J. Phys. Chem. 1993,97, 8535-8540
8535
Dissociation Energy and Enthalpy of Formation of Gaseous Silver Dimer Qingsheng Ran, Richard W. Schmude, Jr., Karl A. Gingerich,' and Dale W. Wilhitef Department of Chemistry, Texas A&M University, College Station, Texas 77843-3255
Joseph E. Kingcade, Jr. Blinn College, Division of Natural Science, Brenham, Texas 77833 Received: March 18, 1993; In Final Form: May 1 I , 1993
The equilibrum Agz(g) = ZAg(g), has been measured by Knudsen cell mass spectrometry, and thermal functions for Agz(g) have been evaluated from new spectrometricdata. From these data the dissociation energy of Agz(g) has been calculated and combined with reevaluated previous experimental data to obtain the selected value of Doo[Ag2(g)] = 158.0 f 3.4 kJ mol-' or Wa,298.15[Ag2(g)] = 160.3 f 3.4 kJ mol-'. From these together with pertinent literature data the standard enthalpy of formation, Wf,zg~.15[Agz(g)]= 409.9 f 3.5 kJ mol-' and the dissociation energy of Ag2+, D0o[Ag2+(g)] = 166.1 f 3.4 kJ mol-' have been derived. It has been noticed that the dependence of the ratio of the monomer/dimer ionization cross section on the energy of the ionizing electrons affects the determination of the pressure constants and hence the dissociation energy remarkably.
Introduction The diatomic silver molecule, Ag2(g), has been drawing the attention of scientists in different respects. Experimentalistshave studied its physical and structural data; also the theoretical methods and models have been developed. The equilibrium partial pressures of Ag and Ag2 have been measured in several Knudsen effusion mass spectrometrystudies, this information along with estimated thermal functionsare then used in evaluating the dissociation energy of Ag2.1-7 In these experiments,silver is heated and a beam of Ag(g) and Ags(g) is formed. This beam is ionized by electron impact, and the Ag+ and Ag2+ ion ratios are measured which are then converted to partial pressures of atomic and diatomic silver. The dissociation energy of Ag2 has been reviewed,8-"Jbut in all cases, assumptions on the relative ionization cross sections and the bond length of Ag2 were made which differ from recent experimental results. Several experimental studies on the structure of Ag2(g) have been carried out. The first determinations of the vibrational frequency of the silver dimer in the ground state were made in the 195Os.11-13 With one exception,14 all later experimental datalSl8 are consistent with the frequency reported by Kleman and Lindkvist.12 The study on the absorption and emission spectra of gaseous silver dimerl1-l8resulted in the lX,+ ground state and in six excited states which are all above 2.85 eV.9J9 Before the recent experimental investigations of rotational analysis of the ground-state band,20-22 no reliable values for the bond length and the rotational constants were available. Simard et a1.2l used the pulsed laser-induced fluorescence method to determine the spectroscopic constants for the ground and the A O,+ excited state. The results are in excellent agreement with those of Kramer et a1.,22who studied the topic by sub-Doppler laser spectroscopy, as well as with the result of Butler,20but differ from the earlier assumed value19 and another study.23 Severaltheoretical studies19J4 have been carried out on Ag2(g) by calculating the spectroscopic data such as the vibrational frequency, bond lengthand electron energy levels, and dissociation energy. In all cases, no low-lying electronic states are predicted. In a recent investigation25 the ratio of the ionization cross sections of the silver monomer to dimer have been measured in the energy range 10-120 eV. Silver has been commonly used as a standard for pressure calibration in Knudsen effusion mass spectrometry,26due to its t
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relative inertness, its convenient temperature of vaporizationand its well-known thermodynamic properties.2' In our laboratory we observed that sometimes when a low melting eutectic can form, the method of calibrating by total vaporization of Ag and integrating the I+ T product, or the comparison of I,+ with the literature vapor pressure (which requires Ag at unit activity) is not always possible. But in such cases, a pressure calibration using the Ag2(g) = 2Ag(g) equilibrium is still possible.28 In this method a comparably small difference in the value of Doo[Ag~(g)]has a marked influence on the resulting kb (see eq 1) and the pressures derived from it. Having quite a scatter in the literature values (see Table V), e.g., refs 1, 2, and 4 (from the same laboratory)and refs 6 and 7 (from our laboratory)motivated us to perform a redetermination (runs 1 and 7). We also included runs 2-6 and 8 where we have studied the Agz(g) = 2Ag(g) equilibrium in the context of other objectives (see Table I). New experimental results on the bond of Agz and the relative ionization cross sections of Ag(g) and AgZ(g)25 also made the reevaluation of both the thermal functions and dissociation energy of Ag2 necessary. In this report we combine our data from new experimentswith those recalculated from data obtained earlier'-7 to obtain the dissociation energy, Doe, the atomization enthalpy, AHoa,298.15,and the standard enthalpy of formation, M0f,298.15, for AJ32W.
