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Mass action law
About: Mass action law is a research topic. Over the lifetime, 168 publications have been published within this topic receiving 2684 citations.
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TL;DR: In this article, the general thermodynamic equations derived in the first paper are integrated by means of a new equation of state for gas mixtures, and the energy, heat content, entropy and thermodynamic potentials of a mixture of real gases, and chemical potential and fugacity of a gas in a mixture are expressed as integrated functions of $V, T, {n}_{1, 1, n}, n, 1}, {n, 2, n, 2}, \ensuremath{\cdots}$, and the constants of the pure gases composing the mixture
Abstract: The general thermodynamic equations derived in the first paper are integrated by means of a new equation of state for gas mixtures. Thus the energy, heat content, entropy and thermodynamic potentials ${F}_{V,T}$ and ${F}_{p,T}$ of a mixture of real gases, and the chemical potential and fugacity of a gas in a mixture are expressed as integrated functions of $V, T, {n}_{1}, {n}_{2}, \ensuremath{\cdots}$, and the constants of the equation of state of the pure gases composing the mixture. The expression for the thermodynamic potential ${F}_{V,T}$ is a fundamental equation in the Gibbs sense. A mass action law for reactions between real gases is given, the "mass action constant" ${K}_{p}$ being expressed in terms of the variables $V, T, {x}_{1}, {x}_{2}, \ensuremath{\cdots}$, ${\ensuremath{
u}}_{1}, {\ensuremath{
u}}_{2}, \ensuremath{\cdots}$, and the equation of state constants of the pure gases composing the equilibrium mixture. The determination of the values of the various integration constants are discussed for the following cases: (a) non-isothermal and (b) isothermal variations in the state of a system composed of gases which react chemically, (c) non-isothermal and (d) isothermal variations in the state of a system composed of nonreacting gases.
5 citations
5 citations
TL;DR: In this article, the transfer of particles among free carrier, free exciton, and bound exciton states under an external excitation was studied in the presence of free carriers, and the model of the free carrier trapped by the impurities was obtained for the QW system with low defect concentration.
Abstract: Free exciton and bound exciton photoluminescence (PL) of a quantum well (QW) in the presence of free carriers is studied in a model that includes the transfer of particles among free carrier, free exciton, and bound exciton states under an external excitation It is shown that the free carrier state is important not only at high temperature but also at low temperature General formulas for the free exciton, bound exciton, and free carrier PL are developed The two‐dimensional (2D) law of mass action for the free carrier and free exciton PL is reproduced at high temperature, and the model of the free exciton trapped by the impurities is obtained for the QW system with low defect concentration Free exciton and bound exciton PL for high defect concentration is also discussed and the 2D law of mass action is obtained at high temperature as well Experimental observations such as the thermal behavior of free exciton and bound exciton PL, the recently observed sharp temperature‐induced reduction of the PL line
5 citations
TL;DR: A mathematical analysis of the Bjerrum function is carried out in this paper, where it is shown that there is only one positive root of the BFP, and thus that only a single equilibrium state can exist.
Abstract: A mathematical analysis of the Bjerrum function is carried out. This function arises from the Stepwise Equilibrium Model, which is used to describe successive complex formation in systems consisting of free metal ion, free ligand, and all theMLi complexes that can form in solution. The appropriate root of the Bjerrum polynomial allows the determination of the concentrations of all species present in solution, given the initial concentrations of metal and of ligand, and the equilibrium constants governing the system. It is proved that there is only one positive root of the Bjerrum polynomial, and thus that only a single equilibrium state can exist. It is also shown that the positive root of the Bjerrum polynomial can be reliably obtained by Newton's method, but only if the initialization point is properly chosen, and that the initial concentrationL of ligand is the optimum such point. Finding this root is a calculation that typically must be carried out at each iteration in nonlinear least squares procedures for determining equilibrium constants. Finally, the necessary mathematical analysis is carried out to determine the optimum initial concentrations of metal and lgand which maximize the resulting concentration of a particularMLi complex.
4 citations
TL;DR: In this article, the authors presented a simple and direct method to calculate the micellar average aggregation number from surface tension data and the proposed surface equation, which can be used to study fluid-fluid interfaces in connection with the micelle formation process.
4 citations