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Ahmed AD, Eyube ES, Omugbe E, Onate CA, Timtere P. Bound-state energy spectrum and thermochemical functions of the deformed Schiöberg oscillator. Sci Rep 2023; 13:20386. [PMID: 37989877 PMCID: PMC10663450 DOI: 10.1038/s41598-023-47235-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2023] [Accepted: 11/10/2023] [Indexed: 11/23/2023] Open
Abstract
In this study, a diatomic molecule interacting potential such as the deformed Schiöberg oscillator (DSO) have been applied to diatomic systems. By solving the Schrödinger equation with the DSO, analytical equations for energy eigenvalues, molar entropy, molar enthalpy, molar Gibbs free energy and constant pressure molar heat capacity are obtained. The obtained equations were used to analyze the physical properties of diatomic molecules. With the aid of the DSO, the percentage average absolute deviation (PAAD) of computed data from the experimental data of the 7Li2 (2 3Πg), NaBr (X 1Σ+), KBr (X 1Σ+) and KRb (B 1Π) molecules are 1.3319%, 0.2108%, 0.2359% and 0.8841%, respectively. The PAAD values obtained by employing the equations of molar entropy, scaled molar enthalpy, scaled molar Gibbs free energy and isobaric molar heat capacity are 1.2919%, 1.5639%, 1.5957% and 2.4041%, respectively, from the experimental data of the KBr (X 1Σ+) molecule. The results for the potential energies, bound-state energy spectra, and thermodynamic functions are in good agreement with the literature on diatomic molecules.
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Affiliation(s)
- A D Ahmed
- Department of Physics, Faculty of Physical Sciences, Modibbo Adama University, P.M.B. 2076, Yola, Adamawa State, Nigeria
| | - E S Eyube
- Department of Physics, Faculty of Physical Sciences, Modibbo Adama University, P.M.B. 2076, Yola, Adamawa State, Nigeria.
| | - E Omugbe
- Department of Physics, University of Agriculture and Environmental Sciences, P.M.B. 1038, Umuagwo, Imo State, Nigeria
| | - C A Onate
- Department of Physics, Kogi State University, Anyigba, Nigeria
| | - P Timtere
- Department of Physics, Faculty of Physical Sciences, Modibbo Adama University, P.M.B. 2076, Yola, Adamawa State, Nigeria
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Onyeaju MC, Omugbe E, Onate CA, Okon IB, Eyube ES, Okorie US, Ikot AN, Ogwu DA, Osuhor PO. Information theory and thermodynamic properties of diatomic molecules using molecular potential. J Mol Model 2023; 29:311. [PMID: 37698769 DOI: 10.1007/s00894-023-05708-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2023] [Accepted: 08/25/2023] [Indexed: 09/13/2023]
Abstract
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.
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Affiliation(s)
- M C Onyeaju
- Theoretical Physics Group, Department of Physics, University of Port Harcourt, Choba, Rivers State, Nigeria.
- Department of Physics, Faculty of Basic and Applied Science, University of Africa, Toru-Orua, Bayelsa State, Nigeria.
