12978
J. Phys. Chem. B 2009, 113, 12978–12987
Thermodynamic and Kinetic Characterization of Hydrogen-Deuterium Exchange in β-Phase Palladium Weifang Luo,* Donald F. Cowgill, and Rion A. Causey Sandia National Laboratories, 7011 East AVenue, LiVermore, California 94551 ReceiVed: April 20, 2009; ReVised Manuscript ReceiVed: June 15, 2009
A Sieverts’ apparatus coupled with a residual gas analyzer (RGA) is an effective method to detect composition variations during isotopic exchange. This experimental setup provides a tool for the thermodynamic and kinetic characterization of H-D isotope exchange on Pd. The H or D concentrations in the gas and solid phases during the exchanges starting from (H2 + PdxD) and (D2 + PdxH) in β-phase Pd were monitored over a temperature range from 173 to 298 K. The equilibrium properties, i.e., the H-D separation factors R and equilibrium constants KHD, were obtained and found to be very close to those in the literature. The values of equilibrium constant reported here are the only experimental KHD data for H-D-Pd system. The H-D exchange rates on β-Pd were measured for both exchange directions. A comprehensive kinetic model is proposed that correlates the exchange rate and the driving force composed of the reactant concentrations and the extent of deviation from equilibrium. The rate constants were obtained using this model for two exchange directions. The rates for the two exchange directions were found to be close to each other at 173 K, but they differ with temperature increase in such a way that the (D2 + PdxH) has a higher rate than (H2 + PdxD). The exchange activation energies obtained are 2.0 and 3.5 kJ/mol for the (H2 + PdxD) and (D2 + PdxH) directions, respectively. The difference in activation energies results from the difference in the energy states of (H2 + PdxD) and (D2 + PdxD). The calculated exchange profiles using this model agree with the experimental values reasonably well. Dge ) [D2]e + 1/2[HD]e ;
1. Introduction Hydrogen isotope effects attract research attention because of their importance for both fundamental and technical reasons.1-14 Hydrogen isotope exchange is a technique that can be applied to isotope separation for enrichment in the heavier hydrogen isotopes.10,14 Here the symbols of H*D and D*H will be used below to denote the exchange directions starting with (H2 + PdxD) and (D2 + PdxH), respectively. The isotopic separation factor, R, describes the partitions of hydrogen isotopes in the gas and in the solid phases when an H-D-Pd exchange system reaches equilibrium. The net exchange process stops when this quantity reaches its equilibrium value. The R value is the dominating factor for the efficiency of hydrogen isotope exchange. For the H-D-Pd system R is defined as2
R)
DgeHse HgeDse
(1)
Here the subscript “g” denotes a quantity in gas phase; the subscript “s” denotes a quantity in solid phase, and the superscript “e” denotes a quantity in the equilibrium. The symbols of Hg and Dg are used here to denote the total amounts of H or D in the gas phase, respectively, in moles or pressure units, and they are defined as * Corresponding author. Tel.: (925) 294-3729. Fax: (925) 294-3410. E-mail:
[email protected].
Hge ) [H2]e + 1/2[HD]e
(2) There are R values reported in literature1-6 for the H-D-Pd system, both experimental and those calculated from models, as well as their dependences on temperature and the H/D ratio in the solid. The equilibrium constant KHD, in an exchange has also been considered,2,8,15 i.e., H2 + D2 S 2HD, is defined as:
KHD )
(PHDe)2 PH2ePD2e
(3)
The only experimental KHD value in the literature is for H-D-Pt at 293 K,15 according to our knowledge. Other KHD values in literature are calculated using Bose-Einstein and Fermi-Dirac statistics9 for the H2-D2 system. The equilibrium KHD value approaches 4 at high temperature, about 973 K, and it decreases when temperature decrease.9 There is no question that for a mixture of H2 and D2 in a chamber with a clean catalytic surface, the composition of these three gas components, H2, HD, and D2, should reach the equilibrium values. Isotopic concentration variations during complete desorption from β-phase were reported and discussed previously16 for a mixed isotope-hydride (β-phase) with a known isotopic composition. The experimental apparatus used has been shown to be acceptable for isotope exchange measurements. The present study will focus on the equilibrium properties, both R and KHD, and also on the kinetics for both exchange directions for H-D-Pd.
