1977). CO: G. J. Schulz, Rev. Mod. fhys., 45, 378 (1973). (54) E. R. Fisher and G. K. Smith. ADD/. Oot.. 10. 1803 (1971). (55) J. Costeilo, M. A. D. Fluendy,' a i d K. P. Lawley, Faraday Discuss. Chem. Soc., 62, 291 (1977). (56) K. A. Kohler, R. FeNgen, and H. Pauly, fhys. Rev. A , , 15, 1407 (1977). (57) S. J. Riley and D. R. Herschbach, J. Chem. fhvs.. 58. 27 (1973). (58) S. M. Freund, G. A. Fisk, D. R. Hershbach, and W. Klemperer, j . Chem. fhys., 54, 2510 (1971). (59) D. S. Y. Hsu and M. C. Lin, Chem. Phys. Lett., 42, 78 (1978). (60) F. A. Cotton and G. Wilkinson, "Advanced Inorganic Chemistry", Interscience, New York, N.Y., 1972, p 711. (61) G. Karl, P. Kruus, and J. C. Polanyi, J. Chem. fhys., 46, 224 (1967). (62) A. C. Vikis and D. J. LeRoy, Chem. fhys. Lett., 21, 103 (1973). (63) J. Berkowitz, W. A. Chupka, and T. A. Walter, J . Chem. Phys., 50, 1497 (1969). (64) J. Tuiiy, J . Chem. fhys., 62, 1893 (1975); R. G. Shortridge and M. C. Lin, ibid., 64, 4076 (1976). (65) R. Burnham and N. Djeu, J . Chem. fhys., 61, 5158 (1974).
(20) P. D. Morten, C. G. Freeman, R. F. Claridge, and L. F. Phillips, J . fhotochem., 3, 285 (1974). (21) A. M. Renlund, unpublished results. (22) R. Pepped, Z. Naturforsch. A , 25, 927 (1970). (23) V. Mahaven, N. N. Lichtin, and M. 2. Hoffman, J. fhys. Chem., 77, 875 (1973). (24) A. Granzow, M. Z. Hoffman, and N. N. Lichtin, J . fhys. Chem., 73, 4289 (1969). (25) B. L. Earl and R. R. Herm, J. Chem. Phys., 60, 4568 (1974). (26) I. N. Siara and L. Krause, Can. J . fhys., 51, 257 (1973); M. Czajkowski, L. Krause, and G. M. Skandis, ibid., 51, 1582 (1973). (27) A. Callear and J. McGurk, J . Chem. Soc., Faraday Trans. 2, 69, 97 (1973). (28) R. P. Blickensderfer,W. H. Breckenridge, and D. S. Moore, J. Chem. fhys., 63, 3681 (1975). (29) S. Lln and R. E. Weston, Jr., J . Chem. Phys., 65, 1443 (1976). (30) P. L. Lijnse, "Review of Literature on Quenching, Excitation, and Mixing Collision Cross-sections for the first Resonance Doublets of the Alkalis", Report 398, Fysisch Laboratorium, Rijksuniversiteit Utrecht, The Netherlands. (31) J. C. Slater and J. G. Kirkwood, fhys. Rev., 37, 882 (1931). (32) Landolt-Bornstein, "Zahlenwerte und Funktionen", Vol. 6, Aufrage I, 1 and 3; M. J. Bridge and A. P. Buckingham, Roc. R. SOC. London, Ser. A , 295, 334 (1966); A. B. Tipton, A. P. Dean, and J. E. Boggs, J . Chem. fhys., 40, 1144 (1984). (33) L. N. Shabouna, Opt. Spectrosc., 27, 205 (1969). (34) H. A. Hyman, Chem. fhys. Lett., 31, 593 (1975). (35) B. L. Earl, R. R. Herm, S. M. Lin, and C. A. Mims, J . Chem. Phys., 56, 867 (1972). (36) J. R. Barker and R. E. Weston, Jr., J. Chem. fhys., 65, 1427 (1976). (37) L. G. Piper, J. E. Velazco, and D. W. Setser, J. Chem. fhys., 59, 3323 (1973). (38) E. A. Gisiason and J. G. Sachs, J . Chem. fhys., 62, 2878 (1975). (39) E. Bauer, E. R. Fisher, and F. R. Gilmore, J. Chem. fhys., 51, 4173 (1969). (40) P. L. Lijnse, J. Quant. Spectrosc., Radiat. Transfer, 14, 1143 (1974). (41) J. E. Velazco, J. H. Kolts, and D. W. Setser, J . Chem. Phys., 65, 3468 (1976).
Reaction of Excited Cadmi~rn(~P,)and Cadmium('P,) Atoms with Hp, HD, and DP. Quenching Cross Sections and CdH(CdD) Yields W.
