Pioneers of Chaos-Who are the pioneers? How did everything begin? For the Greeks, in the beginnin... more Pioneers of Chaos-Who are the pioneers? How did everything begin? For the Greeks, in the beginning there was Chaos. Rebel, Rameau and Haydn set chaos (and the separation of the four elements) to music. Simon Schama declared Turner the 'painter of chaos'. Feigenbaum, a pioneer in chaos theory, drew inspiration from the paintings of Turner and van Gogh. In the arts, fragmentation (atomization) led to chaos. In the 1950s and 60s writers, painters and composers rejoiced in chaotic methods of creation, and scientists followed them with powerful aleatory techniques to solve complex problems. Chaos means gas and disorder is measured by entropy. This lecture is a random walk across time and space guided by the sciences and the arts. Quem são os pioneiros? Quando ou como tudo começou? Para os Gregos, no princípio era o Caos. Rebel, Rameau e Haydn puseram em música o desembrulhar do caos (e a luta dos quatro elementos para se separarem uns dos outros). Turner foi, no dizer de Simon Schama, "o pintor do caos". Feigenbaum inspirou-se nas pinturas de Turner e de van Gogh para encontrar soluções para questões de turbulência e outros problemas não-lineares. A borboleta e o atractor de Lorenz confundem-se. A fragmentação nas artes gerou caos. Nos anos 1950 e 60, escritores, pintores e compositores reuniram-se à volta do caos, e os cientistas aproveitaram a moda para inventar poderosos métodos aleatórios para resolver os mais diversos problemas. Para um químico, caos é sinónimo de gás e a desordem é medida pela entropia. A criatividade vive paredes-meias com o caos. A palestra será um passeio aleatório através dos tempos sobre o caos, guiado pelas ciências e pelas artes.
We present a new method based on a corresponding-states approach to evaluate the equation-of-stat... more We present a new method based on a corresponding-states approach to evaluate the equation-of-state parameters of a van der Waals-type equation of state which is valid for simple, non-polar molecules, both spherical and non-spherical, and their mixtures. The proposed method, which has been tried on fourteen liquids, predicts well pure component liquid molar volumes over a large temperature range. The
ABSTRACT The total vapour pressure of liquid mixtures of methane and ethene has been measured as ... more ABSTRACT The total vapour pressure of liquid mixtures of methane and ethene has been measured as a function of composition at 103.94 and 115.77 K. The results have been used to estimate the excess Gibbs energy GE at these temperatures. The volume of mixing VE has been determined at 103.94 K and is found to be small and negative. In a comparison with the values of GE obtained by other authors, an attempt was made to estimate the value of HE, the molar enthalpy of mixing. The results are interpreted in the light of some simple theories of mixtures, suggesting that this is a case where the Lorentz rule of combination of collision diameters is valid.
Abstract Calado, J.C.G. and Staveley, L.A.K., 1979. The thermodynamics of the system krypton—nitr... more Abstract Calado, J.C.G. and Staveley, L.A.K., 1979. The thermodynamics of the system krypton—nitric oxide and their interpretation in terms of monomer—dimer association of the oxide. Fluid Phase Equilibria, 3: 153–166. Measurements hav ebeen made of the total vapour pressure of KrNO mixtures at 115.76 K, from which the excess Gibbs energy GE has been calculated. The excess molar volume VE has also been measured at the same temperature. The system has a positive azeotrope, and VE is throughout positive and a somewhat asymmetric function of composition. An attempt has been made at a quantitative interpretation of the pressure results on the basis of equilibrium between nitric oxide monomers and dimers, with the value of the equilibrium constant given by a previous magnetic susceptibility study. We have assumed that there is an ideal relationship between monomers and dimers in a solution, but not between these species on the one hand and krypton molecules on the other. We find that, assuming the experimental value of the total vapour pressure at the highest and lowest krypton concentration studied, the total vapour pressure at the remaining concentrations can be calculated to better than one per cent. Roughly, 60 per cent of the observed non-ideality for the equimolar mixture appears to be due to the monomer—dimer association, and the remainder to the interaction between the two forms of nitric oxide and the krypton molecules,
The total vapour pressures, the excess Gibbs energy GE (at 90.69 and 103.99 K) and the excess mol... more The total vapour pressures, the excess Gibbs energy GE (at 90.69 and 103.99 K) and the excess molar volume VE (at 103.99 K) are reported for liquid mixtures of methane and ethane. The results are compared with those obtained by previous investigations and interpreted in the light of some simple theories of liquid mixtures.
