A method for predicting the molar heat capacities of HBr and HCl gases based on the full set of molecular rovibrational energies

In this study, the improved Tietz potential was used to describe the internal vibration of diatomic molecules. By employing the expression for upper bound vibrational quantum number and canonical partition function of the system, equation for the prediction of constant pressure (isobaric) molar heat capacity of diatomic molecules was derived. The analytical model was used to predict the isobaric molar heat capacity of the ground state CO, BBr, HBr, HI, P2, KBr, Br2, PBr, SiO, and Cl2 molecules. The upper bound vibrational quantum number obtained for the molecules are 85, 100, 21, 21, 115, 301, 89, 157, 110, and 67. The calculated average absolute deviations are 2.3462%, 1.1342%, 2.3350%, 1.9078%, 0.7268%, 2.4041%, 1.7849%, 1.8989%, 2.5209%, and 2.1523% from experimental data. The results obtained are in good agreement with available literature data on gaseous molecules.

Section: Resultsmentioning

confidence: 99%

Section: The Canonical Partition Functionmentioning

confidence: 99%

“…The isobaric molar heat capacity C p (J mol À1 K À1 ) of the ITP can be deduced from the following expression [25].…”

Section: The Isobaric Molar Heat Capacity Model Of the Itpmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Isobaric molar heat capacity model for the improved Tietz potential

Eyube

Notani

Dlama

et al. 2022

“…Deriving thermodynamic data for gaseous substances such as the specific heat capacity, the enthalpy function, the Helmholtz function and the entropy of gas requires a thorough understanding of molecular partition functions. The internal partition function

Q_{italicint} (T)

of a molecule can be calculated by a direct discrete sum of all quantized rovibrational energy levels and can be represented as [34].

\begin{array}{c} Q_{int} ((), T) goodbreak= σ \sum_{n}^{n_{\max}} ((), 2 goodbreak- δ_{normalΛ, 0}) ((), 2 S goodbreak+ 1) \sum_{v}^{v_{\max}} \sum_{J}^{J_{\max}} ((), 2 J goodbreak+ 1) \\ ^{*} \exp ((), goodbreak- italichc \frac{E_{n, v, J} - ε_{0}}{kT}), \end{array}

where,

h

is Plank constant,

k

is Boltzmann constant,

ε_{0}

is the lowest rovibrational energy,

v, J, n

are the vibrational, rotational, and electronic quantum numbers, respectively,

(2 - δ_{Λ, 0}) (2 S + 1)

represents the electron degeneracy,

(2 J + 1)

refers to the rotational degeneracy.…”

Section: Applicationmentioning

confidence: 99%

Potential energy curves, partition functions and line intensities of HF and HCl molecules under the improved Hulburt‐Hirschfelder quantum mechanical anharmonic oscillator model

Tian

Fan

et al. 2022

Self Cite

An improved Hulburt‐Hirschfelder (IHH) quantum mechanical anharmonic oscillator model which describes the exact analytical potential energy curves (PECs) of diatomic molecules is presented. The IHH analytical potential function that involves a variable parameter, four empirically determined low‐order molecular vibrational and rotational spectral constants and the dissociation energy was applied to the ground electronic states of HF and HCl, yielding a good agreement between the Rydberg‐Klein‐Rees (RKR) potential energy points and the calculations. Correspondingly, with the determined IHH PECs, the partition functions at temperatures 300–6000 Kelvin (K) and rovibrational line intensities are evaluated, and coincide well with those quoted in the HITRAN2020 database compilation. The methodology could be valuable for the detection of molecules in interstellar clouds using infrared spectroscopy, as well as thermochemical reactions.

Study on macroscopic thermodynamic properties of ClO molecule based on the improved Hulburt–Hirschfelder potential energy function

Fan

Wen

Jian

et al. 2022

Self Cite

The improved Hulburt-Hirschfelder potential energy function is used as a proposal to emulate the behavior of intramolecular motion of a gas composed of diatomic molecules. In this work, the rovibrational energies of ClO molecule in the ground electronic state are obtained by solving the one-dimensional Schrödinger equation with the improved Hulburt-Hirschfelder potential energy curve. And then, the molar heat capacities, molar entropies, molar enthalpies and reduced Gibbs free energies of ClO macroscopic gas are calculated by the quantum statistical ensemble theory. The results are compared with those calculated by using RKR potential energy curve from experiment and Morse potential energy function. It is found that the macroscopic thermodynamic properties of ClO calculated by the improved Hulburt-Hirschfelder potential energy function are closer to the experimental values, which provides a new way to calculate the macroscopic thermodynamic quantities of diatomic gas based on molecular microscopic information.