Experimental Section Several series of experiments have been carried out in our laboratory to determine the dissociation energy and the ionization enthalpy of Agz(g). The equipment arrangement and the experimental procedure were principally the same as previously described.29 Samples were placed into Knudsen cells or into a crucible that was inserted into the Knudsen cell. The orifice diameter of the Knudsen cell was 1.0 mm in all cases. Vapor effusing from the cell was ionized by electron bombardment. The cell/crucible material, charge amount, and energy of the ionizing electronsare summarized in Table I. In runs 2 4 and 8 the silver dimer equilibrium was investigated for calibration purposes involving other molecular species to be studied. Ion currents of Ag+ and Ag2+were measured with a single focusing 30.5 cm radius, 90° magnetic deflection mass spectrometer. Temperatures were measured with a calibrated Leeds & Northrup optical pyrometer that was focused into a blackbody cavity at the bottom of the Knudsen cell. In some experiments, the pyrometer was also 0 1993 American Chemical Society
8536 The Journal of Physical Chemistry, Vol. 97, No. 32, 1993
Ran et al.
TABLE I: Summaw of Exwrimental Conditions and the Pressure Constants for the Present Runs run no.
a
sample (amt, me)
cell/crucible
electron energy, eV
Ag (200) Ag ( 8 5 ) , Ni (200) Ag (go), Si (1 50) Ag (loo), Si (150) Ag(12),Si(147),Y (153) Ag(l2), Si ( 7 9 , Sc (53) Ag (200) Ag (35), NisSil
Tajgraphite Talgraphite graphite/BN graphite/BN Tal-
20122 21 30 15 16 16 20 15
Mo/Talgraphite Ta/BN
ul\e2~45
2.0 1.95 1.7 2.5 2.45 2.45 2.0 2.5
bar K-I A-I 0.019(4) ., 22(5) 1.0(2) 0.83(5) 0.19(6) 0.024(7) 0.16(4) 2.22(8)
&,Q~,@ bar K-’A-I
O.OlO(3) ., 11(3) 0.62( 16) 0.34(6) 0.078(28) 0.0010(3) 0.08(2) 0.89( 16)
no.‘ 19 6 10 8 10 7 6 4
Figures in parentheses are the statistical uncertainty. Uncertainties were calculated additionally with 10%error for ub2/u& and 15% for yb2+/ Numbers of measurements on which the evaluations of k . are ~ based.
y&+.
