J . Chem. SOC., Faraday Trans. 1, 1984, 80, 3233-3238 Kinetics of the Reaction of Lead@) Oxide with Hydrogen Bromide in the Temperature Range 398-548 K BY PHILIP G. HARRISON* AND RICHARD SMITH Department of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD Received 1st June. 1983 The kinetics of the reaction of both the tetragonal and orthorhombic modifications of lead(1r) oxide with hydrogen bromide at a pressure of 1.33 kN m-2 have been studied in the temperature range 398-548 K. Additionally, the reaction with the orthorhombic modification has been examined at HBr pressures of 0.67, 3.33 and 6.65 kN m-2. The kinetic behaviour of the two modifications is substantially different, an observation which is largely attributed to the difference in particle size.Reaction profiles for the orthorhombic modification (mean particle diameter ca. 15 pm) comprise a rapid initial reaction followed by a slow diffusion-controlled reaction giving conversions to lead@) bromide of ca. 5 % at 398 K rising to ca. 62 % at 548 K after 300 min. In contrast, reaction with the tetragonal modification (mean particle diameter ca. 2 pm) is rapid at all temperatures giving much higher conversions of ca. 47 % at 398 K rising to ca. 92 % at 548 K after only 40 min. Analysis of the rapid reaction in terms of a phase-boundary model yields rate constants (kpB) varying from 1.54 x lop4 s-' at 448 K to 2.55 x lop4 s-' at 548 K. The slow, limiting reaction observed for the orthorhombic modification is best described by the diffusion-controlled model of Zhuravlev, Lesokhin and Tempel'man, with derived rate constants (kZLT) varying from 1.65 x lo-* s-l at 398 K to 7.86 x loM6 s-' at 548 K, essentially independent of applied HBr pressure.Activation energies determined from Arrhenius analysis of the rate-constant data showed that for the phase-boundary-controlled reaction with the tetragonal modification is much lower [ 10.6(5) kJ mol-'1 than that for the diffusion-controlled reaction with the orthorhombic phase [71.8(17) kJ mol-'1. The only previous report of the reaction between lead@) oxide and hydrogen bromide is a study of the chemisorption of the gas onto vapour-deposited lead(I1) oxide in the temperature range 113-293 K.l In this study, the reaction was proposed to proceed by the initial chemisorption of a monolayer of HBr and the formation of dilead oxide dibromide on the surface followed by, at room temperature, a rapid reaction with lower layers of oxide.In this investigation we report a detailed account of the reaction of the orthorhombic (massicot) and tetragonal (litharge) modifications of lead(1r) oxide with hydrogen bromide in the temperature range 398-548 K. EXPERIMENTAL The vacuum line, microbalance and general procedure have been described previously.2 Hydrogen bromide (purity 99.8%, B.D.H.) was purified on a gas-purification vacuum line by collection in a 77 K trap after being passed through a stainless-steel coil immersed in a 197 K bath. It was further purified by means of a series of slush baths at 190 and 183 K and was finally collected and stored in storage bulbs.Lead@) oxide of the orthorhombic modification (East Anglia Chemicals) had the specification PbO > 98 % ,chloride < 0.02 % ,insoluble matter < 1 % , Cu < 0.002%, Fe < 0.0005%, Ag < 0.005%, Bi < 0.02%, Sb < 0.005% and As < 0.0005%. The sample of tetragonal lead oxide (Koch Light Chemicals) had a purity specification of 99.999%. 32333234 REACTION OF PbO WITH HBr For each kinetic run ca. 0.15 g of the oxide was accurately weighed into a silica reaction bucket, which was suspended from the quartz spring microbalance. The reaction system was evacuated overnight at a pressure of ca. lo-’ kN mP2 Torr) and brought to thermal equilibrium at the desired temperature. Hydrogen bromide was introduced into the reaction system at the required pressure and the extension of the spring monitored by means of a cathetometer. All experiments were performed in duplicate with a reproducibility of During the course of the reaction the samples of both oxide modifications underwent a colour change from yellow to pale grey because of the formation of lead@) bromide, and also changed from a loose powder into a self-supporting compact because of the greater molar volume of the bromide.Reaction products were examined by X.r.d. and by elemental analysis. X.r.d. showed that lead@) bromide was produced at the expense of lead(@ oxide. However, in reaction products obtained at higher temperatures (> 473 K), traces of dilead oxide dibromide were observed, formed by a subsequent solid-state reaction between lead(@ oxide and newly formed lead(I1) br~rnide.