Thermodynamics of Liquid Al-Ni-Zr and Al-Cu-Ni-Zr Alloys.-The partial and the integral enthalpies... more Thermodynamics of Liquid Al-Ni-Zr and Al-Cu-Ni-Zr Alloys.-The partial and the integral enthalpies of mixing of liquid alloys in the title system are measured calorimetrically at 1565 K. Based on the ∆H values, the excess entropy and Gibbs energy of mixing are estimated using an empirical relation. The results confirm that the strongest tendency towards chemical short-range ordering in liq. Al-Cu-Ni-Zr alloys occurs near the ternary composition Al 0.42 Ni 0.42
Journal of the Chemical Society, Faraday Transactions, 1994
ABSTRACT The adsorption isotherm of heptane–hexanol on activated carbon at 298 K is presented and... more ABSTRACT The adsorption isotherm of heptane–hexanol on activated carbon at 298 K is presented and compared with our earlier work on heptane–ethanol and heptane–butanol mixtures under similar conditions. The data show that the preferred adsorption shifts from the alkane to the alkanol as the length of the alkanol chain, relative to that of the alkane chain, increases. The surface mole fraction, interfacial tension differences and surface activity coefficients have been estimated based on an approximate theoretical model (surface phase model). These results show that the minimum thickness of the layers required to achieve thermodynamic consistency between the surface phase model and the experimental data increases as the length of the alkanol chain decreases. All the systems exhibit smaller deviations from ideality in the adsorbed phases than in the bulk.
Journal of the Chemical Society, Faraday Transactions, 1991
ABSTRACT Measurements of the adsorption by activated carbon of the three binary mixtures involvin... more ABSTRACT Measurements of the adsorption by activated carbon of the three binary mixtures involving n-dodecane, n-heptane and n-butanol were made at 298 K. The data were tested for thermodynamic consistency by calculating the excess surface Gibbs energy of the interface between the pure liquids and the activated carbon surface. The adsorption data were also used to test the validity of the monolayer model of adsorption. This model is compatible with the data for (n-dodecane–n-heptane)/activated carbon, but a minimum thickness of two layers for (n-dodecane–n-butanol)/activated carbon and (n-heptane–n-butanol)/activated carbon is required to achieve thermodynamic consistency between the surface phase model and the experimental data. Surface activity coefficients were calculated for the last two systems and show that the adsorbed phases exhibit smaller deviations from ideality than the bulk phases.
Bond-enthalpy contribution values D(Mo–Me)= 149·5 kJ mol–1 and D(W–Me)= 197·8 kJ mol–1 have been ... more Bond-enthalpy contribution values D(Mo–Me)= 149·5 kJ mol–1 and D(W–Me)= 197·8 kJ mol–1 have been derived from the standard enthalpies of formation ΔH°f[Mo(η-C5H5)2Me2, c]=(283·8 ± 3·8) kJ mol–1 and ΔH°f[W(η-C5H5)2Me2, c]=(295·6 ± 3·5) kJ mol–1 obtained from measurements of the reaction enthalpies of Mo(η-C5H5)2Me2(c) and W(η-C5H5)2Me2(c) in an aqueous solution of hydrochloric acid.
The 36 Ar-40 Ar vapor pressure isotope effect in the liquid and solid phases has been experimenta... more The 36 Ar-40 Ar vapor pressure isotope effect in the liquid and solid phases has been experimentally determined at about 100 temperatures between 83 and 97 K using a high-accuracy double-differential manometric technique. Differences between the vapor pressure of a highly enriched sample of 36 Ar and that of natural argon were measured simultaneously with the absolute vapor pressure of natural argon. Absolute and differential vapor pressure measurements show an estimated accuracy of 0.15% and 0.001%, respectively, with respect to the absolute vapor pressure of argon. Data were obtained in both the solid and liquid regions. The vapor pressure of 36 Ar is always higher than that of 40 Ar by about 0.5%. Triple-point temperatures and pressures were also measured for both isotopes. All data compare favorably with previous results reported in the literature and are nicely interpreted within the framework of Bigeleisen's theory of isotope effects. Using a large temperature extrapolation of our data, liquid-vapor isotope fractionation factors were successfully inferred from the vapor pressure measurements; the estimated values agree with the experimental ones up to close to the critical point. The isotopic difference in the molar enthalpies of vaporization and sublimation was also calculated from the vapor pressure data. Additionally, molar volume and second virial coefficient isotope effects are estimated using several different theoretical approaches.
... which was calibrated by measuring the saturation vapour pressure of ethane as a function of t... more ... which was calibrated by measuring the saturation vapour pressure of ethane as a function of temperature between 158 and 163 K . In this way the temperature at which the measurements were performed, 16 1.4 K, could be estimated to within & 0.1 K. Ethene was provided by ...
