Knudsen Effusion Technique Research Articles

Mass spectrometric determination of the dissociation energies of the molecules CuLi, AgLi and AuLi

Equilibria involving gaseous species CuLi, AgLi and AuLi have been investigated using a Knudsen effusion technique combined with mass spectrometric analysis of the vapour composition. The following dissociation energies were derived by the third law procedure from the measured ion intensities, free energy functions and auxiliary data: D°0(CuLi)= 189.3 ± 8.8 kJ mol–1, D°0(AgLi)= 173.6 ± 6.3 kJ mol–1, D°0(AuLi)= 280.8 ± 6.5 kJ mol–1. The measured dissociation energies are considerably lower than those calculated from the Pauling model of the polar bond.

Dissociation energy of CeO2 and Ce2O2 molecules

A combination of Knudsen effusion and mass spectrometric techniques has been employed in studying the gaseous species in thermodynamic equilibrium with condensed CeO2 and with condensed Ce–CeO2 mixtures. A thermodynamic treatment of ion currents yields a value of ΔH°298=135±6 kcal mole−1 for the heat of vaporization of CeO2(s). The following reactions: Ce(g)+CeO2(g)⇄ 2CeO(g), (1), Ce2O2(g)⇄ 2CeO(g), (2), have been studied and it has been found that ΔH°298=−19±4 kcal mole−1 and ΔH°298=90±6 kcal mole−1 for Reactions (1) and (2), respectively. Utilizing these heats of reaction, the CeO2 and Ce2O2 atomization energies at 298°K were determined to be D°298(CeO2)=350±15 kcal mole−1 and D°298(Ce2O2)=474±15 kcal mole−1.

The sublimation thermodynamics of zinc(II) fluoride

The congruent sublimation of ZnF2 to the gaseous monomer has been studied by targetcollection Knudsen-effusion techniques over the temperature range 901 to 1125 K. The vapour pressures of solid ZnF2 may be represented by log 10 { p ( Zn F 2 ) / atm } = − ( 1318 5 ± 7 2 ) K / T + ( 8.43 7 ± 0.07 1 ) . At 1015 K, ΔHos = (60.33±0.33) kcalth mol−1 and ΔSos = (38.60±0.33) calthK−1 mol−1. Combination of these second-law results with estimated and measured heat capacities yields ΔHo(298.15 K) = (64.01±0.90) kcalth mol−1 and ΔSo(298.15 K) = (44.5±1.2) calth K−1 mol−1 for the sublimation reaction. At an extrapolated normal boiling temperature of (1695±50) K, ΔHov = (46.9±1.6) kcalth mol−1 and ΔSov = (27.7±1.2) calth K−1 mol−1. Third-law values were derived by use of thermal functions based on two models.

Heat of dissociation of As4(g) and the heat of formation of As2(g)

The equilibrium As4(g)=2As2(g) has been studied in detail over solid phase MoAs2 and Mo2As3 using the Knudsen effusion technique combined with a mass spectrometer. A ``see-through'' ion source and a liquid-nitrogen cooled condensation plate were used to eliminate the spurious As4(g) which has been encountered by other investigators. Excellent agreement was obtained between the second- and third-law enthalpies. From equilibrium constants measured between 807 and 1050°K, the following third-law heats were determined: As4(g)=2As2(g), Δ H0°=53.95± 1.1, Δ H298°=54.26± 0.7, Δ H0°(f)[As2(g)]=45.65± 0.7, Δ H298(f)°[As2(g)]=45.45± 0.7, all in kilocalorie mole−1, the errors being estimates of total error. The results obtained when GaAs, Mo5As4, and Zn3As2 were used as source phases are briefly described. The results of previous investigations of the As4(g)=2As2(g) equilibrium are critically discussed.