~ Good agreement was found for the amount of bromine in the product by both microanalysis and by calculation from the gravimetric data.5 % . RESULTS AND DISCUSSION Reaction profiles for the reaction of the orthorhombic and tetragonal modifications of lead@) oxide with hydrogen bromine at a pressure of 1.33 kN rn-, in the temperature range 398-548 K are illustrated in fig. 1-3 in terms of percentage conversion of the oxide according to: PbO + 2HBr --+ PbBr, + H20. Quite clearly, the character of the kinetic behaviour of the two modifications is different. The profiles for the orthorhombic modification (fig. 1 and 2) are composed of two distinct components, a rapid initial reaction followed by a much slower, limiting reaction giving a conversion of ca.5% at 398 K rising to ca. 62% at 548 K after a period of 300 min. In contrast, reaction with the tetragonal modification is rapid at all temperatures giving conversions of ca. 47% at 398 K rising to ca. 92% at 548 K after only 40 min. Although the reaction profiles for temperatures > 448 K are smooth curves over this period, those observed at 423 and 398 K exhibit distinct discontinuities after ca. 20 min, indicative of a change of mechanism (fig. 3). For both modifications the rate of reaction increases with increasing temperature, with reaction profiles which are deceleratory throughout the course of the reaction. The observed difference in the behaviour of the two modifications may be attributed to three possible causes: (i) a fundamental difference in the solid-state structure, (ii) the presence or otherwise of impurities in the oxide and.(iii) a difference in the particle size of the two samples.Although the densities of the two modifications are different (the tetragonal phase has a higher density of 9.53 compared with 8.0 for the orthorhombic phase), the solid-state structures are quite similar.*? Structural consi- derations would therefore predict a lower reactivity for the more tightly packed tetragonal phase, contrary to observation. The orthorhombic phase (thermodynami- cally stable at 488 K) is stabilized at ambient temperatures by the presence of impurities, which would be expected to facilitate reaction via nuclei-growth mechan- isms, again contrary to observation.The major difference between the two oxide samples is particle size, the mean particle diameters being ca. 15 and ca. 2 pm for the orthorhombic and tetraganal modifications, respectively, corresponding to surface areas of ca. 2.5 x and ca. 0.2 m2 g-l. Thus, the oxide surface area of the tetragonal modification available for reaction is ca. 8 times that of the orthorhombic phase, which for a heterogeneous solid-gas reaction is a significant difference and would be expected to lead to a more rapid reaction.P. G. HARRISON AND R. SMITH 3235 tlmin Fig. 1. Reaction profiles for the reaction of orthorhombic lead oxide with hydrogen bromide at a pressure of 1.33 kN m-2 and a temperature of 0, 398; A, 423 and 0, 448 K (only every third data point plotted).n s tlmin Fig. 2. Reaction profiles for the reaction of orthorhombic lead oxide with hydrogen bromide at a pressure of 1.33 kN m-2 and a temperature of a, 473; A, 498; A, 523 and 0,548 K (only every third data point plotted). The three principal types of model which have been applied to the interpretation of solid-gas kinetic data are : (i) nuclei-growth models, (ii) phase-boundary models and (iii) diffusion-controlled models. Some of the more commonly used solid-state reaction-rate equations have recently been briefly summarised by O'Brien.g In the present case, the initial rapid reaction component of the reaction profile for the orthorhombic phase corresponds to a surface reaction, during which a coherent layer of lead@) bromide is formed, through which the diffusion of HBr is rate determining for the slower, limiting reaction. The most widely used diffusion model is the one formulated by Jander,',* and described by kJ t = [l -(1 -x);l2 where k, is the rate constant and x is the fraction of the reaction completed in time t .However, plots of the function [ 1 - (1 - x)4I2 against time for the present data deviate from linearity. Of the other models available, that of Zhuravlev, Lesokhin and Tempel'man (ZLT),* in which the Jander analysis is modified by assuming that the activity of the reacting material is proportional to the fraction unreacted, best3236 REACTION OF PbO WITH HBr 1 oc 90 80 70 n 60 5 c *; 50 z O0 40 30 20 10 0 b A . A A 0 * ' Q 0 0 ' 4 b I I I I 1 10 20 30 40 50 t/min Fig. 3. Reaction profiles for the reaction of tetragonal lead oxide with hydrogen bromide at a pressure of 1.33 kN m-2 and a temperature of 0, 398; V, 423; 0, 448; Y7, 473; A, 498; 0, 523 and A, 548 K (only every third data point plotted).describes the experimental data for the diffusion-controlled reaction. In this model, the rate equation is given by 1 --x After a short initial period (ca. 15 min) plots of the ZLT function against time, shown in