Pioneers of Chaos-Who are the pioneers? How did everything begin? For the Greeks, in the beginnin... more Pioneers of Chaos-Who are the pioneers? How did everything begin? For the Greeks, in the beginning there was Chaos. Rebel, Rameau and Haydn set chaos (and the separation of the four elements) to music. Simon Schama declared Turner the 'painter of chaos'. Feigenbaum, a pioneer in chaos theory, drew inspiration from the paintings of Turner and van Gogh. In the arts, fragmentation (atomization) led to chaos. In the 1950s and 60s writers, painters and composers rejoiced in chaotic methods of creation, and scientists followed them with powerful aleatory techniques to solve complex problems. Chaos means gas and disorder is measured by entropy. This lecture is a random walk across time and space guided by the sciences and the arts. Quem são os pioneiros? Quando ou como tudo começou? Para os Gregos, no princípio era o Caos. Rebel, Rameau e Haydn puseram em música o desembrulhar do caos (e a luta dos quatro elementos para se separarem uns dos outros). Turner foi, no dizer de Simon Schama, "o pintor do caos". Feigenbaum inspirou-se nas pinturas de Turner e de van Gogh para encontrar soluções para questões de turbulência e outros problemas não-lineares. A borboleta e o atractor de Lorenz confundem-se. A fragmentação nas artes gerou caos. Nos anos 1950 e 60, escritores, pintores e compositores reuniram-se à volta do caos, e os cientistas aproveitaram a moda para inventar poderosos métodos aleatórios para resolver os mais diversos problemas. Para um químico, caos é sinónimo de gás e a desordem é medida pela entropia. A criatividade vive paredes-meias com o caos. A palestra será um passeio aleatório através dos tempos sobre o caos, guiado pelas ciências e pelas artes.
We present a new method based on a corresponding-states approach to evaluate the equation-of-stat... more We present a new method based on a corresponding-states approach to evaluate the equation-of-state parameters of a van der Waals-type equation of state which is valid for simple, non-polar molecules, both spherical and non-spherical, and their mixtures. The proposed method, which has been tried on fourteen liquids, predicts well pure component liquid molar volumes over a large temperature range. The
ABSTRACT The total vapour pressure of liquid mixtures of methane and ethene has been measured as ... more ABSTRACT The total vapour pressure of liquid mixtures of methane and ethene has been measured as a function of composition at 103.94 and 115.77 K. The results have been used to estimate the excess Gibbs energy GE at these temperatures. The volume of mixing VE has been determined at 103.94 K and is found to be small and negative. In a comparison with the values of GE obtained by other authors, an attempt was made to estimate the value of HE, the molar enthalpy of mixing. The results are interpreted in the light of some simple theories of mixtures, suggesting that this is a case where the Lorentz rule of combination of collision diameters is valid.
Abstract Calado, J.C.G. and Staveley, L.A.K., 1979. The thermodynamics of the system krypton—nitr... more Abstract Calado, J.C.G. and Staveley, L.A.K., 1979. The thermodynamics of the system krypton—nitric oxide and their interpretation in terms of monomer—dimer association of the oxide. Fluid Phase Equilibria, 3: 153–166. Measurements hav ebeen made of the total vapour pressure of KrNO mixtures at 115.76 K, from which the excess Gibbs energy GE has been calculated. The excess molar volume VE has also been measured at the same temperature. The system has a positive azeotrope, and VE is throughout positive and a somewhat asymmetric function of composition. An attempt has been made at a quantitative interpretation of the pressure results on the basis of equilibrium between nitric oxide monomers and dimers, with the value of the equilibrium constant given by a previous magnetic susceptibility study. We have assumed that there is an ideal relationship between monomers and dimers in a solution, but not between these species on the one hand and krypton molecules on the other. We find that, assuming the experimental value of the total vapour pressure at the highest and lowest krypton concentration studied, the total vapour pressure at the remaining concentrations can be calculated to better than one per cent. Roughly, 60 per cent of the observed non-ideality for the equimolar mixture appears to be due to the monomer—dimer association, and the remainder to the interaction between the two forms of nitric oxide and the krypton molecules,
The total vapour pressures, the excess Gibbs energy GE (at 90.69 and 103.99 K) and the excess mol... more The total vapour pressures, the excess Gibbs energy GE (at 90.69 and 103.99 K) and the excess molar volume VE (at 103.99 K) are reported for liquid mixtures of methane and ethane. The results are compared with those obtained by previous investigations and interpreted in the light of some simple theories of liquid mixtures.