TABLE II: Cibbs Energy Function -(CT- Ho)/Tand the Enthalpy Increment Function HT - HOfor Ag&) HT- Ho, -(GT- Ho)/ T, HT- Ho, kJ mol-’ T , K J K-I mo1-I kJ mol-’ 298.15 600 700 800 900 1000
222.85 247.30 252.8 1 257.61 261.87 265.69
10.180 21.386 25.115 28.847 32.581 36.317
1100 1200 1300 1400 1500 1600
269.15 272.33 275.25 277.96 280.49 282.86
40.053 43.791 47.529 5 1.267 55.006 58.746
focused on the orifice of the Knudsen cell. This served as a check for temperature gradients within the Knudsen cell. The ionic species Ag+ and Ag2+ were identified by their mass/charge ratio ( m l e ) , isotopic abundances, and ionization efficiency. The appearance potential of Ag2+ was determined as 7.3 f 0.3 eV by thelinear extrapolation method using that of Ag+ (7.57 eV30)for calibrating the electron energy. Evaluation of the Thermal Functions for Agz(g). In addition to the ’E8+ground state, six excited states have been reported for Agz(g) at 22 977.9,35 818.6, 37 620.8,39 002.7,40 136.7, and 58 259.8 cm-1, re~pectively.~~ All ofthemare far abovethe energy where the influence of the electron transition on the thermal function is nonnegligible. Theoretical analysis concluded that there is no excited state below 2 eV which could have nonnegligible contribution to the thermal f ~ n c t i o n s . ’ ~ J ~ J ~ The Aglbond length is selected as 2.5304 A which is the average of the recent experimental values 2.530,20 2.5310,21 and 2.5303 A.22 The earlier accepted bond length, 2.48 A, was stated to be based on a less reliable experimental method.19 The vibrational frequency has been measured in several studiesI1-l8and the value of 192.4 cm-l can be regarded as well established. Using the above parameters, i.e. we = 192.4 cm-1, re = 2.5304 A, and the atomic weight of 107.86832theGibbs energy functions -(GT - Ho)/ T and the enthalpy increments HT - HOfor gaseous silverdimer Agz(g) were calculated using the rigid rotor harmonic oscillator method. The results with reference to 1atm of pressure are given in Table I1and referred to as the “new thermal functions” in this paper. Evaluationof ExperimentalData from the Present Study. The dissociation energy of the silver dimer has been calculated for the reaction Ag,(g) = 2Ag(g) with the thermal functions for Ag(g) taken from ref 27 and the thermal functionsfor Ag2(g) evaluated in this study. A correction of the thermal functions from the reference state of 1 atm to the standard state of 1 bar is far below the level of the experimental uncertainty. The resulting thermodynamic properties, therefore, are considered as values under standard state of 1 bar pressure. The experimental data with the corresponding evaluation summarized in Table I11 and Table 1 s are in the sequence of taking the data within every run.
The pressure constants of Ag, kAg,have been evaluated using the vapor pressure data for pure silver27 by the relation where P is the equilibrium partial pressure, Z is the ion intensity measured when silver is at unit activity, and T the corresponding temperature. When an alloying possibility between silver and other sample components existed, only those ion intensity values of Ag+ have been used for the evaluation of k which were taken h? before the samples had ever reached the melting point of silver, the lowest-melting element in all the samples used, so that unity actvity of silver can be assumed. The consistency of the k b values calculated from the readings taken at different temperatures, both before and after reaching any solidus, has been checked with an Ag/Si sample (run 4) which has the eutectic temperature of 1108 K.33 The result supports the assumption of no reaction before reaching the silver melting temperature and therefore of unit silver activity. The pressure constants for Agz(g), k,,, were then derived from k , using the relation