H. Breckenridge*+ and Anita M. Renlundt:
Department of Chemistry, University of Utah, Salt Lake City, Utah 84 I12 (Received February IO, 1978) Publication costs assisted by the Petroleum Research Fund
Cross sections and primary CdH(CdD) yields have been measured for the quenching of Cd(3PJ)and Cd(lP1) by Hz, HD, and Dz. Cross sections for Cd(lPJ are larger and show less isotopic selectivity than those for the quenching of Cd(3P~).The cross sections for the quenching of Cd(3P~) are not markedly temperature dependent, with Arrhenius activation energies 52.0 kcal/mol. The total yield of CdH + CdD in the quenching of Cd(lP1) by the isotopic hydrogens is 50.50 of the CdH + CdD yield in the quenching of Cd(3PJ),which in turn is near unity. There is no isotope effect on the total CdH + CdD yield in Cd?P& or Cd(lP1) quenching. The product ratio of CdD to CdH in the quenching of Cd(3PJ) by HD is 1.9 k 0.2, but in the quenching of Cd('P1) by HD is 1.2 f 0.1. The isotope effects on cross sections and relative CdD/CdH yields for Cd(3P~) quenching are discussed in terms of an adiabatic chemical reaction in which Cd(3Pl) attacks Hz, HD, or Dz side-on, and where the production of CdH or CdD is either thermoneutral or slightly endothermic. It is postulated that Cd(lP1) quenching by Hz involves an efficient nonadiabatic surface crossing, and that a charge-transfer potential surface is likely involved due to the lower ionization potential of Cd(lP,). It is also suggested that with the higher-energy Cd('P1) state there may be no constraint to side-on attack of hydrogen, perhaps accounting for the lack of isotopic specificity as compared to the reactions with Hz of Cd(3P1)or the 3P states of Hg. Introduction In previous papers,112 we have reported the determination of absolute cross sections and major exit channels
'
Camille and Henry Dreyfus Foundation Teacher-Scholar, 1973-1978. Department of Physical Chemistry, Cambridge University, Cambridge, England. 0022-3654/78/2082-1484$01.00/0
for the quenching of the two lowest-lying excited states of the Cd atom, C d ( 3 P ~and ) Cd(lPl), by several gases. Here we describe a more detailed comparative study of the quenchinn of these states by the simplest of molecular quenchers Hz, HD, and Dz. -Using the technique of resonance-radiation flash photolysis, it has been possible to measure the temperature dependence of the cross Sections for Cd(3PJ quenching, to measure the different relative 0 1978 American
Chemical Society
The Journal of Physical Chemistry, Vol. 82,No. 13, 1978 1485
Reaction of Cd(3P,) and Cd('P,) with H2, HD, and D,
TABLE I: Absolute Rate Constants and Arrhenius Parameters for Quenching of C d ( 3 P ~and ) Cd('P,) by H,, HD, and D, ~~~
temp, C
quenching rate constant Absolute Rate k, [Cd('P,) quenching] 1.79k7 + k, [ Cd( 'PJ) quenching] 1.57k, + k, [ c ~ ( ~ qGenching] P~) 1.37k7 + k, [ Cd( 'PJ) quenching]
230 190 230 280
Ka HDa Constants for Quenching of C d ( 3 P ~and ) Cd('P,) (3.4 i 0.3) x 10" (3.1 t 0.3) x 10" (1.62 i 0 . 2 4 ) x 10" (1.56 i 0.20) X 10"
(3.0 i 0.3) x 10" (7.1 t 0.8) x 10"
(1.75 i 0.32) x 10"
(1.18i 0.18) x 10"
( 7 . 0 i 0 . 6 ) ~l o i o
0.22) x 10"
(1.48 * 0.20) x 10"
(7.1 i 1.1)X 10"
(1.79
i
D2 a
Arrhenius Parameters for the Quenching of Cd( 3PJ), k = Ae-Ea/RT Ea, kcal/mol log A, L mol-' s-' 11.5 10.9 10.9
+ 0 . 6 r 1.5
-0.5
i
1.5
0.0 5 1.5
Units are L/mol s.
yields of CdH and CdD from the quenching of Cd(3PJ) and Cd(lP1) by HD, and to compare the different branching ratios for CdH CdD production for the isotopic hydrogens in the quenching of C d ( 3 P ~and ) Cd('P1).
+
Experimental Section The technique and procedures used in this study have been described in previous papers.lI2 Results The methods by which it is possible to excite Cd(lP1) only, or Cd(3PJ ) only, using cadmium resonance radiation flash photolysis have been discussed previously.lI2 The C d ( 3 P ~state ) can also be produced indirectly by adding a large excess of Nz gas, which transforms Cd(lP1) t o C d ( 3 P ~by ) collisional deactivation.2 The processes of interest in the experiments reported here can be shown as follows: Cd('S,) t hu(2288 A ) Cd('P,) + Cd('S,) Cd('P,)
+ N,
-+
Cd('P,)
+ hu(2288 A )
Cd('P,,,) t N, Cd(lS,) + N,
Cd('P,) + HD -+ CdH
+D
CdD t H
Cd('S,)
+HtD
Cd(3P,,,) + HD Cd('S,) [Cd('S,)
+ hu(3261 A ) -
+ HD Cd('P,)]
Cd('P,)- Cd(lS,) t hu(3261 A ) Cd(3P,) + M -+ Cd(3P,) + M Cd('P,) + M Cd('P1) + M -+
Cd(3P,) + N, Cd(3P,) + N, Cd('PI) + HD
Cd('P,)
+
-+
Cd('S,)
+ N,
Cd('S,) + N, CdH + D CdD + H Cd(IS,) + HD HD + CdH + D CdD + H Cd('S,) + HD -+
-+
I n further discussion below, the total rate constant for a particular process, i.e., h6a 4- &, will be written with only
the numerical subscript, Le., h6. Note that HD is used as the most general example of quenching possibilities for isotopic hydrogens. It is assumed that any Cd(3P2)formed in reaction l a is rapidly converted to Cd(3P1) or Cd(3P,J under the conditions of all our experiments. The maximum equilibrium fraction of Cd(3P2) for the Cd(3Po,l,z) J-state distribution at the highest temperature used is only 0.04, so for simplicity we have ignored possible contributions of Cd(3P2)reactions. (i) Absolute Rates of Quenching of Cd('P1)and C d t P J ) by the Isotopic Hydrogens. The absolute rate constants for quenching by Hz, HD, and D2 of Cd(3PJ) a t various temperatures, and of Cd(lP1) at 230 "C, are shown in Table I. The Cd(lP1) rate constants were taken from ref 2 (preceding paper), The Cd(3PJ ) quenching rate constants a t 280 "C were determinedl by direct excitation of CdPP1) a t 3261 A, with a filter surrounding the reaction vessel to prevent Cd(lP1) excitation. The Cd(3Po,l)concentration, as well as the concentration of the initial product, CdH(CdD), were monitored as functions of the pressure of isotopic hydr0gen.l Under the conditions of these experiments, the collisional interconversion rates (reaction 3) are much faster than the net decay of either Cd(3Po)or Cd(3P1), so that the measured quantity is actually a composite quenching rate constants, (h3/k-3)k7 hg. This quantity is a population-weighted s u m of the two rate constants appropriate for the J-state equilibrium distribution of Cd(3Po,l)a t a particular temperature.l The measurements a t 230 and 190 OC were made using the same technique, but Cd('PJ) was produced via the indirect method, i.e., by exciting Cd(lP1) in the presence of excess N2, then monitoring both Cd(3Po) and Cd(3P1) in absorption as a function of added pressure of isotopic hydrogen. Experiments were performed by adding very small pressures of isotopic hydrogen, 10.2 Torr, to mixtures of 15-50 Torr of N2,the total pressure being made up to 400 Torr with argon. The total pressure of H2 must be kept low in order to avoid net depletion of ground-state Cd('So) by formation of CdH following excitation of Cd(lP1). The concentration of Cd(lSo) was monitored in absorption a t 2288 A. Under such conditions, >95% of the Cd(lP,) is quenched, and the quenching is entirely by N2,only 1% of the Cd(lP1) being quenching by isotopic hydrogen even a t the highest isotopic hydrogen pressures. Because N2is a very ineffective quencher of Cd(3P~), the lifetime of Cd(3P,) is only slightly shortened by Nz quenching under these conditions (-13% a t 15 Torr) if the quenching rate constant for N2 at 190 and 230 "C is not appreciably different from the rate a t 280 "C.l Serious error in our measurements would only occur if there were a very steep inverse temperature dependence of the rate