| | - E Omugbe
- Department of Physics, University of Agriculture and Environmental Sciences, P.M.B. 1038, Umuagwo, Imo State, Nigeria
| | - C A Onate
- Department of Physics, Kogi State University, Anyigba, Kogi State, Nigeria
| | - I B Okon
- Theoretical Physics Group, Department of Physics, University of Uyo, Uyo, Nigeria
| | - E S Eyube
- Department of Physics, Faculty of Physical Sciences, Modibbo Adama University, P.M.B. 2076, Yola, Adamawa State, Nigeria
| | - U S Okorie
- Department of Physics, Akwa Ibom State University, P.M.B 1167, Ikot AkpodenUyo, Nigeria
| | - A N Ikot
- Theoretical Physics Group, Department of Physics, University of Port Harcourt, Choba, Rivers State, Nigeria
| | - D A Ogwu
- Department of Physics, Faculty of Science, University of Delta, Agbor, Delta State, Nigeria
| | - P O Osuhor
- Department of Physics, Faculty of Science, University of Delta, Agbor, Delta State, Nigeria
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5
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Edet CO, Amadi PO, Ettah EB, Ali N, Asjad M, Ikot AN. The magnetocaloric effect, thermo-magnetic and transport properties of LiH diatomic molecule. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2059025] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- C. O. Edet
- Department of Physics, Cross River University of Technology, Calabar, Nigeria
| | - P. O. Amadi
- Theoretical Physics Group, Department of Physics, University of Port Harcourt, Choba, Nigeria
| | - E. B. Ettah
- Department of Physics, Cross River University of Technology, Calabar, Nigeria
| | - Norshamsuri Ali
- Faculty of Electronic Engineering Technology, Universiti Malaysia Perlis, Arau, Malaysia
| | - Muhammad Asjad
- Department of Applied Mathematics and Sciences, Khalifa University, Abu Dhabi, United Arab Emirates
| | - A. N. Ikot
- Theoretical Physics Group, Department of Physics, University of Port Harcourt, Choba, Nigeria
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6
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Al-Raeei M. Morse oscillator equation of state: An integral equation theory based with virial expansion and compressibility terms. Heliyon 2022; 8:e09328. [PMID: 35520603 PMCID: PMC9062208 DOI: 10.1016/j.heliyon.2022.e09328] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2021] [Revised: 01/03/2022] [Accepted: 04/21/2022] [Indexed: 11/30/2022] Open
Abstract
A number of interaction energy types are employed in the vibrations studies, especially in the spectroscopic analysis, such as the harmonic oscillator and Morse oscillator. In this research, a derivation of an analytical formula of equation of state of Morse oscillator is considered by employing the approximations used in the simple fluids theory. The compressibility formula of the pressure and the virial expansion formula of the pressure using the solutions of the main equation of the simple fluids theory with one of the approximations of the theory are employed for the purpose of the derivation. The virial coefficients of the total Morse oscillator pressure (the first order one, and the second order one) are found for Morse oscillator with respect to the fractional volume of the components, where we conclude that the first order term is proportional to the absolute temperature directly and depends on the diameter of the particles, while we concluded that the second order coefficient term is more complicated than the first order one with temperature, and also, depends on the three Morse oscillator parameters and the diameter of the particles. Besides, we conclude that the total pressure of Morse oscillator, generally, depends on the minimum energy of the well of Morse oscillator, the width parameter of Morse oscillator, and the equilibrium bond distance of the oscillator, in addition to their dependence on the absolute temperature of the components, and the diameter of the particles. The formula of the Morse oscillator equation of state which is found in this research can be applied to multiple materials described using Morse oscillator such as lots of dimers in the vibrations spectroscopy.
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Affiliation(s)
- Marwan Al-Raeei
- Faculty of Sciences, Damascus University, Damascus, Syrian Arab Republic
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7
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Eyube E. Reparametrised Pöschl–Teller oscillator and analytical molar entropy equation for diatomic molecules. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2037774] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- E.S. Eyube
- Department of Physics, Faculty of Physical Sciences, Modibbo Adama University, Yola, Nigeria
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8
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Eyube E, Notani P, Izam M. Potential parameters and eigen spectra of improved Scarf II potential energy function for diatomic molecules. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1979265] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- E.S. Eyube
- Department of Physics, School of Physical Sciences, Modibbo Adama University of Technology, Yola, Nigeria