Determination of the Heats of Atomization of the Molecules RhC2, RhC, and TiC2 by High Temperature Mass Spectrometry

The mass spectrometric Knudsen effusion technique has been used in the determination of the thermodynamic properties of the gaseous molecules RhC, TiC2, and RhC2 over a TiP–Rh–C system. The third law enthalpies, ΔH0o, in kcal of the reactions (1) Rh(g)+C(graph)=RhC(g), (2) Ti(g)+2C(graph)=TiC2(g), (3) Rh(g)+2C(graph)=RhC2(g), (4) RhC2(g)+Rh(g)=2RhC(g), (5) TiC2(g)+Rh(g)=RhC2(g)+Ti(g), and (6) RhC(g)=Rh(g)+C(g) have been determined as 33.1± 0.5, 62.0± 0.8, 93.6± 1.1, −26.0± 0.7, 32.2± 1.3, and 137.4± 0.9, respectively. The second law value of ΔH0o corresponding to Reaction (1) is 29.7±0.6 kcal. These reaction enthalpies have been combined with appropriated literature data to yield the dissociation energy D0o(RhC)=138.0± 2.0 kcal mole−1 and the heats of atomization, Δ Hatm,0o[RhC2(g)]=247± 5.0 kcal mole−1 and Δ Hatm,0o[TiC2(g)]=277± 2.0 kcal mole−1. The bond dissociation energies, D0o, for Rh–C2 and Ti–C2, have been determined as 105± 5 and 135± 4 kcal mole−1, respectively. The standard heats of formation, Hf,298o, of gaseous RhC, TiC2, and RhC2 have been derived as 164.1± 2.3, 174.4± 2.1, and 225± 5 kcal mole−1, respectively.

Thermodynamics of formation of compounds in the Ce-Mg, Nd-Mg, Gd-Mg, Dy-Mg, Er-Mg, and Lu-Mg binary systems in the temperature range 650°to 930°K

The vapor pressures of magnesium over a series of two-phase alloys of Mg with Ce, Nd, Gd, Dy, Er, and Lu have been measured by the Knudsen effusion technique in the temperature range 650 to 930 K. These vapor pressure measurements were combined with data concerning the terminal solubility of magnesium in the rare earths and the vapor pressure of pure magnesium to evaluate the standard free energies of formation of the twenty-four intermediate phases in these six binary systems. Trends in the data correlate with the number of unpaired 4f electrons of the lanthanon component, and the inference is that the 4f electrons make a contribution to the bonding interactions. There is also evident a shift in the pattern of the free energies of formation of the phases with the shift occurring as the atomic number of the lanthanon component is increased. This implies modification of the bonding interactions by some additional factor which might be either a size factor or a crystal-environmental dependence of the strength of the 4f bonding contributions. Experiments are proposed to distinguish between the possibilities.

Solid‐Gas Phase Equilibria and Thermodynamic Properties of Cadmium Selenide

The investigation of the solid‐gas phase equilibrium of revealed that at about 400° sublimes initially by losing selenium to form nonstoichiometric , where ; the resulting compound sublimes congruently. Since existing thermodynamic data for are either incomplete or show significant differences, the high‐temperature thermodynamic properties of were reinvestigated using the Knudsen effusion technique. With the heat capacity function for measured for the first time in this work and with tabulated thermochemical data, the vapor pressure measurements were evaluated in terms of the standard heat of formation [ (third‐law evaluation)] and the absolute entropy [ (second‐law evaluation)] of . Previous investigations are reviewed and compared with present results.

Gaseous Metal Nitrides. IV. The Dissociation Energy of Cerium Mononitride

The CeN molecule has been identified in the vapor phase over a Au–Ce–CeS–BN–C mixture, using a combination of Knudsen effusion and mass spectrometric techniques. The third law enthalpies for the reactions 2CeN(g)=N2(g)+Ce2(g), 2CeN(g)+Au2(g)=2CeAu(g)+N2(g), 2CeN(g)=2Ce(g)+N2(g), and 2CeN(g)+2Au(g)=2CeAu(g)+N2(g) were determined. Combined with published ancillary data, these reaction enthalpies yielded the following thermodynamic properties for gaseous CeN: CeN(g)=Ce(g)+N(g); D0° = 123.0 ± 5.0 kcal mol−1 or 514.6 ± 21 kJ mol−1 Ce(s)+0.5 N2(g)=CeN(g); ΔHf,298° = 90.1 ± 4.0 kcal mol−1 or 377.0 ± 17 kJ mol−1.