+
-
1486
The Journal of Physical Chemistry, Vol. 82, No. 13, 7978
W. H. Breckenridge and A. M. Renlund
TABLE 11: CdD/CdH Product Ratios gases and pressures 20 Torr of HD 1 2 Torr of HD
+ 1 0 5 Torr of He + 280 Torr of He 8 Torr of HD + 2 9 2 Torr of He 2 0 Torr of HD + 380 Torr of N, 8 Torr of HD + 392 Torr of N, 8 Torr of HD + 392 Torr of N, 8 Torr of HD + 3 9 2 Torr of N, 20 Torr of HD + 88 Torr of CH, 20 Torr of HD 2 0 Torr of HD
10 Torr of H, 10 Torr of H,
+ 10 Torr of D, + 1 0 Torr of D,
1 0 Torr of H, t 1 0 Torr 1 0 Torr of H, + 1 0 Torr 5 Torr of H, + 5 Torr of 4 Torr of H, + 4 Torr of
of D, + 280 Torr of He of D, + 280 Torr of He D, t 290 Torr of He D, t 2 9 2 Torr of He
+ 4 Torr of D, + 298 Torr of Ar 10 Torr of H, + 10 Torr of D, + 380 Torr of N, 1 0 Torr of H, t 10 Torr of D, + 3 8 0 Torr of N, 4 Torr of H, + 4 Torr of D, + 392 Torr of N, 4 Torr of H, + 4 Torr of D, + 392 Torr of N, 4 Torr of H, + 4 Torr of D, t 2 5 5 Torr of N, 4 Torr of H, + 4 Torr of D, t 398 Torr of N, 4 Torr of H, t 4 Torr of D, t 398 Torr of N, 1 0 Torr of H, + 1 0 Torr of D, t 88 Torr of CH,
+
CdD/CdH
220 230
1.30 f. 0.15 1 . 1 4 i: 0.15
230 230 230
1.30 i- 0.09 1.26 i- 0.14 1.19 0.13
220 220 250 280
1.65 1.88 1.91 1.84
i-
230
1.88
f
220 230
0.65 i 0.07 0.72 i: 0.08
*
220 230 230 230
4 Torr of H,
of quenching of Cd(3PJ)by Nz, which would certainly not be expected. To check for such a possibility, however, we conducted experiments in high pressures of N2 (400 Torr), and measured the yield of CdH from pressures of H, up to those where Cd(lSo)depletion began to occur at 230 and 210 "C. This Nzpressure should have resulted in an effective lifetime decrease of Cd(3PJ) of a factor of 5, corresponding to 80% quenching. By assuming the rate constant for Cd(3PJ) quenching of H2 a t 230 "C shown in Table I, it was possible from this data to calculate values for ( h 3 / k 3 ) h 5 k,, the composite rate constant for quenching of equilibrated Cd(3PJ) by N2,of (1.15 f 0.20) X los and (1.03 f 0.13) X los L mol-l s-l, for 230 and 210 "C, respectively, which can be compared to the value determined a t 280 OC1 of (1.03 f 0.20) X los L mol-l s-l. It may be shown rigorously that there is no fortuitous combination of changes in the values of k4, k5, h7 and h8 over this temperature range which would lead to the observed data, and we must therefore conclude that the effective rate of quenching of Cd(3PJ)by N2does not vary markedly over this temperature range. From the data in Table I, it is obvious that there are also no substantial changes in the effective rate constant for quenching of Cd(3PJ) by any of the isotopic hydrogens over this temperature range. We have fit the data to the simple Arrhenius expression using a least-squares routine, and calculated the best-fit activation energies for these quenching processes. The Arrhenius parameters are shown in Table I. Within the estimated total error of k1.5 kcal/mol, the activation energies for quenching of Cd(3PJ) are certainly small and quite similar for all the isotopic hydrogens. (ii) Relative Yields of CdH Vs. CdD in the Quenching of Cd(IPl) and C d ( 3 P ~by ) the Isotopic Hydrogens. It is possible, using the separated C-X (1,O) bands of CdH and CdD,3p4to determine relative yields of CdH and CdD under any experimental conditions where there is a source of both deuterium and hydrogen atoms available. In this case, we have chosen to measure the relative CdD/CdH yields from
temp, "C
0.59
0.08
i 0.52 i 0.09 i: 0.10
f
0.07
0.04
i 0.07 0.68 i 0.05
0.88 0.68
+
0.10
230
0.65
f
0.08
220 220 220 220 230 250 280 230
0.41 0.44 0.33 0.44 0.42 0.42 0.39 0.43
i- 0.05 i- 0.05 i-
0.06
i 0.04 i- 0.03 k 0.02
*
f
0.02 0.02
TABLE 111: Product Ratios of CdD and CdH for Quenching of Cd( 'P, ) and Cd( 'PJ)by HD and by H,/D, Mixtures temp, "C 220 230 250 280 230
excited state Cd(3P~) Cd(3P~) Cd('Pj) Cd(3P~) Cd(lP,)
CdD/CdH
1:l HJD, 0.43 f 0.06 0.42 i: 0.03 0.42 0.02 0.39 f. 0.02 0.69 f 0.09
*
HD 1.88 i: 0.52 0.07
1.88 f. 1.91 2 1.84 1.24 t
0.09
* 0.10 0.10
the quenching of Cd(lP1) and Cd(3PJ)by HD and by a 1:l mixture of H2 and Dz. The relative effective FranckCondon factors at the peak maxima for the CdH C-X (1,O) band (2391 A) and the CdD C-X (1,O) band (2415 A) were determined by assuming that the Franck-Condon factors were equal for the very diffuse D-X (0,O) band a t 2267 A for both CdH and CdD. The diffuse D-X (0,O) band positions and shapes for CdD and CdH were virtually indistinguishable. Further, a t any one temperature under Cd(3PJ) production conditions, the peak height for the D-X (0,O) band is the same in pure Hz, D2, or HD within about k6% error. The only reasonable way to interpret such data is to conclude that the branching ratios for CdH and/or CdD formation in the quenching of Cd(3PJ) by H2, HD, and D2are all the same and that the Franck-Condon factors for the D-X (0,O) bands for CdH and CdD are also identical within experimental error. All the C-X and D-X bands of CdH and CdD follow the Beer-Lambert law under the conditions of these experiments. The CdD/CdH ratios determined for a variety of experiments are shown in Table 11. We interpret these results in the following manner. There are certain experimental conditions in which the reactant primarily responsible for CdH(CdD) production is Cd(3PJ),and other conditions in which Cd(lP1) is the primary reactant. Specifically, when large excesses of Nzor CH4 are present, only Cd(3PJ) produced by collision-induced intersystem crossing is reacting with the isotopic hydrogen. In contrast,
The Journal of Physical Chemistry, Vol. 82, No. 13, 1978 1487
Reaction of Cd(3P,) and Cd('P1) with H, HD, and D,
TABLE IV: Data for Determining the Relative Yield of CdH in the Quenching of Cd('P,) and Cd(3PJ) by H, reaction mixture 1 5 Torr of H, t 285 Torr of 1 5 Torr of H, + t 275 Torr of 15 Torr of H, + t 255 Torr of 1 5 Torr of H, t t 235 Torr of 1 5 Torr of H, t 285 Torr of
Ar 1 0 Torr of N,
Fa
Cd H (arbitrary units)
corr CdH (arbitrary units)
1.00
32.8 i 1.9
36.6
0.70
44.1
1.4
47.5
0.44
54.8 + 2.6
57.4
0.32
59.3 i 1.7
61.3
0.076
75.0
75.3
i
Ar 30 Torr of N, Ar 50 Torr of N, Ar
i
1.4
N,
a F is equal to the fraction of Cd('P,) quenched by H, divided by the fraction of Cd('P,) quenched by H, and N,. CdH yield is corrected by dividing the raw CdH yield by the fraction of Cd('P,) quenched by H, and N, .