10.1021/jp903633b CCC: $40.75 2009 American Chemical Society Published on Web 09/08/2009
Hydrogen-Deuterium Exchange in Palladium
J. Phys. Chem. B, Vol. 113, No. 39, 2009 12979
There are reports in the literature of kinetic studies of the H-D exchange in Pd for specific devices.10,13,14 Deviations of the reported exchange activation energies are apparent.13,14 In the present study the kinetic properties of H-D exchange in Pd at various temperatures will be examined in a closed sample chamber with the isotopic gas added batchwise to the β-phase Pd. Isotopic composition variations in the gaseous and solid phases during exchange are obtained using a Sieverts’-type apparatus coupled with a residual gas analyzer (RGA). On the basis of these results R and KHD, exchange rates at various temperatures and the exchange activation energy will be determined using Arrhenius plots and the proposed kinetic model. The calculated exchange profiles using this model will be compared with the experimental measurements. The experimental results for isotope exchange are very sensitive to the cleanliness of the metal surfaces. Any impurities may lead to erroneous conclusions. In the current study two samples of the same Pd powder were used, and the reproducibility was found to be very good. Very carefully designed cleaning procedures for the test system, highvacuum equipment application, and RGA monitoring ensure the quality of the data obtained. In addition an independent experiment of H-D exchange on platinum has been carried out. The KHD value determination using this test system agrees well with the literature value, and this ensures the quality of the current experimental setup for the isotope composition measurement.
The relations between the four rate constants can be determined from the following. By inserting the equilibrium conditions, i.e., dDs/dt ) 0 and (Dge/Hge)/(Dse/Hse) ) R, into eq 5, we have
k1PD2eHse + k2PHDeHse - k-1PHDeDse - k-2PH2eDse ) 0 or k1{(PD2e + k2 /k1PHDe)Hse - (k-1 /k1PHDe + k-2 /k1PH2e)Dse} ) 0
(6)
Since k1 * 0, the following equation results from eq 6:
(PD2e + k2 /k1PHDe)Hse ) (k-1 /k1PHDe + k-2 /k1PH2e)Dse or PD2e + k2 /k1PHDe k-1 /k1PHDe + k-2 /k-1PH2e
(Hse /Dse) ) 1
(7)
Equation 1 can be rearranged to
(Hse /Dse) ) R(Hge /Dge)
(8)
By inserting eq 8 into eq 7, we obtain 2. Thermodynamic and Kinetic Considerations for the H-D-Pd Exchange System There are a series of consecutive elementary steps for the H-D exchange, i.e., H2 (D2) diffusion from the gas phase to the Pd surface, H2 (D2) dissociative adsorption on the Pd surface, diffusion of the dissociated H (D) on the Pd surface and from the Pd surface into the bulk, H (D) diffusion from the bulk Pd to the surface, the recombination of the dissociated H (D) with D (H) to form D2 or HD (HD or H2) on Pd surface, molecules of D2 or HD (H2 or HD) desorption from Pd surface to gas phase, and the reverse directions of the above process as well. In this study we consider the overall thermodynamic and kinetics of H-D-Pd exchange and the elucidation of the elementary steps mentioned above are not within the scope of this article. For isotope exchange in the H-D-Pd system in the β-phase the Hs and Ds are used to denote the quantity of H or D per mole of Pd, and therefore, an exchange process via a two-step reaction can be expressed as follows:
PD2e + (k2 /k1)PHDe
PH2e + 1/2PHDe
PD2e + 1/2PHDe (k-1 /k1)PHDe + (k-2 /k1)PH2e
From eq 9 the relations between the four rate constants can be determined
k2 ) 1/2k1 k-1 ) 1/2k1R k-2 ) k1R
(10)
By insertion of eq 10 into eq 5 we obtain
[ ( )]
k1
D2 + HsSHD + Ds k-1
k2
k-2
(4)
1 R
(9)
dDs /dt ) k1(DgHs - RHgDs) ) k1DgHs 1 - R/
HD + HsSH2 + Ds
)
DgHs HgDs (11)
During an exchange process (DgHs/HgDs) varies and reaches R when the system is at equilibrium. In the part below R′ will be employed to denote the non-equilibrium quantity of (DgHs)/ (HgDs). Equation 11 can be rewritten as
Here k1 and k-1 are the observed rate constants for the forward and backward directions of step 1, respectively, and the k2 and k-2 are for the step 2. The exchange rate equation can be expressed as
dDs /dt ) k1DgHs(1 - R/R′)
(12)
Similarly we can use the same approach to determine dHs/dt
dDs /dt ) k1[D2][Hs] + k2[HD][Hs] - k-1[HD][Ds] k-2[H2][Ds] (5)
as
dHs /dt ) k1DsHg(R - R′)
(13)
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J. Phys. Chem. B, Vol. 113, No. 39, 2009
Luo et al.