where u , ~ J u , is the ionization cross section ratio at the experimental ionizing energy25 and y~g,+/y&+is the relative multiplier gain. The multiplier gain for Ag2+, yh2+,was not measurable and was estimated as to equal to y,+. The resulting pressure constants, kAg and kb,,,have been included in Table I together with the u ~ , / aratios , ~ from Franzreb et al.25 for each run. The number of data points used in the evaluation of k h is also given in Table I. The error for kAg correspondsto the standard deviation. The errors for kAgl have been arrived by additionally taking a 10%error for the experimental U ~ ~ / Cratio,25 T A ~ and a 15% error for the estimated relative multiplier gain, yAs2+/yb+ into account. When the pressure constant is known for a species, its partial pressure can be calculated from eq 1. If only the ion intensity ratio Z A ~ ~ + / Z A is~ +available, as is the case in some studies, the partial pressure for the dimer can be calculated from
(3) With the partial pressures,the dissociationenergy and the enthalpy of atomizationof AgZ(g) can be calculated by the third law method:
Doo = -RT In K p - T A [
HOO)]
(4)
where R is the gas constant (8.314 JK-I mol-’). The enthalpy of atomization, at the mean temperature of the data, AHH,,~, can be calculated with the second-law method. Essentially one uses eq 5 and plots In K p versus T1 and determines the slope which will equal AH,,T/R. The equilibrium constant, Kp,corresponds
Gaseous Silver Dimer
The Journal of Physical Chemistry, Vol. 97, No. 32, 1993 8537
TABLE III: Evaluation of the Dissociation Energy of Agl(g) from the Data of Present Rum, -AGEF = -A[(t+ Taking Run 1 as an Example, with the Full Listing Available as Table 1s -AGEF, J K-I mol-'
KP 1121 1158 1126 1148 1172 1221 1195 1125 1136 1164 1201 1183 1207 1215 1245 1215 1208 1234 1253 1168 1240
1.31 X 3.35 x 1.38X 2.42 X 5.38 X 1.53 X 7.84X 1.25 X 1.73 X 3.62 X 8.78 X 6.00X 1.07 X 1.33 X 2.11 x 1.13 X 9.05 X 1.53 X 2.31 X 2.33 X 1.47 X
10-8 10-8 10-8 10-8 10-8 lk7
10-8 10-8 10-8 10-8 10-8 10-8 lt' 10-7
lk7
10-8 lW7 lP7 10-8
2.89 X 1.60 X 3.25 X 6.79 X 1.99 X 9.41 X 3.76 X 3.40 X 4.43 x 1.40 X 4.14 X 2.50 X 5.26 X 7.55 x 1.48 X 5.79 x 4.00x 9.58 X 1.66 X 6.92X 8.74X
2.47 X 2.99 X 2.45 X 3.63 X 6.29 X 1.12 x 7.21 X 1.91 X 2.83 X 4.03 X 8.26 X 6.27 X 9.70X 1.05 X 1.38 X 9.83 X 9.13 X 1.11 x 1.49 X 3.37 x 1.13 X
lCF1] 10-l1
10-" 10-12
10-l1 10-I' 10-" 10-" 10-11
1Wo 10-11 10-1'
1WI l0-Io 10-12 10-"
TABLE I V Summary of the Experimental Values of the Dissociation Energy of Silver Dimer, DOdAgs(g)l, in kJ mol-', from the Present Study third-law dev temp no. of second-law value value from Av run no. range, K data 1 2 3 4 5 6 7 8
1121-1253 1315-1603 1315-1524 13761492 1165-1335 1223-1309 1223-1513 1243-1391
21 25 8 4 12 7 36 10
171.2k9.2 150.9k7.4
156.7 k 1.5 154.7 f 2.0 156.0f 1.2 158.9 f 3.2 131.4k6.9 157.6 f 1.4 159.1 f 3.7 173.1 i5.6 158.4 k 1.9 174.9f22.4 157.8 i 2.4 av = 157.2k 1.5
-0.5 -2.5 -1.2 1.7 -0.4 1.9 1.2 -0.6
to the reaction Agz(g) = 2Ag(g).