with excitation a t 2288 A only (e230 "C) with neat isotopic hydrogen, or with helium or argon present in excess, the primary reactant is taken to be Cd(lP1). Helium and argon are known to be very ineffective in the collisional production of Cd(3PJ)from Cd(1P1).2 Shown in Table I11 are the average CdD/CdH ratios that result from these assumptions. The isotopic reactivity of Cd(lP1) is obviously different from that of Cd(3PJ). The only uncertainty arises from the possibility that the isotopic hydrogens themselves collisionally induce the production of Cd(3PJ)from Cd(lP,). If so, the CdD/CdH ratios listed for Cd(lP1) are actually some weighted average of Cd(lP1) and Cd(3PJ) isotopic specificity. However, the production of Cd(3PJ) in the quenching of Cd(lP,) by Hz, HD, or Dz has not been detected, and upper limits for the branching ratios for Cd(3PJ) production are 0.15 for Hzand HD, and 0.05 for Dz.z Earlier preliminary results of Breckenridge and Callear were apparently much less precise than those of the current s t ~ d y . ~ (iii) Relative C d H Yields in the Quenching by H z of Cd(lP1)Vs. Cd(3PJ).It is possible to show that much more CdH is produced in the quenching by Hz of Cd(3PJ) than in the quenching of Cd(lP1). Results which allow the determination of an upper limit for the branching ratio for CdH production in the quenching of Cd(lP1) by Hz are shown in Table IV. Experiments were performed a t 230 "C in which increasing amounts of Nzwere added to 15 Torr of Hz,the total pressure always being made up to 300 Torr with argon. Argon was chosen as the bath gas because argon and nitrogen have similar collisional line-broadening characteristics, and it is important in these experiments that the total Cd(lP1) production rate not be altered by changes in the absorption line shape. As more and more Ar is replaced by Nz, the CdH yield changes progressively from that produced entirely by Cd(lP,) to that produced by an amount of Cd(3PJ) which is equal to or less than the total amount of Cd(lP1) produced in pure argon. Because H z quenches Cd(3PJ) -2000 times more efficiently than Nz under these conditions, essentially all (>99%) of any Cd(3PJ) formed will be quenched by Hz under all conditions reported in Table IV. From the known quenching efficiencies of Cd(lP1) by Ar, Nz, and Hz under these conditions, it is also possible to calculate the fraction of Cd(lP1) which decays radiatively or is quenched by Ar, Nz, or H z for each experiment. The percentage of Cd(lP1) quenched by Hz divided by the percentage quenched by Hz and Nz, the factor F, is shown as a column in Table IV. If for all conditions listed in Table IV the total amount of Cd(lP1) quenched by either H2 or Nz were constant, the intercepts a t F = 1 and F = 0 of a plot of CdH vs. F would give, respectively, the relative amount of CdH produced in the quenching of Cd(lP,) by Hz and that produced in the quenching of an amount of Cd(3PJ)
75.01
The
.
Flgure 1. A plot of the CdH yield vs. the fraction ( F )of Cd('P,) quenched by H2 vs. N,. See text and Table IV. The filled circle corresponds to an experiment in which on&N, is present as buffer gas, while the open circles correspond to experiments in which the buffer gas was predominantly Ar with some N, added.
which is less than or equal to that amount of Cd(lP1). However, the percent of total Cd(lP,) which decays by quenching by Hz and Nz varies from 89.7% a t 15 Torr of H z + 285 Torr of Ar to 99.4% a t 15 Torr of Hz + 285 Torr of Nz.Thus each CdH yield must be corrected for incomplete quenching by H z Nz. A plot of F vs. the corrected CdH yield is shown in Figure 1. From the CdH yield values a t F = 0 and F = 1,the upper limit of the yield of CdH in the quenching by Hz of Cd(lP1) vs. Cd(3PJ) is 0.50. Thus, it is possible to place an upper limit of 0.50 on the absolute branching ratio ( k z a / k z )of CdH formation in the quenching of Cd(lP1) by Hz. Note that only the data for the cases in which the major line-broadening gas was argon were used for the least-squares line shown in Figure 1. The apparently higher yield of CdH in pure Nzwould result if the line-broadening characteristics of 285 Torr of Nzwere sufficiently different from those of 285 Torr of Ar to cause production of only 5% more Cd(lP1). There is apparently no isotope effect on the branching ratio for total CdH + CdD formation in the quenching of Cd(3PJ) or Cd(lP1) by the isotopic hydrogens. As pointed out above, the total yield of CdH + CdD (as measured by the D-X (0,O) band intensity) was the same for Hz, HD, or Dz under conditions where Cd(3PJ) was the primary reactant. Similarly, within *lo% uncertainty there was no variation in the D-X (0,O) band intensity on substitution of H D or Dz for H z under conditions in which Cd(lP1) is the primary reactant.