fig. 4, afforded good linear fits to the experimental data for each temperature over the time period considered (300 min). Rate constants (kzLT) calculated using this analysis are collected in table 1 and range from 1.65 x low8 s-l at 398 K to 7.86 x loL6 s-l at 548 K. Analysis using either nuclei-growth or phase-boundary models gave unsatisfactory results.To investigate the effect of applied pressure of HBr on the reaction, kinetic data for the same temperature were collected for applied pressures of 0.67, 3.33 and 6.65 kN m-2. The reaction profiles obtained were very similar to those for an HBr pressure of 1.33 kN m-2, comprising a fast initial surface reaction and a subsequent much slower diffusion-controlled reaction. Rate constants derived using the ZLT analysis for the four HBr pressures are summarized in table 1, from which it can be seen that the rate constants are essentially independent of applied HBr pressure. Activation energies for the diffusion-controlled reaction calculated from least-squares analysis of linear Arrhenius plots are also summarized in table 1, yielding a mean value of 71.8(1.7) kJ mol-l.P.G. HARRISON AND R. SMITH 0 0 0 0 0 0 0 3237 Fig. 4. Plot of {[l/(l -x)]i- l}z against t for the reaction of orthorhombic PbO with HBr (pressure 1.33 kN m-2) at a temperature of 0 , 4 7 3 ; A, 498; A, 523 and 0, 548 K. Table 1. Rate-constant and activation-energy data for the reaction of orthorhombic lead oxide with hydrogen bromide. -1n kZLT HBr pressure/kN m-2 TIK 0.67 1.33 3.33 6.65 398 423 448 473 498 523 548 activation energy/kJ mol-l 18.13 17.26 16.25 15.46 14.21 13.30 12.01 73.0 17.92 16.76 16.42 15.17 14.03 13.35 11.75 71.1 17.77 17.81 17.08 16.97 16.38 16.30 15.16 15.03 14.03 13.82 13.35 13.08 12.12 11.72 69.7 73.3 The initial rapid component of the reaction profile for the orthorhombic phase is probably to be identified with the whole of the reaction profile for the reaction observed with the tetragonal phase.Not surprisingly, analysis of the kinetic data in this latter case by the KLT method showed that the reaction was not diffusion controlled. The application of nuclei-growth models also proved unsatisfactory. Phase-boundary analyses, however, provide a good representation of the experimental data in the temperature range 448-548 K, indicating that the lead@) bromide product layer is porous to HBr and that bond-making and/or bond-breaking is the rate- determining step. Some deviation from this analysis is observed for the later parts of the reaction profiles, the percentage conversion at which this deviation occurs increasing with increasing temperature, and can be attributed to a change in mechanism from phase-boundary control to diffusion control as the porosity of the product layer decreases.The deviation is most marked in the reaction profiles obtained at 398 and 423 K, where the reaction can be resolved into two distinct parts: an initial3238 REACTION OF PbO WITH HBr Table 2. Rate-constant data for the reaction of tetragonal lead oxide with hydrogen bromide at a pressure of 1.33 kN m-2 -In k,, 448 8.78 473 8.70 498 8.58 523 8.40 548 8.27 fast reaction and a second slower reaction, where diffusion through the product layer is now rate determining. Rate constants (kPB) derived using the expression kt = l-(l-x){ are listed in table 2, from which an activation energy of 10.6(5) kJ mol-l was derived by least-squares analysis of the Arrhenius plot.Thus, in conclusion, it would appear that particle size, rather than some fundamental difference in solid-state constitution, is primarily responsible for the observed difference in kinetic behaviour between the two samples of lead@) oxide studied. The initial reaction with HBr, when the lead@) bromide product layer still allows facile access to the oxide, is phase-boundary controlled. When the product layer becomes coherent, the reaction becomes diffusion controlled. Consequently, for smaller particles with large surface area, the rapid phase-boundary-controlled reaction proceeds to a greater extent. We thank the S.E.R.C. and the Associated Octel Company Ltd for support in the form of a CASE Award to R.S. A. H. Boonstra and R. M. A. Sidler, J. Electrochem. SOC., 1972, 119, 1193. * P. G. Harrison and R. Smith, J. Chem. Soc., Furuduy Trans. I , 1980, 76,442. F. W. Lamb and L. M. Niebylski, J . Am. Chem. Soc., 1953,75, 511. W. J. Moore and L. Pauling, J. Am. Chem. Soc., 1941, 63, 1393. J. Lecleiewicz, Actu Crystallogr., 1961, 14, 66. P. OBrien, J. Chem. SOC., Dalton Trans., 1982, 1173. ’ W. Jander, 2. Anorg. Chem., 1927, 163, 1. * S. F. Hulbert, J. Br. Cerum. SOC., 1969, 6, 1 1. * V. F. Zhuravlev, I. G. Lesokhin and R. G. Tempel’man J. Appl. Chem. USSR, 1948,21, 887. lo N. B. Hannay, Treatise on the Solid State (Plenum Press, New York, 1976), vol. 4. (PAPER 3/867)