Thermodynamics of Liquid Al-Ni-Zr and Al-Cu-Ni-Zr Alloys.-The partial and the integral enthalpies... more Thermodynamics of Liquid Al-Ni-Zr and Al-Cu-Ni-Zr Alloys.-The partial and the integral enthalpies of mixing of liquid alloys in the title system are measured calorimetrically at 1565 K. Based on the ∆H values, the excess entropy and Gibbs energy of mixing are estimated using an empirical relation. The results confirm that the strongest tendency towards chemical short-range ordering in liq. Al-Cu-Ni-Zr alloys occurs near the ternary composition Al 0.42 Ni 0.42
Journal of the Chemical Society, Faraday Transactions, 1994
ABSTRACT The adsorption isotherm of heptane–hexanol on activated carbon at 298 K is presented and... more ABSTRACT The adsorption isotherm of heptane–hexanol on activated carbon at 298 K is presented and compared with our earlier work on heptane–ethanol and heptane–butanol mixtures under similar conditions. The data show that the preferred adsorption shifts from the alkane to the alkanol as the length of the alkanol chain, relative to that of the alkane chain, increases. The surface mole fraction, interfacial tension differences and surface activity coefficients have been estimated based on an approximate theoretical model (surface phase model). These results show that the minimum thickness of the layers required to achieve thermodynamic consistency between the surface phase model and the experimental data increases as the length of the alkanol chain decreases. All the systems exhibit smaller deviations from ideality in the adsorbed phases than in the bulk.
Journal of the Chemical Society, Faraday Transactions, 1991
ABSTRACT Measurements of the adsorption by activated carbon of the three binary mixtures involvin... more ABSTRACT Measurements of the adsorption by activated carbon of the three binary mixtures involving n-dodecane, n-heptane and n-butanol were made at 298 K. The data were tested for thermodynamic consistency by calculating the excess surface Gibbs energy of the interface between the pure liquids and the activated carbon surface. The adsorption data were also used to test the validity of the monolayer model of adsorption. This model is compatible with the data for (n-dodecane–n-heptane)/activated carbon, but a minimum thickness of two layers for (n-dodecane–n-butanol)/activated carbon and (n-heptane–n-butanol)/activated carbon is required to achieve thermodynamic consistency between the surface phase model and the experimental data. Surface activity coefficients were calculated for the last two systems and show that the adsorbed phases exhibit smaller deviations from ideality than the bulk phases.
Bond-enthalpy contribution values D(Mo–Me)= 149·5 kJ mol–1 and D(W–Me)= 197·8 kJ mol–1 have been ... more Bond-enthalpy contribution values D(Mo–Me)= 149·5 kJ mol–1 and D(W–Me)= 197·8 kJ mol–1 have been derived from the standard enthalpies of formation ΔH°f[Mo(η-C5H5)2Me2, c]=(283·8 ± 3·8) kJ mol–1 and ΔH°f[W(η-C5H5)2Me2, c]=(295·6 ± 3·5) kJ mol–1 obtained from measurements of the reaction enthalpies of Mo(η-C5H5)2Me2(c) and W(η-C5H5)2Me2(c) in an aqueous solution of hydrochloric acid.
The 36 Ar-40 Ar vapor pressure isotope effect in the liquid and solid phases has been experimenta... more The 36 Ar-40 Ar vapor pressure isotope effect in the liquid and solid phases has been experimentally determined at about 100 temperatures between 83 and 97 K using a high-accuracy double-differential manometric technique. Differences between the vapor pressure of a highly enriched sample of 36 Ar and that of natural argon were measured simultaneously with the absolute vapor pressure of natural argon. Absolute and differential vapor pressure measurements show an estimated accuracy of 0.15% and 0.001%, respectively, with respect to the absolute vapor pressure of argon. Data were obtained in both the solid and liquid regions. The vapor pressure of 36 Ar is always higher than that of 40 Ar by about 0.5%. Triple-point temperatures and pressures were also measured for both isotopes. All data compare favorably with previous results reported in the literature and are nicely interpreted within the framework of Bigeleisen's theory of isotope effects. Using a large temperature extrapolation of our data, liquid-vapor isotope fractionation factors were successfully inferred from the vapor pressure measurements; the estimated values agree with the experimental ones up to close to the critical point. The isotopic difference in the molar enthalpies of vaporization and sublimation was also calculated from the vapor pressure data. Additionally, molar volume and second virial coefficient isotope effects are estimated using several different theoretical approaches.
... which was calibrated by measuring the saturation vapour pressure of ethane as a function of t... more ... which was calibrated by measuring the saturation vapour pressure of ethane as a function of temperature between 158 and 163 K . In this way the temperature at which the measurements were performed, 16 1.4 K, could be estimated to within & 0.1 K. Ethene was provided by ...
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