+
Discussion Comparison with Quenching of Other Excited Metal
1400
The Journal of Physical Chemistry, Vol. 82,
No. 13,
W. H. Breckenridge and A. M. Renlund
1978
TABLE V: Cross Sectionsu for Quenching of Excited Electronic States of Metal Atoms by the Isotopic Hydrogens metal atom excited state
excitation energy, kcal/mol
Cd('P,) Hg(3Pl) Hg(3P,) ZII(~P~)
125.0 112.7 107.6 92.4, 92.9, 94.0
Cd(3P~)
86.1, 87.6
Mg(3P~)
62.4, 62.5, 62.6
cross sections, 8' H, HD D,
temp, K
cross section measured U(lP1) 0.(3P1)c 43p,) 0.540(~P,)+ 1.00u ( ~ P ,t) 0 . 6 2 ~ ( ~ P , ) 1.370(~P,)+ 1.00 u(3P,) O . ~ ~ U ( ~+ P0.34,) u ( 'PI) t 0.54(3P,)
503 298 298 578
24 33 -5 43
27 36
30 34 -6 35
553
12
12
7
800
0.030
A H , kcal/mol (M* t H, -+ MH t H )
-37.3 -17.7 -12.7 -10.2
i:
i: t t
0.1 0.1 0.1 0.5
0.0 * 0.1 - 5 i 12
a u = k Q / U ; iT= [ 8 k T / r p ] ' " , the mean Boltzmann speed. Cross sections either from this work or ref 1,5, or 6. that the branching ratio for the formation of Hg(3P,) in the quenching of Hg(3P,) by H, is 60.03.'.8
Note
TABLE VI: Examination of the Possibility of Charge-Transfer Mechanisms in the Quenching of Certain Excited States of Metal Atoms by H, metal atom excited state, M*
cross section for quenching by H,, A' (see Table V ) 24 24 33 -5 43 12 0.03
Atom States by Hydrogen. It is obvious from the results presented here t h a t both Cd('P1) and Cd(3PJ) are quenched quite efficiently by the isotopic hydrogens, and that chemical exit channels are very important in the resultant collisional energy disposal. It is interesting to compare the quenching of these excited states of cadmium by Hz to that of analogous excited states of the valence isoelectronic atoms Hg, Zn, and Mg. Shown in Table V are the available cross sections for quenching of Cd(lP,), C~?PJ)H , g ( 3 P ~ )Hd3P1), , ZII(~PJ),and M d 3 P ~by ) the isotopic hydrogens. Also shown are the excitation energies of the metal atom excited electronic states, and AH for the process es M* -t H,
--t
MH t H
where M* is the highest energy multiplet state involved in the quenching. For Cd(lP1),Hgt3P1),and Zn(3PP,),the quenching cross sections are essentially gas kinetic, with very little isotope effect. For these states as well as for Hg(3Po)and Cd(3PJ), for which there is moderately efficient quenching, chemical exit channels (either M H H or M + H H) are known to be major.1*2,9,10 The very low cross section for quenching of Mg(3PJ) by H2 may, in fact, be an indication that the process Mg(3PJ) H2 MgH + H is endothermic. The bond energy of MgH is uncertain by *12 kcal.'lJ2 It appears that quenching of these states involves pathways on H-M-H potential surfaces which can lead efficiently to MH + H products, and that E-to-V transfer to produce vibrationally excited Hz is of minor i m p ~ r t a n c e .This ~ is in contrast to the quenching of the first resonance doublets of the alkali metals, where cross sections of up to 25 A2 are obtained13 for Hz quenching even though the formation of the alkali metal hydride is substantially endothermic in all cases and the process is necessarily E-to-V transfer. This difference in behavior is probably due to M+Hzcharge-transfer surfaces which facilitate E-to-V transfer for the excited alkali atom doublets but which lie a t higher energies for the 3P states of Mg, Zn, Cd, and Hg-all of
+
+
-
+
[IP(M*)- EA(H2)I
est hard-sphere collision diameter, A , o f M* t H,
157 157 203 208 198 195 189
3.20 3.20 3.15 3.15 3.05 3.20 3.25
A , kcal/mol
which have substantially higher ionization potentials than the excited alkali atoms. Because the charge- transfer curve-crossing model was found to be useful in rationalizing the rough magnitudes of cross sections for quenching of Hgt3P,), Hg(3Po),Cd(lP,), and C d ( 3 P ~by ) certain molecules (see ref 2, previous paper), a brief discussion of the possible role of M+Hzcomplexes in the quenching of the states listed in Table V is appropriate. The important parameter in this model is the difference between the ionization potential of the excited metal atom and the electron affinity of the quenching molecule, designated A, because the lower the value of A the greater the distance a t which a chargetransfer potential surface M+H2- will cross the M*-H2 surface, thus providing an entry channel for efficient quenching. In Table VI, values of A are listed for the quenching processes in Table V, as well as the quenching of Li(2P)by H2for comparison. One difficulty which arises immediately is that of estimating the proper electron affinity for Hz. The electron-scattering shape resonance for H z is very broad due to the short life of the Hzresonance state,14J5 so we have chosen to represent the electron affinity of Hz as the negative of the maximum in the scattering resonance, -75 kcal/mol. It should be kept in mind, however, that the width of the scattering peak is -45 kcal/m01.'~8~~ The hard-sphere collision diameter for all the quenching rocesses listed in Table VI are estimated to be -3.2 (with a slightly lower value for Zn(3PJ) Hz). Using a value of 40 A3 for the polarizability of the charge-transfer complex: only in the case of Cd('P1) and Lit2P) would there be a crossing of the charge-transfer surface a t distances of -3.3 A, while the other chargetransfer curves would cross a t 3.0 A or less. Although it is possible that the effective electronic affinity for H2 in this process has been underestimated by 20-25 kcal/mol by taking the value a t the maximum of the e--Hz shape resonance, it is also possible that the effective polarizability for M+H2- is less than the 40 A3 assumed for the larger quenching molecules, which would have the opposite effect. Since the charge-transfer mechanism is likely to be the
+
8:
The Journal of Physical Chemistry, Val. 82, No. 13, 1978
Reaction of Cd(3P,) and Cd(’P,) with Hp, HD, and D,
TABLE VII: Yields of MH and/or MD for the Reactions M* t XY
--
reaction
A H a , kcal/mol
Cd(’P,) + H, CdH t H t D, CdD + D tHD-CdD+H t HD CdH + D Hg(3Pl)+ H, HgH t H + D, HgD t H tHD-HgDtH t HD-HgHt D Hg(3Po)t H, HgH t H t D, HgD + H tHD+HgDtH tHD-HgHtD C d ( 3 P ~+) H, -t CdH t H t D, CdD t D + HD-CdDtH +HD-CdHt D
