Research paperPrediction of enthalpy for the gases Cl2, Br2, and gaseous BBr
Graphical abstract
Introduction
A closed-form expression of the molar enthalpy of the system is very helpful for calculations of the enthalpy change during the process, but achieving an efficient closed-form representation of enthalpy for gaseous substances remains elusive, in part because of the lack of simple and efficient ways to treat the internal vibration of a molecule. For example, to the best of our knowledge, there have been no reports of available closed-form representation of the molar enthalpy for the gases Cl2, Br2, and gaseous BBr. Cl2 gas is a poisonous oxidizing agent that is used in drinking water purification and used extensively in organic and inorganic chemistry and in substitution reactions, leading to a wide range of industrial and consumer products [1], [2]. Due to the interaction of Br2 and Cl2 species with the combustion process, there is a renewed interest in the thermochemical properties of Br2 and Cl2 gases, in particular at higher temperatures [3], [4], [5]. Enthalpy is an important basic datum involved in diversified scientific and engineering applications, including biomass and coal gasification [6], [7], [8], phase transition [9], [10], and adsorption [11], [12], [13], [14], [15]. In general, the negative or positive value of the enthalpy change in an adsorption process determines whether the process is exothermic or endothermic, respectively. Modeling the enthalpy change in a physical or chemical process is very useful for prediction of heat effects outside the range of experimental conditions.
Through the introduction of the dissociation energy and equilibrium bond length as explicit parameters for a diatomic molecule, the improved versions have been achieved for the well-known Manning-Rosen, Rosen-Morse, Frost-Musulin, Tietz, and Pöschl-Teller oscillators [16], [17], [18]. Recent work from our laboratory and other teams on molecular vibrational energies and thermochemical properties for some gaseous molecules has taken advantage of these improved molecular oscillators [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34]. Based on the improved Manning-Rosen oscillator in the description of the internal vibration of a molecule, Wang et al. [29] presented a three-parameter molar entropy calculation model for gaseous BBr, and successfully predicted the molar entropy values of gaseous BBr in the temperature range of 298–6000 K. This work arises from the application of the improved Manning-Rosen oscillator in describing the internal vibration of a molecule, and provides a new explicit representation of molar enthalpy for gaseous substances. To verify our calculation scheme, we simulate the variation of molar enthalpy with respect to temperature for the gases Cl2, Br2, and gaseous BBr. For the dissociation energies, equilibrium bond lengths, and harmonic vibration frequencies of the two dihalogens and halogen-containing molecule BBr, the corresponding experimental values are taken from the literature [35], [36], [37]. Our approach involves only three molecular constants, and has proved useful for predicting the molar enthalpy values of a variety of gaseous diatomic substances by comparing the calculated results with the experimental data.
Section snippets
Analytical representation of enthalpy
Our aim is to construct a simple and acceptable prediction model of the enthalpy for gaseous substances, which contains few parameters with explicit physical significance. Here we utilize the improved Manning-Rosen oscillator to give reasonable representation of the internal vibration of a molecule. The vibrational partition function of the improved Manning-Rosen oscillator can be represented as [19]where
Applications
Here, we test our model by simulating the variation of the total molar enthalpy with respect to temperature for Cl2, Br2, and gaseous BBr. The experimental values of molecular constants , , and are listed in Table 1 and collected from the literature as indicated in Table 1. In Fig. 1, the experimental values of the molar enthalpy for the gases Cl2, Br2, and gaseous BBr as a function of temperature are compared with the values predicted according to Eq. (8). The experimental enthalpy
Conclusions
This work demonstrates that the present new enthalpy prediction model is capable of reasonable predictions of molar enthalpy values of the gaseous substances. The agreement between predictions and experimental data shows that the proposed molar enthalpy model can reproduce with satisfactory accuracy the molar enthalpy values for the gases Cl2, Br2, and gaseous BBr. The calculation procedure involved in the present predictive method is simple and straightforward. The proposed enthalpy prediction
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.
Declaration of interest statement
The authors declare no conflict of interest.
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