Prediction of Gibbs free energy for the gases Cl2, Br2, and HCl

Non-relativistic energy equations for diatomic molecules constrained in a deformed hyperbolic potential function

CONTEXT

In this paper, the approximate analytical energy equations for the deformed hyperbolic potential have been obtained for arbitrary parameters of the potential. The potential function was transformed to a molecular potential by subjecting it to the Varshni conditions which allows for the determination of the energy levels of diatomic molecules. The molecular vibrational energy spectra for [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] diatomic molecules were obtained and found to match with the results obtained with another analytical approach, potential functions, and experimental data. The noticeable slight differences in the approximate energy spectra obtained in this work and existing literature may be ascribed to the analytical method, computational approach, and the accuracy of the molecular potential functions. The obtained energy equations were used to determine the energy of a particle for arbitrary parameters of the potential function. The obtained energy is bounded and increases with the increase in the quantum numbers. The results conformed to the ones obtained via the path integral approach and numerical solutions obtained via the MATHEMATICA program.

METHOD

The energy spectra equations were obtained via the Nikiforov-Uvarov approach and semi-classical WKB approximation. The Pekeris approximation has been applied to resolve the difficulty in solving the complete energy spectrum of the non-relativistic wave equation for the potential function. The numerical data of the energy spectra was obtained using the MATHEMATICA program.

Information theory and thermodynamic properties of diatomic molecules using molecular potential

Owing to the devise applications of molecules in industries, the bound state solution of the non-relativistic wave equation with a molecular potential function has been obtained in a closed-form using the Nikiforov-Uvarov method. The solutions of the bound state are then applied to study the information-theoretic measures such as the one-dimensional Shannon and Renyi entropic densities. The expectation values for the position and momentum spaces were obtained to verify the Heisenberg's uncertainty principle. Utilizing the energy spectrum equation, the thermodynamic vibrational partition function is obtained via the Poisson summation. Other thermodynamic function variations with absolute temperature have been obtained numerically for four diatomic molecules (H2, N2, O2, and HF) using Maple 18 software. The Shannon global entropic sum inequality has also been verified. The Renyi sum for constrained index parameters satisfies the global entropic inequality. The thermodynamic properties of the four molecules are similar and conform to works reported in the existing literature. The obtained vibrational energies are in fair agreement with the ones obtained using other forms of potential energy. The result further indicates that the lowest bounds for the Shannon, Renyi, and Heisenberg inequalities are ground states phenomena.

Aqueous-Based Synthesis of Photocatalytic Copper Sulfide Using Sulfur Waste as Sulfurizing Agent

Most of the copper sulfide synthetic approaches developed until now are still facing issues in their procedure, such as long synthesis duration, high energetic consumption, and high implementation costs. This publication reports a facile and sustainable approach for synthesizing copper sulfides on a large scale. In particular, an industrial by-product of sulfur waste was used as a sulfurizing agent for copper sulfide synthesis in a water medium. The reaction was performed in the hydrothermal environment by following a novel proposed mechanism of copper sulfide formation. The investigation of morphological and optical properties revealed that the target products obtained by using waste possess the resembling properties as the ones synthesized from the most conventional sulfurizing agent. Since the determined band gap of synthesis products varied from 1.72 to 1.81 eV, the photocatalytic properties, triggered under visible light irradiation, were also investigated by degrading the methylene blue as a model pollutant. Importantly, the degradation efficiency of the copper sulfide synthesized from sulfur waste was equivalent to a sample obtained from a reference sulfurizing agent since the value for both samples was 96% in 180 min. This very simple synthetic approach opens up a new way for large-scale sustainable production of visible-light-driven photocatalysts for water purification from organic pollutants.

Predictions of Entropy and Gibbs Energy for Carbonyl Sulfide

Many chemical and physical equilibrium conditions can be determined from minimizing the Gibbs free energies of the system. Efficient analytical representations of the entropy and Gibbs free energy of carbonyl sulfide remain elusive in the communality of science and engineering. Here, we report two analytical representations of the entropy and Gibbs free energy for carbonyl sulfide, and the prediction procedures only involve six molecular constants of the carbonyl sulfide molecule. In the temperature range from 300 to 6000 K, the average relative deviations of the predicted molar entropy and reduced Gibbs free energy values of carbonyl sulfide from the National Institute of Standards and Technology database are arrived at 0.150 and 0.189%, respectively.

Thermodynamic Properties for Carbon Dioxide

We first report three reliable analytical expressions of the entropy, enthalpy and Gibbs free energy of carbon dioxide (CO₂) and perform predictions of these three thermodynamic quantities on the basis of the proposed analytical expressions and in terms of experimental values of five molecular constants for CO₂. The average relative deviations of the calculated values from the National Institute of Standards and Technology database over the temperature range from 300 to 6000 K are merely 0.053, 0.95, and 0.070%, respectively, for the entropy, enthalpy, and Gibbs free energy. The present predictive expressions are away from the utilization of plenty of experimental spectroscopy data and are applicable to treat CO₂ capture and storage processes.

Thermodynamic Properties of Gaseous Carbon Disulfide

Efficient analytical representations of the thermodynamic properties for carbon disulfide remain open challenges in the communality of science and engineering. We present two analytical representations of the entropy and Gibbs free energy for gaseous carbon disulfide which we find to be of satisfactory accuracy and convenient for future use. The proposed two analytical representations merely rely on five molecular constants of the carbon disulfide molecule and avoid applications of a large number of experimental spectroscopy data. In the temperature range from 300 to 6000 K, the average relative deviations of the predicted molar entropy and reduced Gibbs free energy values from the National Institute of Standards and Technology database are 0.250 and 0.108%, respectively.