For a meaningful second-law evaluation the number of the data sets and the temperature range should exceed certain minimum requirements. In this study the second-law evaluation has been made for runs with at least 10 data sets taken over the temperature range of 100 K or larger. Listed in Table I11 are the measured intensities of Ag+ and Ag2+, the corresponding values for the equilibrium constant Kp, the Gibbs energy function change, and the resulting dissociation energy DO0 for each temperature, taking run 1 as example. The data for all eight runs are listed in Table 1s. In run 1, while most data were taken at 20 eV, some were taken at 22 eV, and by the evaluation they have been converted to the equivalent at 20 eV. The average experimental dissociationenergies from runs 1-8, based on the third-law method, are listed in Table IV. The overall average third-law dissociation energy for the present investigation is calculated to be Doo[Ag2(g)] = 157.2 f 1.5 kJ mol-' where the uncertainty is the standard deviation. This value is the weighted average of the eight values in Table IV with each value receiving a weight proportional to the square root of the number of data sets. A second-law evaluation of all the values listed in Table 1s yields AH1319 = 164.7 f 2.9 kJ mol-' or D"0[Ag2(g)l = 158.1 f 2.9 kJ mol-', in good agreement with the corresponding third-law value. Reevaluation of Earlier Experimental Data. A number of investigationshave been conducted previously with the Knudsen cell mass spectrometry equilibriumvapor pressure determination, from which dissociation energy values of Ag2(g) were derived.
10-3
lP3 lk3
lW3 lt3 10-2
lk3 lt3
lW3 lP3 lk3 lCF3
lC3 lk3 10-2
10-3
89.407 89.576 89.430 89.531 89.638 89.850 89.739 89.425 89.476 89.603 98.765 89.687 89.791 89.825 89.950 89.825 89.795 89.904 89.982 89.621 89.929
- fi)/n
Doot kJ mol-' 156.2 159.7 157.0 156.4 154.4 155.3 156.3 159.2 157.1 157.7 155.7 156.0 154.9 155.2 156.3 155.8 155.6 157.1 156.6 160.0 157.7 av = 156.7 f 1.5
Recent experimental results on the bond length of Agz(g)2G22 and the ionization cross sections of Ag and Agzz5as well as of their ratios as a function of the ionizing electron energies have made it possible to evaluate the thermal functions of Agz(g) more accurately and to obtain more reliable silver monomer and dimer partial pressure ratios. Therefore, experiments which have been carried out and evaluated earlier have been reevaluated. Drowart and Honig's reported second-lawand third-law values of the silver dimer dissociation energy without giving the data points measured. SchisseP measured the equilibrium vapor pressure of Ag(g) and Ag2(g) at 14 points during three runs over the temperature range 1275-1485 K, and a dissociation energy was given for Agz(g). Ackerman et ale4derived the Agz(g) dissociation energy value from seven data points taken in the temperaturerange 1 3 3 6 1502 K. Hilpert and GingerichSreported 13 ratios of ion intensities Z A ~ ~ + / Z Ataken ~ + over the temperature range 1402-1599 K in three runs. Using a similar method Kingcade6 and Wilhite' measured the ion intensities of Ag+ and Ag2+at 31 (1219-1457 K) and 8 (1197-1338 K) temperatures, respectively. For the reevaluation of the data from refs 6 and 7 the original Ag pressure constants k A g were accepted and k,, calculated with eq 2 using new U A , / U . Q values. In the reevaluation of the data where the ion intensity ratios Z,Q,+/ZA~+ were reported, the new ionization cross section ratios U . Q J U ~ were taken from the experimental work of Franzreb et al.25for each of the energies of the electrons used for the ionization. P,Q,/P,Q ratios were reevaluated using the new U , Q , / U A ~ ratios in the formula P,, = (U ~ ~ ~ + Z ~ ~ ~ + / which U ~ is,obtained ~ ~ ~ by~ combining + ~ A ~ + ) P ~ eqs 1 and 2. In other cases partial pressure ratios PAg,/PAg were reported. These were reevaluated by
The dissociation energy was then calculated with eq 4. The ratio of the multiplier gains, YA~,+/YA~+,was taken as 1, as in the present investigation. References 1 and 2 did not report detailed original data. We took their value at the mean temperature of their experiment, T = 1285 K, and P,,/PA~ = 6.5 X 1 V . In ref 4 the authors used ionizing electrons of the energy 5-70 eV, without specifying the value to which the reported ion currents correspond to. Since the work reported in refs 1 and 2 and that reported in ref 4 came from the same laboratory we assumed that 70 eV electrons were also
Ran et al.