36.2 - 37.2 - 36.6 -17.7 -16.3 -17.4 -16.9 - 12.7 -11.3 -12.4 -11.5 t 0.0 + 1.2
-
-+
-+
-
-+
- 37.3 -
t0.2
+ 0.8
-
MX t Ya yield of MH or MD 0.50b 0.50b 0.28b 0.22b 0.67 c 0.04 0.76 * 0.05 0 . 7 0 + 0.09 0.13 c 0.02 1 . o o c 0.08 0.88 1. 0.08 0.82* 0.08 0.18 5 0.02 (1.00 * 0.06)c (1.00 c 0.06) (0.65 c 0.05) (0.35 c 0.03)
total yield (MH + MD) 0.50b 0.50b 0.50b
1
0.67 0.76
t
0.83
1
1.00
t
1.00
1.00 0.88
1.ooc 1.00
M = Hg(3Po),Hg(’P,), C d ( 3 P ~ )Cd(’P,); , XY = H,, HD, D,. Values for Hg(3Po)and Hg(3P,)taken from ref 9. Yield of CdH set equal t o 1.00 (see text), Relative values correct. limits. Relative values correct. only viable explanation for the efficient quenching of Li(2P) by Hz, there is a strong likelihood that Cd+H2charge-transfer potential surfaces play a large role as well in the quenching of Cd(lP1) by H2 However, the ordinary charge-transfer mechanism would appear to be much less favorable for the quenching of the 3Pstates of Mg, Zn, Cd, and Hg by HP. Adiabatic pathways from M(3P) + H z to MH H , with small activation barriers, provide a more reasonable explanation of the rates and mechanisms of q~enching.~,~ It should be pointed out, however, that H 2 is a rather unusual species with regard to the energetics of electron acceptance. If the H-H bond is sufficiently lengthened, as obviously will be the case when an excited metal atom is in the process of breaking the H-H bond, the electron affinity of H 2 eventually becomes positive instead of negative,15 so that M+Hz- potential energy surfaces may still play a role in the dynamics of the late “chemical” stages of the formation of MH + H from M(3P) + Hz. Detailed speculation is of course hampered by the lack of theoretical knowledge of the potential surfaces involved. Although calculations of the prototypical system BeHz have been carried 0ut,16J7 only the linear symmetric portion of the ground-state surface has been examined. Branching Ratios for M H Formation in M* + H z M H H. It is interesting to compare the results obtained here for the yields of CdH in the quenching of Cd(lP,) and Cd(3PJ) by H2 with the detailed information obtained by Callear and co-workers on HgH formation in the quenching of Hg(3Pl) and Hg(3Po)by the isotopic hydrogen^.^ We believe that the yield of CdH in the quenching of H2 by Cd(3PJ) is nearly unity. It has been shown by Agius and D a r w e n P that the quantum yield of Hz formation in the Cd(3Pl) photosensitized decomposition of propane is 1.0, consistent with the postulated mechanism for totally chemical quenching
+
-
+
-
Cd(,P,) t C,H, C,H, t CdH CdH- Cd + H H + C,H, C,H, t H, -+
2C3H,
-+
C,H,,
We have recently shownlg that the extrapolated yield of CdH in the quenching of Cd(3PJ) by C3H8is 0.8 f 0.3 that of the CdH formed in the quenching of Cd(3PJ) by H2 It is quite likely, therefore, that the quenching of Cd(3PJ) results primarily in the formation of CdH, with little E-to-V transfer to form vibrationally excited Hz (i.e., that
1489
Upper
h6,/h6 = 1.0). This conclusion is similar to that reached by Callear and co-workers that chemical quenching predominates in the deactivation of Hg(3Pl) and Hg(3Po) by Hz.9,20 Shown in Table VI1 are the branching ratios for MH formation in the quenching of Cd(lP1), Hg(3P1),Hg(3Po), and Cd(3PJ) by the isotopic hydrogens. First of all, the isotope effect for the total formation of MH + MD is very small for all four excited species. Only for Hg(3P1)is there an indication of different total MH MD yields, and even then the error limits are very nearly overlapping for the three isotopic hydrogens. This is readily understood, of course, for Cd(3PJ) and Hg(3Po)where MH formation is apparently the only exit channel of importance. Second, there appears to be a definite trend to lower MH branching ratios as this channel becomes more exothermic with Hg(3P1)and particularly with Cd(lP1). Callear and c o - w ~ r k e r have s ~ ~ shown ~~ that for Hg(3Po)and Hg(3Pl), the M H H exit channel accounts for essentially the balance of the quenching events, and this would appear to be quite likely in the Cd(lP1) case as well. Since the bond strengths of CdH and HgH differ greatly (15.6 vs. 8.6 kcal/mo1)lZ a more meaningful parameter for correlation might be the ratio of the MH bond strength to AHo for the MH + H exit channel. This ratio changes from 0.68 for Hg(3Po) to 0.48 for Hg(3Pl) to 0.42 for Cd(lP1), correlating well with the total MH MD yield. Thus, as one might expect, it is apparently more difficult for an MH product molecule to stay together as the exothermicity of the channel (relative to the M H bond strength) increases. Statistical models predict the same trend, but application of phase-space theory to the Hg(3Po,l)+ Hz case has shown that the production of HgH is much more prevalent than expected,8 and the same conclusion must therefore also apply to Cd(3PJ) Hz quenching. We are able to determine only an upper limit for CdH production in the quenching of Cd(’P1) by Hz, and therefore cannot compare the yield of CdH with statistical predictions. The great variation in CdD/CdH yield in the quenching of these states by H D is obviously important mechanistically, and is discussed below. Quenching of Cd(3PJ) by the Isotopic Hydrogens. The quenching of Cd(3PJ by Hz is probably best viewed as an adiabatic chemical reaction between Cd(3P,) and H2 to produce CdH + H. The appropriate adiabatic surface could result from an avoided crossing between a triplet CdHz surface which correlates Cd(3P) + Hz into an excited
+
+ +
+
+
1490
The Journal of Physical Chemistry, Vol. 82, No. 13, 1978
M. Renlund
W. H. Breckenrldge and A.
TABLE VIII: Relative Gross Sections for the Chemical Exit Channels in the Quenching of Cd( 'P1)by H, , HD, and D, (T = 280 C) expt quenching reaction A H . kcal/rnol ,-AHIRT cross section Irel) Cd(3Pl)+ Cd(3Pl)t Cd(3P,) + Cd('P,) t
H,
CdH t H HD CdD t H HD -+ CdH t D D, --* CdD t D
1.oo 0.83 f 0.08 0.48 f 0.05 0 . 3 4 i 0.03
0.o.r 0.1
--).