It can be seen that the exchange rate is a function of the exchange driving force, DgHs(1 - R/R′) or DsHg(R - R′), i.e., each of these rate equations (eqs 12 and 13) include the factors of gas pressures, the solid composition, and the extent of deviations from equilibrium, i.e., the factors in parentheses. The exchange rate will be zero when R′ ) R for both H*D and D*H directions. The magnitude of exchange rate is directly proportional to the concentrations of the reactants in the gas and solid phase, i.e., Hg and Ds for the H*D exchange and Dg and Hs for the D*H exchange. All the isotope composition values in the gas and solid can be measured using a Sieverts’ apparatus, coupled with an RGA, i.e., R and R′ can be determined, and therefore, the dependence of the exchange rate on the driving force can be derived. When the exchange reaction, given by eq 4, is at equilibrium,
K1)(PHDDs)e /(PD2Hs)e)k1 /k-1 K2)(PH2Ds)e /(PHDHs)e)k2 /k-2
(14)
where the K1 and K2 are the equilibrium constants for the first and second exchange reactions shown in eq 4, respectively. From eq 14 we obtain
dH2 /dt ) k2PHDHs - k-2PH2Ds dD2 /dt ) -k1PD2Hs + k-1PHDDs dHD/dt ) k1PD2Hs - k-1PHDDs k2PHDHs + k-2PH2Ds dHs /dt ) - k1PD2Hs + k-1PHDDs k2PHDHs + k-2PH2Ds dDs /dt ) k1PD2Hs - k-1PHDDs + k2PHDHs - k-2PH2Ds
(17)
The initial values of the concentrations of H and D in gas and solid phases are known at t ) 0, i.e., before the exchange and the first derivatives defined in eq 17 can be used to determine the values of the isotopic components during the exchange process by the numerical solution method:
A| tn+1 ) A| tn + (dA/dt)tn(tn+1 - tn)
(18)
Here A denotes any of the concentrations of H2, HD, D2, Hs, and Ds. This method will be used in the following part to fit the experimental exchange profiles based on the rate constants determined in this work. 4. Experimental Section
K1 /K2 ) (PHDe)2 /(PH2PD2)e ) KHD
(15)
In the discussion below the symbol KHD′ will be used to denote the nonequilibrium quantity of PHD2/(PH2PD2), analogous to R versus R′:
KHD′ ) PHD2 /(PH2PD2)
(16)
When the values of the isotopic concentrations in solid or gas phases are measured, the exchange rate constant, k1, can be determined from the slopes of the plot of the rate versus DgHs(1 - R/R′) for the D*H exchange (or the rate vs HgDs(R - R′) for the H*D exchange) according to eqs 12 and 13, and the exchange activation energies and pre-exponential factors can be determined from an Arrhenius plot of the rate constant k1 at various temperatures.
3. Calculated Exchange Profiles Using the Kinetic Model The model shown in eq 4 and the rate constants obtained can be used to calculate the isotopic compositions during an exchange. For example, for the (D2 + PdxH) exchange partial pressure variations with time in the gas and the isotopic concentrations in Pd can be expressed according to eq 4:
A 2.3 g palladium powder (from Englehardt Inc.) was employed for this study. The specific surface area of the sample, 0.2-0.5 m2/g, was obtained by porosimetry method, and therefore, its average particle size was ∼0.6 µm. The maximum diffusion distance, therefore, for the isotopes for exchange is