8538 The Journal of Physical Chemistry, Vol. 97, No. 32, 1993
TABLE V Summary of the Experimental Values of the Dissociation Energy of Silver Dimer, DOa(Agz), in kJ mol-', from Different Sources
temp range, K Tm, K ellen, eV original ref 25 2 1.45 1285 70 1260-1360 refs 1, 2 1 2 1401 20 1275-1485 ref 3 2 1.45 1413 70 1336-1 502 ref 4 1.5 1.8 1501 24 ref 5 1402-1 599 1.5 2.2 1327 17 ref 6 1219-1457 1.5 2.1 1264 18 ref 7 1197-1338 1.7-2.5' 1121-1603 1319 15-30' this work source
0
original
reeval
6.5 X lo" 8.9 X 2.1 x 10-3 1.0 x 1 . O X 10-3 1.4 X 1.9 x 10-3 1.6 x 6.9 X lo" 4.8 X 5.5 x lo" 3.9 x 4.7 x
Doe, kJ mol-' original reeval
lo" 157.3 10-3 171.7 1k3 157.3 10-3 159.2 lo" 167.4 10-4 159.5 10-4
* *
8.7 9.6 9.2 3.3 1.1 1.7
* * * *
dev from av
no. of datal wt factor
5.4 -1.3 -6.4 -1.5 4.6 -2.5 -0.8
10/0.097 1410.115 710.081 13/0.110 3 1 / O . 17 1 810.087 123/0.340
163.4 8.7 156.7 9.6 151.6 9.2 156.6 3.3 162.6 1.2' 155.5 1.7' 157.2 & 1.5' av = 158.0 3.0
Contains only statistical error. For details see Table I.
R e f . 1,2
t 0
Ref. 3 4
0
Ref. 5
+
Ref. 6
0
Ref. 7
AAA4 a/
a
Run 1 Run 2 Run 3
. + 0
Run 4 Run 5 Run 6 Run 7
/ o
0 0
, , , ~ , , , , , I I,
6.60
Run 8
, , i , , , , ~ , , , , , , , l , ~ , , l , , , , , , ~ , , , i , , , , , ) , , I , , , , , , ~
7.50 10000/T, 1/K Figure 1. Plot of -log(Kp) vs 104/T data from different experiments. 6.50
7.00
used in the work of ref 4. In the work of Hilpert and GingerichS no multplier gain correction was necessary by their ion intensity detection which is equivalent to our assumption of Y ~ ~ + / Y A= ~ + 1. The temperature range, mean temperature T,, number of data points, energy of the ionizing electrons, the U.Q~/U,Q ratios, both those being used in the original work and those in the present evaluation, the P ~ g ~ I P ~ ~ r at a tT,i,o sbothobtained in theoriginal work and in the present evaluation,and dissociation energy values derived are summarizedin Table V. Detailed informationon the reevaluation,including the temperature, the ion intensities or the ratioof them (or of thevapor pressures), theGibbsenergy function, and the evaluated dissociation energy, is given in Table 2s. Results and Discussion
With the experiments carried out in our laboratory, the knowledge on the energy change of the reaction Agz(g) = 2Ag(g) have been significantly extended. Averaging all the third-law results of experiments up to date (Table V) according to eq 6, based on 206 date points altogether, we suggest, for the reaction Ag2(g) = 2Ag(g) the following values: Do,,[Ag2(g)] = 158.0 f 3.4 kJ mol-'
= 160.3 f 3.4kJ mol-' AH0a,298,15[Ag2(g)]
8.00
8.50
9.00
The uncertainty 6 is calculated by the formula
6 = [(S/N'/2)2 + +: 6 + 6;]'/2 where S = 4.2 kJ mol-' is the standard deviation, N = 7 is the total number of experimentaldata sources, S/IcnIz = 1.6kJ mol-'
62
gives the estimated standard deviation of the mean of N values. 6~ = 0.014 kJ mol-' is the uncertainty caused by the error in the thermal functions, derived from 6(w,) = 0.04% and S(r,) = 0.1%. 