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.

Introduction

Reduced sulfur species, including carbon disulfide (CS2), sulfur dioxide (SO2), and carbonyl sulfide (OCS) as trace sulfur gases exist in most atmospheric and surface natural water samples, and play a role in the global climate change.[1,2] CS2 originates widely from the combustion process of coal and natural gas, and also originates from industrial processes, such as production of insecticides and manmade cellulose.[3−5] The CS2 radical has long been used as a starting material for production of a variety of useful chemicals for agricultural, medicinal, and pharmaceutical applications. The chemical properties and real applications of the CS2 radical have drawn much recent interest.[6−18] However, as far as we know, the questions of what are efficient analytical representations of thermodynamic quantities for CS2, including entropy, enthalpy, and Gibbs free energy, remain to be solved from the view of the first principles. Knowledge of the thermodynamic properties of substances is essential for understanding natural phenomena such as phase transition, chemical reaction, and adsorption,[19−25] and for the engineering design of industrial processes. Providing efficient analytical representations of thermodynamic quantities for triatomics still remains elusive in the communality of science and engineering.

Our overall strategy for constructing effective analytical representations of thermodynamic quantities relies on exploiting the available oscillators to describe internal vibrations of the CS2 molecule. Recent work from our group on establishing efficient closed-form representations of entropy, enthalpy, and Gibbs free energy for diatomic substances has been performed by taking advantage of the improved Rosen–Morse, Manning–Rosen, and Tietz oscillators to represent the internal vibration of a diatomic molecule.[26−35] Inspired by this work, as well as the importance of the applications for CS2, we further design efficient analytical representations of the thermodynamic quantities for triatomic substances such as carbon disulfide. The purpose of the present study is to establish two analytical representations for the molar entropy and Gibbs free energy of CS2. To evaluate the ability of the proposed prediction models, we utilize five molecular constants of CS2 as an input to determine the molar entropy and Gibbs free energy values in the temperature range from 298 to 6000 K, and compare the predicted values with the experimental data available in the literature.

Results and Discussion

In order to ascertain the validity of the proposed models, the molar entropy and reduced Gibbs free energy are plotted against temperature as shown in Figure , where five molecular constant values for the CS2 molecule are taken from the work reported by Wentink[7] and Yang et al.:[8]De = 35 986.98 cm–1, reCS = 1.553 Å, ωes = 671.4 cm–1, ωea = 1551.9 cm–1, and ωeb = 398.6 cm–1. The reduced Gibbs free energy is defined as Gr = −(G – H298.15)/T. In Figure A, the green solid line stands for the theoretical entropy values predicted by using the improved Tietz oscillator to describe the symmetric stretching vibration of the CS2 molecule, the red solid line represents the entropy values obtained by using the traditional harmonic oscillator to describe the symmetric stretching vibration, and blue solid circles indicate the experimental data from the National Institute of Standards and Technology (NIST) database.[36] We can observe from Figure A that the molar entropy values based on the pure harmonic oscillator to represent the vibrations possess large deviations from the experimental data. All the data predicted from expressions 13 and 14, in the temperature range of 300–6000 K, are in good agreement with the experimental data from the NIST database.[36] The average relative deviations from the NIST data for the entropy and reduced Gibbs free energy values of CS2 are 0.250 and 0.108%, respectively. These deviation values strongly suggest that the proposed analytical representations of the entropy and Gibbs free energy for gaseous carbon disulfide are efficient in the temperature range from 300 to 6000 K.

Figure 1

Temperature variation of the thermodynamic properties of CS2 for (A) molar entropy and (B) molar reduced Gibbs free energy.

Conventional calculation models for the thermodynamic quantities of substances are required to apply a great number of experimental spectroscopy data. The present analytical representations of entropy and Gibbs free energy for CS2 merely require experimental values of five molecular constants of the CS2 molecule. This merit may stimulate one to develop analytical representations of thermodynamic quantities for other triatomics with the help of the present methodology.

Conclusions

In this work, we first construct reliable analytical representations of entropy and Gibbs free energy for gaseous carbon disulfide from the first principles. The average relative deviations of entropy and reduced Gibbs free energy values for CS2 from the NIST database, in the temperature range of 300–6000 K, are 0.250 and 0.108%, respectively. The proposed analytical representations merely rely on experimental values of five molecular constants of the CS2 molecule. The compromise of the simplicity and accuracy of the proposed analytical representations provide a new path toward construction of analytical expressions of thermodynamic quantities for other triatomic systems.

Computational Methods

The CS2 molecule is a linear triatomic molecule. As shown in Figure , the CS2 molecule has four vibration modes, including internal symmetric stretching vibration, antisymmetric stretching vibration, and a degenerate pair of bending vibrations. Herein, the improved Tietz oscillator[37] is used to illustrate the symmetric stretching vibration of the CS2 molecule. The vibrational partition function to represent the symmetric stretching mode of CS2 is given from eq 14 of ref (28) as followswhere De represents the energy to dissociate CS2 into CS and S, k denotes the Boltzmann constant, T denotes the absolute temperature, , , , , , and , here h denotes the Planck constant, μSS is the reduced mass of two sulfur atoms, reSS = 2reCS, reCS stands for the C–S equilibrium distance, q is a dimensionless adjustable parameter. The symbol ± corresponds to two cases that the plus is chosen when q < 0 and the minus is taken if q > 0. The parameter α is determined by , here , c represents the speed of light and ωes stands for the symmetric stretching frequency. The symbol erfi denotes the imaginary error function. The factor e2/3 illustrates the contributions of the excited states of the CS2 molecule to the vibrational partition function. The symbol vmax represents the highest vibrational quantum number which is given by where [x] denotes the greatest integer, which is less than x for the noninteger x.

Figure 2

Schematic diagram of the vibration modes of the CS2 molecule.

To tackle the problems of the antisymmetric stretching vibration and bending vibrations of the CS2 molecule, we choose the harmonic oscillator and write the corresponding vibrational partition function as follows[28]where Θv = hcωe/k, ωe represents the equilibrium frequency.

The vibrational entropy and Gibbs free energy corresponding to four vibration modes can be deduced from the following thermodynamic relationships and expressions 1 and 2

The molar vibrational entropy and Gibbs free energy accompanied by contributions of the symmetric stretching vibration of CS2 are determined as follows, respectivelywhere represents the universal gas constant. The molar vibrational entropy and Gibbs free energy accompanied by contributions of the antisymmetric stretching vibration and two bending vibrations of CS2 can be yielded as follows, respectivelywhere Θva = hcωea/k, Θvb = hcωeb/k, ωea, and ωeb represent the antisymmetric stretching vibration and bending vibration frequencies of CS2, respectively.

The molar entropies accompanied by contributions of translation and rotation of CS2 are given by eqs and 10,[38] respectivelywhere , mCS denotes the mass of the CS2 molecule, μCS denotes the reduced mass of carbon and sulfur atoms, and P denotes the gas pressure. The molar Gibbs free energies corresponding to translation and rotation of CS2 are expressed as follows,[39] respectively

The total molar entropy and Gibbs free energy of CS2 are obtained from eqs –12 as follows, respectively

When we know the experimental values of De, reCS, ωes, ωea, and ωeb for CS2, the molar entropy and Gibbs free energy values can be easily predicted from eqs and 14. Here, we establish the quantitative relationships between the entropy and Gibbs free energy of CS2 and the basic molecular constants. Keeping the pressure invariant, the temperature dependence of the entropy and Gibbs free energy of CS2 can be simply depicted in terms of eqs and 14.