Gaseous phosphorus compounds: Part V. The dissociation energy and heat of formation of carbon monophosphide

The chemical equilibrium CP(g) + P(g) ⇌ P 2(g) + C(g) has been studied by means of the Knudsen effusion technique combined with mass spectrometric analysis of the vapor. The enthalpy of reaction, Δ H O 298− was determined as 6.3 ± 4.0 kcal/mole. Combined with the literature value for the dissociation energy of P 2, the dissociation energy of gaseous carbon monophosphide was calculated as D O 298 = 123.2 ± 4.0 kcal/mole or D O O = 122.1 ± 4.0 kcal/mole. The corresponding value for the standard heat of formation is ΔH O f.298 = 127.5±4.5 kcal/mole. This compares with the selected JANAF value of 111.7 ± 23.1 kcal/mole.

A thermodynamic investigation of the Ag-Mn system

A thermodynamic study has been made of the Ag-Mn system in the temperature range of 1100° to 1200°K, using a modified Knudsen effusion technique. The activities of silver and manganese were determined by analysis of the vapor phase using X-ray fluorescence and appropriate graphical integration of the composition function relating activity and vapor phase composition. Silver-rich solutions, in the single-phase region, were found to exhibit exothermic heats of mixing and negative deviations from ideality for the activity of the solvent and both negative and positive deviations from Raoult’s law for the activity of the solute. Manganese-rich solutions, in the two-phase region, exhibit endothermic heats of mixing and positive deviations from ideality for the activities of both the solute and solvent. The negative excess entropies of mixing in the dilute manganese region are attributed to magnetic and electronic changes which occur at 20 at. pct Mn. These changes in magnetic and electronic properties are a result of a gradual change in the Mn-Mn interatomic separation and electronic structure. With increasing manganese content beyond 20 at. pct Mn, the excess entropies become positive, passing through a maximum as the two-phase boundary is reached. The positive excess entropies of mixing are attributed to lattice distortion resulting from size differences between silver and manganese atoms.

Gaseous Metal Borides. III. The Dissociation Energy and Heat of Formation of Gold Monoboride

The AuB molecule has been identified in the vapor phase over an Au–BN–C mixture and an Au–Ce–CeS–BN–C mixture, using a combination of Knudsen effusion and mass spectrometric techniques. Its appearance potential was measured as 8.7 ± 0.5 eV. The enthalpies for the reactions AuB(g)+Au(g)=Au2(g)+B(g), AuB(g)+Ce(g)=CeAu(g)+B(g), and AuB(g)=Au(g)+B(g) were determined by the second and third law method. Combined with published ancillary data these reaction enthalpies yielded the following thermodynamic properties for gaseous AuB: AuB(g)=Au(g)+B(g), D0° = 87.0 ± 2.5 kcal mol−1 or 364 ± 11 kJ mol−1; Au(s)+B(c)=AuB(g), ΔHf,298° = 135.3 ± 3.0 kcal mol−1or 566 ± 13 kJ mol−1.

Gaseous Phosphorus Compounds. IV. Thermodynamic Study of Gallium Monophosphide with a Mass Spectrometer and Dissociation Energy of Aluminum Diphosphide

Gaseous equilibria involving the GaP molecule have been studied by means of the Knudsen-effusion technique in combination with mass spectrometric analysis of the vapor phase. In order to obtain the desired phosphorus and gallium partial pressures of comparable magnitude, mixtures of gallium and either WP or Th3P4 which were evaporated from a graphite Knudsen cell were employed. From the experimentally determined partial pressures the equilibrium constants and the enthalpies of the reactions Ga(g)+0.5 P2(g)=GaP(g), Ga(g)+0.5 P4(g)=GaP(g)+0.5 P2(g), 0.5 Ga2(g)+0.5 P2(g)=GaP(g), and GaAg(g)+0.5 P2(g)=GaP(g)+0.5 Ag2(g) have been determined. These reaction enthalpies have been combined with appropriate literature data to yield the dissociation energy, D0° = 54.0 ± 3.0 kcal mol−1, the heat of sublimation, ΔHs,298° = 111.2 ± 5.0 kcal mol−1, and the heat of formation ΔHf,298° = 90.3 ± 4.1 kcal mol−1, of gaseous gallium monophosphide. The molecule AlP2 has been observed over the congruently vaporizing AlP(s). The enthalphy of the reaction AlP2(g)=Al(g)+P2(g) was obtained as ΔH0° = 33 ± 5 kcal mol−1. From this value the heat of atomization of AlP2, D0° = 149 ± 6 kcal mol−1, was calculated.