| | - P.P. Notani
- Department of Pure and Applied Sciences, Taraba State Polytechnic, Suntai, Jalingo, Nigeria
| | - M.M. Izam
- Department of Physics, Faculty of Natural Sciences, University of Jos, Jos, Nigeria
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Strekalov ML. Rigorous factorization method of the vibrational and rotational contributions to the ro-vibrational partition function. COMPUT THEOR CHEM 2021. [DOI: 10.1016/j.comptc.2021.113337] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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10
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Inyang EP, William ES, Obu JA, Ita BI, Inyang EP, Akpan IO. Energy spectra and expectation values of selected diatomic molecules through the solutions of Klein–Gordon equation with Eckart–Hellmann potential model. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1956615] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- E. P. Inyang
- Department of Pure and Applied Sciences, National Open University of Nigeria, Abuja, Nigeria
- Theoretical Physics Group, Department of Physics, University of Calabar, Calabar, Nigeria
| | - E. S. William
- Theoretical Physics Group, Department of Physics, University of Calabar, Calabar, Nigeria
| | - J. A. Obu
- Theoretical Physics Group, Department of Physics, University of Calabar, Calabar, Nigeria
| | - B. I. Ita
- Physical/Theoretical Chemistry Group, Department of Pure and Applied Chemistry, University of Calabar, Calabar, Nigeria
| | - E. P. Inyang
- Theoretical Physics Group, Department of Physics, University of Calabar, Calabar, Nigeria
| | - I. O. Akpan
- Theoretical Physics Group, Department of Physics, University of Calabar, Calabar, Nigeria
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11
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Edet CO, Ikot AN. Analysis of the impact of external fields on the energy spectra and thermo-magnetic properties of N2,I2,CO,NO and HCl diatomic molecules. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1957170] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- C. O. Edet
- Theoretical Physics Group, Department of Physics, University of Port Harcourt, Choba, Nigeria
| | - A. N. Ikot
- Theoretical Physics Group, Department of Physics, University of Port Harcourt, Choba, Nigeria
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12
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Hesam A, Nikoofard H, Sargolzaei M. Prediction of thermodynamic properties of formation of HCl at temperatures 200–1000 K. Chem Phys Lett 2021. [DOI: 10.1016/j.cplett.2020.138276] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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13
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Wang CW, Wang J, Liu YS, Li J, Peng XL, Jia CS, Zhang LH, Yi LZ, Liu JY, Li CJ, Jia X. Prediction of the ideal-gas thermodynamic properties for water. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2020.114912] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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14
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Jia CS, Li J, Liu YS, Peng XL, Jia X, Zhang LH, Jiang R, Li XP, Liu JY, Zhao YL. Predictions of thermodynamic properties for hydrogen sulfide. J Mol Liq 2020. [DOI: 10.1016/j.molliq.2020.113751] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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15
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A four-parameters model for molar entropy calculation of diatomic molecules via shifted Tietz-Wei potential. Chem Phys Lett 2020. [DOI: 10.1016/j.cplett.2020.137583] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
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16
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Approximate energy spectra of improved generalized Mobius square potential (IGMSP) for some diatomic hydride molecules. J Mol Model 2020; 26:195. [DOI: 10.1007/s00894-020-04449-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2019] [Accepted: 06/16/2020] [Indexed: 10/23/2022]
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17
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Bound State Solution of Radial Schrodinger Equation for the Quark–Antiquark Interaction Potential. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY, TRANSACTIONS A: SCIENCE 2020. [DOI: 10.1007/s40995-020-00913-4] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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18
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Okorie US, Ikot AN, Chukwuocha EO. The Improved Deformed Exponential‐type Potential Energy Model for
N
2
,
NI
,
ScI
, and
RbH
Diatomic Molecules. B KOREAN CHEM SOC 2020. [DOI: 10.1002/bkcs.12039] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Uduakobong S. Okorie
- Department of Physics, Theoretical Physics GroupUniversity of Port Harcourt Choba Nigeria
| | - Akpan N. Ikot
- Department of Physics, Theoretical Physics GroupUniversity of Port Harcourt Choba Nigeria
| | - Ephraim O. Chukwuocha
- Department of Physics, Theoretical Physics GroupUniversity of Port Harcourt Choba Nigeria