t0.2i: 0.1
-f
+0.8 i: 0.1
t1.2 * 0.1
1.00 0.65 i: 0.09 0.35 i: 0.05 0.53 * 0.07
+
state of CdH (which in turn correlates with Cd(3P) H)l2lz1 quenching of Cd('P1) and Cd(3PJ) by H2, HD, and D, are and H(2Slp), and another triplet CdH, surface which obviously significantly different processes. Quenching of correlates ground-state CdH(X22+) H(2Sl,2) into Cd('P1) occurs a t essentially hard-sphere collision rates ground-state Cd(lSo)plus the first dissociative triplet of with little isotope effect; the total yield of CdH CdD for H2 (the b3&+ state). It is likely that the lowest lying Cd(lP,) is less than 50% of that for Cd(3PJ); and the portions of the triplet surface correspond to a bent Czu preference for CdD vs. CdH is much less marked in the CdH2 geometry. The first excited state of four-electron quenching by HD of Cd(lP1) than of Cd(3PJ). It should symmetric MH2complexes are bent.22 Thus side-on attack also be noted (see Tables V and VII) that although the of H,, by Cd(3PJ) is expected to be most favorable, the quenching of Hg(3Pl) by the isotopic hydrogens also occurs p-orbital density on the Cd excited atom being donated a t gas kinetic rates and with little isotope effect, the symmetrically to the H2 antibonding orbital as the u H z exothermic production of HgD vs. HgH in the quenching electron density is shared into the empty Cd s ~ r b i t a l . ~ ~of~Hg(3P1) ~~ by HD greatly predominates, with an HgD/ As seen in Table V, the production of CdH in the HgH product ratio of 5.4 compared to the CdD/CdH ratio quenching of Cd(3P1)by H2 is exactly thermoneutral, while of 1.2 for quenching of Cd(lP,) by HD.25 The mechanism the chemical exit channels in the quenching of Cd(3P1)by for quenching of Cd(lP1) by H2 may therefore be subHD and D2 are all slightly endothermic. Nevertheless, the stantially different from the quenching of the M(3P) states quenching cross sections are large. Quenching of Cd(3PJ) by Hz,since the greater exothermicity of the chemical exit by H 2 occurs a t a rate corresponding to roughly one in channels MH + H or M + H + H is unlikely to be the sole every three hard-sphere collisions. The reaction must cause of the HD exit channel differences. therefore occur with little or no activation energy (51.0 Since Cd('P1) and H('Slp) do not correlate with a kcal/mol). The simplest model is examined in Table VIII, lower-lying bound electronic state of CdH,26the direct where the relative cross sections for the chemical channels correlation of Cd(lPI) + HA leads to CdH* H a t even are compared to that predicted by assuming that the higher energy. In this case, there is no adiabatic surface differences in endothermicities are equal to the differences available to connect Cd(lP1) + H2(lZ,+)with the products in activation energies. Comparison of cross sections auCdH(X22+) H(2Sljz)or even Cd(lS0) + H('S1/2) $. tomatically allows for the substantially different collision H(2S12). Efficient nonadiabatic surface crossing from the frequencies of H,, HD, and D2 with Cd(3PJ). The model initiai singlet CdH2 potential surface (which could have is certainly qualitatively successful, but there are disa substantial minimum), perhaps directly to the lower crepancies which appear to be slightly outside the untriplet surfaces which correlate with CdH(X22+) + H certainties in the experimental cross sections and bond (2S1/2), or Cd('So) + Hz(b32,+),must therefore be involved. strengths. In the HD case, the theoretical ratio of CdD One would still expect the most favored geometry for the to CdH is 1.7 vs. the experimental ratio of 1.9, but the cross interaction of Cd(lP1) H, to be side-on attack with Czo symmetry, but it is possible at the higher energies involved sections compared to H 2 are smaller than predicted. It is possible for HD that there are also partial geometric in the Cd(lP1) + H2 interaction that almost any approach constraints on the two chemical channels, i.e., that tracan lead equally well to CdH H or Cd H H with no jectories which begin with Cd(3PJ)approaching the D atom activation barrier. This could account for the lack of are less likely to produce CdH, so that the two chemical isotopic selectivity in the quenching of Cd(lP1) by HD, since the selectivity in the Hg(3P1) HD case is likely due exit channels are not truly parallel as assumed in the model. This would bring the predicted cross sections into to the dynamical constraints of a C2" approach geometry, as discussed by Callear and M ~ G u r k . ~ , ~ closer agreement with experiment. The relative experiAnother possibility, perhaps even more reasonable in mental cross section for D2 is also somewhat higher than view of the discussion above, is that the entrance channel that predicted by the simple model. Although it is possible is dominated by Cd+H2-charge transfer states for which that the activation energy difference between H 2 and Dz there is negligible difference in energy for all attack gequenching is less than the endothermicity difference, this ometries. Transfer to the neutral surfaces which lead to would appear to worsen the theoretical agreement for the CdH H or Cd H H could occur with little isotopic HD exit channels. Detailed considerations of the transelectivity, thus accounting for the CdD/CdH ratio near sition-state theory of isotope effect^^^,^^ show that the only unity for HD quenching, and the lack of isotope effect on activated complex which would allow approximate prethe total yield of CdH CdD for the quenching of Cd('P1) diction of the isotope effects for HD as well as D2 would by H2, HD, and D2. be an asymmetric H---Cd-H species with one mode freIn any case, statistical theories of branching ratios fail quency substantially higher than even the free CdH to predict the MD/MH branching ratio for these M* + diatomic stretching frequency, which seems unlikely. One HD processes. For Hg(3Po),Hg(3Pl),and Cd(lP1), simple other possibility is that the closer spacing of D, rotational density-of-states calculations predict an MD/MH ratio of levels allows a more efficient utilization of rotational energy 2.5-3.0, since the translational density-of-states factor is to overcome the reaction endothermicity than for H,. It about the same for MH or MD for these exothermic would be very interesting of course to determine the initial processes but there are approximately twice as many rotational energy distributions of the CdH and/or CdD rotational and 40-5070 more vibrational states available in these endothermic processes, and such experiments may for the MD than for the M H state^.^'^^^ be feasible in the near future. Measurements of initial distributions of CdH and/or Quenching of Cd(lP,) by the Isotopic Hydrogens. The
+
+
+
+
+
+
+ +
+
+
+ +
+
Polyelectrolyte Activity Coefficients
CdD vibrational and rotational product states would be quite valuable in attempting to understand the detailed HD, and D2 react with Cd(lP1), mechanism by which H2, and a new technique currently being developed in our laboratories30 should facilitate a t least partial determination of these distributions in the near future.