Mass spectrometric study of the evaporation of lithium and sodium molybdates and tungstates

The vapor phases in equilibrium with lithium molybdate, lithium tungstate, sodium molybdate and sodium tungstate salts were investigated by a mass spectrometric Knudsen effusion technique in the temperature range 1200–1800°K. Molybdenum and tungsten Knudsen cells were used as containers. Lithium molybdate and tungstate evaporate mainly as molecular Li 2MoO 4( g) and Li 2WO 4 ( g). Sodium molybdate and tungstate are reduced by the crucible material to yield Na( g) and MoO 2( s) and WO 2( s), respectively. Heats of dissociation of Li 2MoO 4( g) and Li 2WO 4( g) to Li 2O( g) and MoO 3( g) and to Li 2O( g) and WO 3( g) are 119±5 kcal/mole and 132±5 kcal/mole, respectively.

Gaseous Metal Borides. II. Mass-Spectrometric Evidence for the Molecules UB2, UB, and CeB and Predicted Stability of Gaseous Diborides of Electropositive Transition Metals

A combination of Knudsen effusion and mass-spectrometric techniques has been used for the investigation of the reactions (1) UB2(g) + 2C(g) = UC2(g) + 2B(g), (2) UB(g) + C(g) = UC(g) + B(g), and (3) CeB(g) = Ce(g) + B(g). The experimental third-law enthalpies have been combined with appropriate literature data to obtain the following dissociation energies or heats of atomization, D0°, in kilocalories/mole: UB, 76 ± 8; CeB, 72 ± 5; and UB2, 227 ± 10. The Pauling model of a strongly polar M–B2 bond has been used to estimate the heats of atomization of gaseous diborides of selected electropositive transition metals.

Saturated vapour pressure of potassium sulphate

The saturated vapour pressure of K2SO4 has been measured by a combination of the Knudsen effusion and transpiration techniques, over the temperature range 1180–1668 K. Between 1180 and 1342 K (the melting point of K2SO4), the vapour pressures may be expressed by the equation log10(P/atm)=–1.47±0.09 × 104/T K+6.84±0.69, the mean heat of sublimation being 67.3±4.0 kcal/mol. Between 1342 and 1668 K the vapour pressures follow the equation log10(P/atm)=–1.27±0.09 × 104/T K+5.37±0.69, the mean heat of evaporation being 58.3±4.1 kcal/mol. Extrapolation to 1 atm gives a theoretical boiling point of 2370±100 K and an entropy of evaporation at the boiling point of 24.6±2.2 cal/mol K.

Vaporization of Uranium Mononitride and Heat of Sublimation of Uranium

The vaporization of uranium mononitride UN has been investigated by the Knudsen effusion technique in combination with a mass spectrometer. The vaporization occurs incongruently by preferential loss of nitrogen forming the two-phase system nitrogen-saturated liquid uranium–uranium-saturated nonstoichiometric uranium mononitride. The vapor pressures of U and N2 have been obtained by silver calibration over the two-phase system UN0.4–UN0.9 in the temperature range 1910–2230°K. The enthalpies ΔH°298 for the simplified reaction (1) UN(s)=U(g)+0.5 N2 (g) and its partial reactions (2) UN(s)=U(l)+0.5 N2(g) and (3) U(l)=U(g) have been obtained from second- and third-law treatments. The experimental third-law value of Partial Reaction (3) of 130.7 ± 2.2 kcal mole−1 may be considered an upper value for the heat of vaporization of uranium metal. The third-law enthalpy of Partial Reaction (2) of 68.9 ± 0.4 kcal mole−1 is in general agreement with literature data for this reaction. The selected value for the enthalpy of Reaction (1) of ΔH°298 = 200.3 ± 4.0 kcal mole−1 yields with appropriate literature data a heat of atomization ΔH°298 = 313.3 ± 4.5 kcal mole−1 for solid UN, and a heat of vaporization ΔH°298 = 127.9 ± 4.9 kcal mole−1 for uranium. The difference of 2.8 kcal mole−1 between this value and the directly measured value for Partial Reaction (3) is attributed to an activity decrease of uranium in nitrogen-saturated liquid uranium that is in equilibrium with the UN phase.