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19
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Ghanbari A, Khordad R. Theoretical prediction of thermodynamic properties of N2 and CO using pseudo harmonic and Mie-type potentials. Chem Phys 2020. [DOI: 10.1016/j.chemphys.2020.110732] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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20
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Buchowiecki M. Vibrational Partition Function for the Multitemperature Theories of High-Temperature Flows of Gases and Plasmas. J Phys Chem A 2020; 124:4048-4052. [DOI: 10.1021/acs.jpca.0c01161] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Marcin Buchowiecki
- Insitute of Physics, University of Szczecin, Wielkopolska 15 St, 70-451 Szczecin, Poland
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21
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22
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Tang B, Wang YT, Peng XL, Zhang LH, Jia CS. Efficient predictions of Gibbs free energy for the gases CO, BF, and gaseous BBr. J Mol Struct 2020. [DOI: 10.1016/j.molstruc.2019.126958] [Citation(s) in RCA: 36] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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23
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Chanana G, Batra K, Prasad V. Exploring response of Li2 molecule to external electric field: A DFT and SAC-CI study. COMPUT THEOR CHEM 2019. [DOI: 10.1016/j.comptc.2019.112620] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
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24
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Jia CS, Wang YT, Wei LS, Wang CW, Peng XL, Zhang LH. Predictions of Entropy and Gibbs Energy for Carbonyl Sulfide. ACS OMEGA 2019; 4:20000-20004. [PMID: 31788634 PMCID: PMC6882136 DOI: 10.1021/acsomega.9b02950] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/10/2019] [Accepted: 10/29/2019] [Indexed: 06/10/2023]
Abstract
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.
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Affiliation(s)
- Chun-Sheng Jia
- State
Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, Sichuan, People’s Republic
of China
| | - Yi-Ting Wang
- State
Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, Sichuan, People’s Republic
of China
| | - Lin-Sheng Wei
- Engineering
Technology Research Institute, PetroChina
Southwest Oil and Gasfield Company, Chengdu 610017, People’s
Republic of China
| | - Chao-Wen Wang
- State
Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, Sichuan, People’s Republic
of China
| | - Xiao-Long Peng
- State
Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, Sichuan, People’s Republic
of China
| | - Lie-Hui Zhang
- State
Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, Sichuan, People’s Republic
of China
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Wang J, Jia CS, Li CJ, Peng XL, Zhang LH, Liu JY. Thermodynamic Properties for Carbon Dioxide. ACS OMEGA 2019; 4:19193-19198. [PMID: 31763543 PMCID: PMC6868907 DOI: 10.1021/acsomega.9b02488] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2019] [Accepted: 10/21/2019] [Indexed: 05/13/2023]
Abstract
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.
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26
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Chen XY, Li J, Jia CS. Thermodynamic Properties of Gaseous Carbon Disulfide. ACS OMEGA 2019; 4:16121-16124. [PMID: 31592480 PMCID: PMC6777084 DOI: 10.1021/acsomega.9b02303] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/23/2019] [Accepted: 08/30/2019] [Indexed: 06/10/2023]
Abstract
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.
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Affiliation(s)
- Xiao-Yu Chen
- Petroleum
Engineering School and State Key Laboratory of Oil and Gas Reservoir
Geology and Exploitation, Southwest Petroleum
University, Chengdu 610500, People’s Republic
of China
| | - Ji Li
- Petroleum
Engineering School and State Key Laboratory of Oil and Gas Reservoir
Geology and Exploitation, Southwest Petroleum
University, Chengdu 610500, People’s Republic
of China
| | - Chun-Sheng Jia
- Petroleum
Engineering School and State Key Laboratory of Oil and Gas Reservoir
Geology and Exploitation, Southwest Petroleum
University, Chengdu 610500, People’s Republic
of China
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27
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Jiang R, Jia CS, Wang YQ, Peng XL, Zhang LH. Prediction of Gibbs free energy for the gases Cl2, Br2, and HCl. Chem Phys Lett 2019. [DOI: 10.1016/j.cplett.2019.04.040] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
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28
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Analytical calculations of thermodynamic functions of lithium dimer using modified Tietz and Badawi-Bessis-Bessis potentials. COMPUT THEOR CHEM 2019. [DOI: 10.1016/j.comptc.2019.03.019] [Citation(s) in RCA: 32] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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29
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