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, and to the National Science Foundation, for support of this research. We are also grateful to the University of Utah Research Committee for a graduate fellowship awarded to A.M.R. One of us (W.H.B.) thanks Dr. R. J. Donovan, University of Edinburgh, for very helpful discussions which were facilitated by a NATO Research Grant.
References and Notes (1) W. H. Breckenridge, T. W. Broadbent, and D. S. Moore, J. Phys. Chem., 79, 1233 (1975). (2) W. H. Breckenridge and A. M. Renlund, J. Phys. Chem., paper preceding in this issue.
(3) W. H. Breckenridge and A. Callear, Trans. Faraday SOC.,67,2009 (1971). (4) M. A. Khan. Proc. Phvs. SOC..80. 1264 (1962). (5) R. P. Blickensderfer, W: H. Breckenridge,and D. S:Moore, J. Chem. Phys., 63,3681 (1975). (6)S.Yamamoto, T. Takei, N. Nishimura, and S. Hasegawa, Chem. Left., 1413 (1976), (7) H. Horiguchl and S. Tsuchya, Bull. Chem. SOC.Jpn., 50,1661 (1977). (8) A. 6. Callear and J. C. McGurk, J . Chem. SOC.,Faraday Trans. 2 , 69,97 (1973). (9) A. B. Callear and J. C. McGurk, J. Chem. Soc., faiaday Trans. 2, 68,289 (1972).
The Journal of Physical Chemistry, Vol. 82, No. 13, 1978
1491
(10) P. Bender, Phys. Rev., 36, 1543 (1930). (11) P. E. Cade and W. M. Huo, J. Chem. Phys., 47,649 (1967). (12) A. G. Gaydon, ”Dissociation Energies and Spectra of Diatomic Molecules”, 3rd ed, Chapman and Hall, London, 1968. (13) S. Lin and R. E. Weston, Jr., J. Chem. Phys., 65, 1443 (1976). (14) C. Bottcher and C. V. Sukumar, J . Phys. B , 10, 2853 (1977). (15) G. Schulz, Rev. Mod. Phys., 45,378 (1973). (16) R. Hosteny and S. Hagstrom, J . Chem. Phys., 58, 4396 (1972). (17) G. Gallup and J. Norbeck, Chem. Phys., 2, 19 (1973). (18) P. Agius and 6. deB. Darwent, J . Chem. Phys., 20, 1679 (1952). (19) W. H. Breckenridge and A. M. Renlund, to be submitted for publication. (20) A. B. Callear and P. M. Wood, J. Chem. SOC.,Faraday Trans. 2 , 68,302 (1972). (21) M. A. Khan, Proc. Phys. SOC.,80, 1264 (1962). (22) A. D. Walsh, J . Chem. SOC.,2260 (1953). (23) A. Persky and F. Klein, J. Chem. Phys., 44,3617 (1966). (24) C. Collins and N. Bowman, Ed., ACS Monog., No. 167 (1970). (25)It should be pointed out that the CdD/CdH ratio in the quenching of Cd(‘P,) by HD is formally an upper limit, since any Cd(3PJ)formed by deactivation of Cd(’P,) by H, (515%) will react with HD to form CdD and CdH in a 1.9:l.Oratio. Also, the yield of CdH -I-CdD in the quenching of Cd$P,) by HD is at least twice the yield in the Cd(’P,) case, so the effect of Cd( PJ) participation would be magnified. This may be the reason, for example, that the apparent CdD/CdH ratio in the quenching of Cd(’P,) by a 1:l H,/D, mixture is 0.69f 0.09, while the ratio of quenching rates is slightly higher, 0.88 f 0.10,even though the branching ratio for CdH from H is the Same as CdD from D., The CdD/CdH ratii for quenching of CdPP,) by a 1:l H2/D2mixture is 0.42 under these conditions. (26) M. A. Khan, Proc. Phys. Soc., 80,599 (1962). (27) G. Herzberg, “Spectra of Diatomic Molecules”, 2nd ed, Van Nostrand-Reinbold, New York, N.Y., 1950. (28)J. L. Kinsey, J . Chem. Phys., 54, 1206 (1971). (29) R. P. Levine and A. Ben-Shaul, “Chemical and Biochemical Applications of Lasers”, Vol. 11, C. 8. Moore, Ed., Academic Press, New York, N.Y., 1977. (30) W. H. Breckenridge, K. blmin, W. Nikohi, and D. Oba, to be submitted for publication.
Mean and Single Ion Activity Coefficients of Sodium Halides in Aqueous Sodium Polyphosphate and Sodium Carrageenan Solutions Marie Kowblansky, Margaret Tomasula, and Paul Ander * Department of Chemistry, Seton Hail University, South Orange, New Jersey 07079 (Received December 5, 1977) Publication costs assisted by Seton Hall University
Chloride, bromide, iodide, and sodium single ion activity coefficients and their mean activity coefficients have been determined in aqueous solutions of sodium polyphosphate and sodium b-carrageenan at 25 “C. For the sodium polyphosphate solutions, 0.00100,0.00500,and 0.0100 M NaC1, NaBr, and NaI were used and for the sodium L-carrageenan solutions, 0.00100,0.00500,and 0.0100 M NaC1, NaBr, and NaI were used. The equivalent concentration ratios of polyelectrolyte to simple salt ranged from 0.10 to 8.0. The experimental results are correlated with those predicted from the limiting laws of Manning and of Iwasa, McQuarrie, and Kwak.
Counterion, coion, and mean activity coefficients have been determined for several polyelectrolytes and simple ~ a l t s . l -For ~ aqueous solutions of sodium polyvinylsulfate,4 of sodium K - and A-carrageenad containing NaC1, and of DNA,6 the activity coefficient of the Na+ ion was found to be lowered to a much greater extent than that of the C1- ion. Recent studies have shown that ionic activity coefficients are reliable when compared with their determined mean activity coefficient values, which can be correlated with theory without the use of extra-thermodynamic An understanding of the solution properties of polye0022-3654/78/2082-1491$01 .OO/O
lectrolytes is important not only for its own sake, but as an aid to the elucidation of many biological phenomena. In recent years the interactions of small ions with polyelectrolytes have received increasing attention among investigators, certainly in major part due to the Manning theory of polyelectrolyte solution^.^^-^^ His infinite line charge model for the polyion combined two effects: the condensation of counterions onto the polyion and the Debye-Huckel interaction of uncondensed counterions and coions with the polyion. While the condensation concept has been shown to be valid experimentally and the theory gives a good representation of the counterion-polyion 0 1978 American
Chemical Society