Mass spectrometric studies at high temperatures. Part 30.—Vaporization of Ga2S3, Ga2Se3and Ga2Te3, and stabilities of the gaseous gallium chalcogenides

The vaporization processes for Ga2S3, Ga2Se3 and Ga2Te3 have been studied at elecated temperatures by the Knudsen effusion and mass spectrometric techniques. The solids vapourize primarily by the reaction Ga2X3(s)= Ga2X(g), where ×= S, Se and Te. The heats of reaction at 298°K for the sulphide, selenide and telluride were 161 ± 6, 168 ± 7 and 162 ± 7 kcal mole–1, respectively. The gaseous molecules GaTe, Ga2Te2 and GaTe3 and the following gaseous equilibria were studied : 2 GaTe(g)=Ga2Te(g)+½Te2(g)ΔH298=–26±4 kcal mole–1, GaTe2(g)= GaTe(g)+½Te2(g)ΔH298= 22±4 kcal mole–1, 2 GaTe(g)=Ga2Te2(g)ΔHr,1012=–62±3 kcal mole–1

Experimental Observations in the Potassium—Graphite System

A gravimetric Knudsen effusion technique has been developed to study the phase equilibria and thermodynamic properties of potassium—graphite lamellar compounds. Using this technique the existence of a C10K phase has been established and phase equilibria in the potassium—graphite, rubidium—graphite, and cesium—graphite systems are shown to be completely analogous. The trends in the heats of reaction of cesium—graphite, rubidium—graphite, and potassium—graphite compounds are discussed.

Knudsen Cell Studies of the Vaporization of Gadolinium and Gadolinium Dicarbide

Vapor pressure of gadolinium metal and carbon-rich gadolinium dicarbide was measured by the Knudsen effusion technique using an automatic recording balance. Knudsen pressures calculated on the basis that Gd(g) is the major gaseous species did not vary significantly as a function of orifice diameter or sample surface area. Corrections were made for a minor gaseous species, GdC2(g). The entropy and heat content of GdC2 were estimated. For the reaction Gd(l) = Gd(g) the third-law ΔH°298 of 95.2 ± 0.3 kcal/g-atom was in agreement with the second-law value of 97.3 ± 0.8 kcal/g-atom. Third- and second-law ΔH°298 were combined to give a value of 125 ± 9 kcal/mole for the reaction GdC2(s) = Gd(g) + 2C(s). From these values the enthalpy of formation of carbon-rich GdC2 was calculated to be — 30 ± 9 kcal/mole. Studies of rare earth dicarbide vaporization behavior are briefly reviewed and discussed, and their possible application to a self-purifying, high-temperature nuclear reactor is considered.

Thermodynamic functions of an FeMn solid solution formed by the Fe(n, p)Mn reaction

A dilute solution ( x u = 3 × 10 −6) of manganese in iron was formed by neutron irradiation of natural iron Fe 54(n, p)Mn 54 and by means of the Knudsen effusion technique the quantity p u x u , where p u is the partial pressure of manganese, was estimated for temperatures between 1073°K and 1673°K. The Raoultian activity coefficient was 0.3 and the variation with temperature was small corresponding to a partial heat of solution of 1.25 kcal/g-atom, (even though the cohesion energy of manganese is 33 kcal/g-atom less than that of iron). The value 0.3 arises from the positive excess entropy of solution. It is suggested that this excess entropy is primarily due to changes of the electronic specific heat of solution rather than changes in the lattice vibrations.