Prediction of enthalpy for the gases CO, HCl, and BF
Graphical abstract
Introduction
An explicit representation of the molar enthalpy of the system can provide a simple and efficient way to perform calculations of the enthalpy change during the process under consideration. However, obtaining a universal closed-form expression of the molar enthalpy for gaseous substances remains a formidable goal in chemical engineering. As far as we know, one has not reported an available closed-form representation governing the molar enthalpy values for the gases carbon monoxide (CO), hydrogen chloride (HCl), and boron fluoride (BF). The enthalpy change of the system is important to address many issues, including the chemical reaction [1], [2], [3], [4], [5], phase transition [6], [7], [8], [9], [10], and adsorption [11], [12], [13], [14], [15]. With the help of gasification technology, any carbonaceous fuel (coal, biomass, waste stream) can be converted into syngas (CO and H2) [5]. The gasification process involves a long list of gas species, including H2, CO, CO2, N2, CH4, H2O, O2, NO2, NO, S, SO2, SO3, H2S, COS, C2H2, and solid carbon [5]. Oxy-fuel combustion has the higher concentration of pollutant components in the flue gas, including sulfur oxides, carbon monoxide, nitrogen oxides, and hydrogen chloride. HCl can affect the oxidation of CO and the formation of nitrogen monoxide (NO) in combustion [16]. The adsorption and sorption processes of CO and CO2 in various adsorbent materials have attracted extensive interest. In general, the negative or positive value of the enthalpy change can tell us whether an adsorption process is to release energy or adsorb energy in the form of heat to its surroundings, respectively. From the well-known van’t Hoff equation, we know that the Langmuir adsorption constant is directly related to the enthalpy change and entropy change. Investigation on the change in enthalpy of the system under consideration is a conventional manipulation in dealing with the gasification, combustion and adsorption problems.
On the basis of the dissociation energy and equilibrium bond length for explicit parameters, the improved versions have been suggested for the well-known Rosen-Morse, Tietz, and Frost-Musulin oscillators [17]. The improved oscillators could be regarded as useful models to calculations of molecular vibrational partition functions and thermochemical properties, including the enthalpy, entropy and Gibbs free energy [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29]. In this work, through describing the molecular internal vibration with the improved Tietz oscillator, we establish a universal four-parameter molar enthalpy calculation model for gaseous substances. To examine the availability of the proposed enthalpy calculation scheme, we model the variations of molar enthalpy values with respect to temperature for the CO, HCl, and BF gases. Large quantity of CO is produced as a byproduct in tail gases, including coke oven gas, carbon black manufacturing tail gas and blast furnace gas. Adsorptive separations of gas mixtures containing CO have become quite important nowadays. Sorption of CO on different materials and electroreduction of CO to liquid fuel and have attracted much interest [11], [30], [31]. The BF molecule is one of the most intriguing diatomic molecules formed from first-row elements, being isoelectronic to CO [32], [33]. An acidic solution is injected into the rock for dissolving the rock and increasing the permeability. Hydrochloric acid (HCl) has been widely used as the main stimulation treatment to improve formation permeability and increase hydrocarbon production [34], [35], [36]. The proposed enthalpy calculation method appears to offer the reliable completely predictive values compared to the experimental data.
Section snippets
Analytical representation of enthalpy
Here, we describe the internal vibration of a molecule by the aid of the improved Tietz oscillator, which possesses the simplicity, accuracy and flexibility. The vibrational partition function of the improved Tietz oscillator is written in the form [18]in which represents the dissociation energy of the diatomic molecule, denotes the Boltzmann’s constant, and is the absolute temperature. In expression
Applications
To determine whether our proposed molar enthalpy calculation scheme is available, we attempt to reproduce the total molar enthalpy values at different temperatures for the CO, HCl, and BF gases. The experimental data of molecular constants , , and are collected from the literature: CO [38], HCl [38], and BF [32]. We give the molecular constant values in Table 1. In terms of expression (10), we calculate the molar enthalpy values for the gases under consideration. The results with
Conclusions
On the basis of the improved Tietz oscillator in the description of molecular internal vibration, we construct a universal efficient closed-form expression of the molar enthalpy for gaseous substances. The proposed molar enthalpy calculation model can accurately predict the molar enthalpy values for the CO, HCl, and BF gases. The proposed model only contains four molecular constants, including the dissociation energy, equilibrium bond length, harmonic vibration frequency and vibrational
Acknowledgments
We would like to thank the kind referee for positive and invaluable suggestions which have greatly improved the manuscript. This work was supported by the Key Program of National Natural Science Foundation of China under Grant No. 51534006 and the Sichuan Province Foundation of China for Fundamental Research Projects under Grant No. 2018JY0468.
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2021, Computational and Theoretical ChemistryCitation Excerpt :In the literature, it has been repeatedly reported on the calculation of the vibrational partition function in an analytical form using the ro-vibrational energy levels of diatomic molecules [2,4–7]. The energy levels were found from a direct solution of the Schrödinger equation with potential models of the varying degrees of complexity [1–8]. With the same success, the presence of these energy levels makes it possible to calculate the ro-vibrational partition function also in an analytical form [9].