Using Ion-Selective Electrodes to Study the Thermodynamics of Solution Ⅴ. The Standard Glbbs Free Energies and Entropies of Transfer of KCl from H_2O to DMF-H_2O Mixture at Seven Temperatures from 283.15K to 318.15K
The results show the maximum ion exchange degree of NH4+ clinoptilolite exchange of Cu2+ is only 0.703, and Δr Hmθ is 7.101 kJ/mol, Δr Gmθ<0, Δr Smθ>0, which indicates that the ion exchange process is an endothermic and entropic increasing reaction. NH4+-clinoptilolite exchange of Cu2+ occurs spontaneously at 20 ℃ and is enhanced as the temperature increases.
We also prove that among all matrix functions with these properties, there exists a distinguished one that maximizes the entropy.
The Arov-Grossman Model and the Burg Multivariate Entropy
In this article we deal with the Arov-Grossman functional model to describe all the solutions of the Covariance Extension Problem for q-variate stationary stochastic processes and we find the density that maximizes the Burg Multivariate Entropy.
With this correspondence, the density that maximizes the Burg Multivariate Entropy corresponds to the function H\equiv0.
An asymptotic behavior of the corresponding entropy numbers is calculated.
Furthermore, the entropic contribution is larger than the enthalpic one in pure water, while in the mixed solvents, the enthalpic contribution predominates.
Entropic effects strongly level the influence of clusterization on the probability of adsorption.
Although the enthalpic contribution was found to be larger than the entropic one, in particular at lower temperatures, an entropy-enthalpy compensation effect was observed for all systems.
We construct examples of an endomorphically closed loop and of an endomorphically closed TS-quasigroup that are not entropic.
Examples are given illustrating the differences in the entropic properties of continuous maps of dendrites with a countable set of branch points and continuous maps of their retracts which are finite trees.