6~ = 1.85 kJ mol-' is the uncertainty caused by the error in the equilibrium constants, derived from the error in the ratio of the ionization cross sections, ~ ( U , Q ~ / U , Q ) = lo%, from the error in the ratio of the multiplier gains, G ( Y ~ ~ + / Y ~ + = ) 15%, and from the error in the reference Ag vapor pressure, 6(Ph) = 5%. bT = 2.39 kJ mol-' is the uncertainty caused by the error in the temperature determination, 6 ( T ) = 10 K, as it affects the equilibrium constant and the Gibbs energy function change. With all the Kpvalues, both from the experimentof the present study and from the reevaluation of the earlier investigations, a second-law value of the atomization enthalpy of Ag2 at 1319 K, hJioL13~9[Ag2(g)]= 165.3f 3.5kJmol-1,andtheAg2dissociation energy, D0o[Ag2(g)] = 158.7 f 3.5 kJ mol-', have beenobtained. This D0o[Ag2(g)] value is in good agreement with the selected value of 158.0 kJ mol-', the weighed third-law value average from different sources. A plot of log ( K p )vs 104/T with all the experimental data is given as Figure 1. Our selected value of D0o[Ag2(g)] of 158.0 f 3.4 kJ mol-', based on our third-law evaluation of all literature data and those of the present investigation compareswith the following selections
Gaseous Silver Dimer
The Journal of Physical Chemistry, Vol. 97, No. 32, 1993 8539
TABLE VI: Comparison of the Dissociation Energy Values, PdAgs(g)l, Calculated with kk Evaluated with the New u /u4 and with Those k Used in the Original Papers, R ~ 6Sand 7,Botb Using %e New and Original Thermal Functions (GEF) dissociation energy in kJ mol-', calculated with
source original G E F / k h ref 6 ref 7
167.4 159.5
new GEF, original kh, new GEF/kb,, 166.6 159.2
162.6 155.5
of the most recent reviews for this property: 1.65 f 0.03 eV mol-' or 159.2 f 2.9 kJ mol-' by Morse;'g 1.66 f 0.09 eV mol-' or 160.2 f 8.7 kJ mol-' by Huber and Herzberg;g 159.0 f 6.3 kJ mol-' by Gingerich.Io Here, Morse has based his assessment on refs 5 and 10 and earlier reviews by Gingerichwv41and Huber and Herzberg have based their assessment on refs 1-4. In all these reviews the work of refs 6 and 7 was not yet available to be included. The selected value for the dissociation energy of Ag gas dimer of 158.0 f 3.4 kJ mol-' can be combined with its ionization potential, IP(Ag2+) = 61747 f 4 cm-1 or 738.66 f 0.04 kJ mol-' recently determined by Beutel et al.42and the ionization potental of monoatomic silver, IP(Ag+) = 7.576 eV or 730.97 kJ mol-' 30 to obtain the dissociation energy of Ag2+(g), D0o[Ag2+(g)l = 166.1 f 3.5 kJ mol-'. The enthalpy of dissociation of the silver dimer was calculated as Mo,,29~.l~[Ag2(g)] = 160.3 f 3.4 kJ mol-, from which the standard enthalpy of formation of the silver dimer, M0f,298.15[Ag~(g)] of 407.9 f 3.5 kJ mol-' was obtained by incorporating the enthalpy of sublimation of silver monomer.27 It is noted that the change in the ionization cross sections causes a significant change in the evaluated dissociation energy. This is shown in Table VI where evaluations of the data of Kingcade6 and Wilhite7 both with the new k h 2 evaluated with the experimental U A ~ J U Aratio ~ in this paper and with those used in the original publications are listed, comparing with the results in the original papers. This suggests the importance of good values of the ionization cross sections in determining the dissociation energy by the Knudsen cell mass spectrometric method. The same would also be true for other elements. Therefore, there is the necessity of checkingthevalue of the dimer dissociationenergy whenever experimental values for the ionization cross section for the monomer and dimer become available. The new value of the dissociation energy of Agz(g) suggests the necessity of revising the value for the dissociation energies of other molecules, which had been determined using the Ag2(g) = 2Ag(g) equilibrium for pressure calibration, such as in refs 34-36. The value of Do,[Ag2(g)] evaluated depends also on the relative multiplier gain, ~ A ~ ~ + / Y Q in + , the same way as it does on the U A ~ J U A ~ratio (see eqs 2-5). This value could not be measured becauseof thecomparatively low intensityof Agz+ions. However, the 7 A 8 , + / ~ A s + ratio can be predicted from experimental data obtained for atomic and molecular ions up to date. The relationship yi = was obtained by Pottie et al.37for 62 atomic species. According to this 'mass effect" one can estimate the 72/71 value as 0.76 in the case of diatomic and monoatomic Ag ions. Because the multiplier gains of molecular species are slightly bigger in comparison to that of the atomic (the 'molecular effect"), the 'mass effect" on the 72/71 value is partly compensated so that this value is changed towards unity. The y2/y1 value equal to 1 was measured experimentally by Kordis et a1.39 for Au2+ and Au+ ions with the accuracy of f17%. For the reason discussed, the value of the relative multiplier gain as equal to 1 was accepted in this work similar to the other authors in refs 1-3 and refs 6 and 7. Ackerman et al.4 have estimated the 7 2 / 7 1 value as 0.66 from the experimental data for several atomic species taking only the "mass effect" into account. The possible error of our estimation of 72/cy1 value should not exceed 15%.
Compared with the ionizationcross section,the change through the present new evaluation of the thermal functions results in only a minor change in the dissociationenergy, as shown in Table VI.
Conclusion On the basis of new experiments and results published earlier, the dissociationenergy and enthalpy of atomization of silverdimer have been determined using thermal functions for Agz(g) which has also been reevaluated. The resulting values are Doo[Ag2(g)] = 158.0 f 3.4 kJ mol-' AH0a,298~15[Ag2(g)] = 160.3 f 3.4 kJ mol-' These values are lower than those given by the earlier review works. The difference has been attributed in a large part to the pressure constant error for Agz(g) resulted from the estimation of the u ~ g ~ / uratios h at different ionization energies made by earlier studies. The nonnegligible effect of this parameter determined here suggests the necessity of checking the results obtained for other molecules in a similar way. The new value of the dissociation energy of Agz(g) suggeststhe necessity of revising the value for the dissociation energies of other molecules, which had been determined using the Agz(g) = 2Ag(g) equilibrium for pressure calibration.
Acknowledgment. The authors are very grateful to Dr. M. Miller for many helpful discussions. They would also like to acknowledge the financial support from the Robert A. Welch Foundation under Grant No. A-0387 and from the National Science Foundation under Grant No. CHE-9117752. Supplementary Material Available: Table 1S, evaluation of the dissociation energy of Agz(g) from the data of present runs. -AGEF = -A[(GT- Ho)/7"JY and Table 2S, dissociation energy of Ag2, reevaluated from data of earlier experiments, -AGEF = -A[(GT(1 1 pages). Ordering information is given on any current masthead page. References and Notes (1) Drowart, J.; Honig, R. E. J . Chem. Phys. 1956, 25, 581. (2) Drowart, J.; Honig, R. E. J . Phys. Chem. 1957, 61, 980. (3) Schissel, P. J. Chem. Phys. 1957, 26, 1276. (4) Ackerman, M.; Stafford, F. E.; Drowart, J. J. Chem. Phys. 1960,33, 1784. (5) Hilpert, K.; Gingerich, K. A. Ber. Bunsen-Ges. Phys. Chem. 1980. 84, 739. (6) Kingcade, J. E., Jr. Ph.D. Thesis, Texas A B M University, College Station, TX, 1983. (7) Wilhite, D. W. Masters Thesis, Texas A&M University, College Station, TX, 1988.
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