Browsing by Author "Fortunatus, Jacob"

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    Explicit Solutions for Real-time Reversible Inhibition Kinetics using Lambert W Function: Towards Progress Curve Analysis
    (Tanzania Journal of Science, 2022-12) Geradius, Deogratias; Makungu, Madirisha; Fortunatus, Jacob
    Accurate estimation of kinetic parameters is challenging due to the dynamics and mathematical nature of the chemical systems. This paper presents simple, yet efficient closed-form solutions for the enzymatic conversion of the substrate to the product in real-time derived using the Lambert W function. The real values of the Lambert W function were calculated from the Lambert package as implemented in MATLAB. The expressions exhibit remarkable robustness in estimating the parameters for randomized data at 1% to 4% variation in noise levels. Furthermore, unlike the initial rates method, the expressions estimate chemical kinetic parameters utilizing a full range of experimental data, thus minimizing the risk of missing information that would be detected at an extended time-span. Thus, the implementation of closed-form solutions presented in this paper for the estimation of kinetic parameters eliminates common pitfalls imposed by the initial rates and double reciprocal methods.
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    Quantum chemical study of structure, vibrational spectra and thermodynamic properties of molecular and ionic clusters existing in vapours over strontium dichloride
    (Taylor and Francis, 2022-02-14) Sospeter, Imani; Fortunatus, Jacob
    The cluster ions SrCl− 3 , Sr2Cl+ 3 , Sr3Cl+ 5 , Sr4Cl+ 7 and Sr5Cl+ 9 that were detected earlier in vapour over strontium dichloride at high temperatures ranging from 1100 to 1500 K have been studied theo retically. The equilibrium geometrical properties, vibrational spectra and thermodynamic properties were investigated by using the DFT, MP2 and MP4 methods. From the alternative structures consid ered, it was observed that the ions SrCl− 3 , Sr2Cl+ 3 , Sr3Cl+ 5 and Sr5Cl+ 9 correspond to D3h symmetry and Sr4Cl+ 7 corresponds to C2v configuration, no isomers were identified for all cluster ions from the considered alternative structures. The enthalpies of formation, fHo(0) of the cluster ions were deter mined (in kJ mol–1): −994 ± 3 (SrCl− 3 ), −410 ± 12 (Sr2Cl+ 3 ), −1202 ± 16 (Sr3Cl+ 5 ), −1962 ± 27 and −2718 ± 20.
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    Structural, vibrational and thermodynamic properties of the isomers of the dimer molecules Ba2X4 (X=F, Cl, Br, or I)
    (Springer, 2022-04-12) Fortunatus, Jacob
    Geometrical parameters and vibrational spectra of the dimer Ba2X4 molecules were calculated; diferent isomeric structures were revealed. For the Ba2F4, Ba2Cl4, and Ba2Br4, three isomers of C3v, C2v, and C2h symmetries were confrmed to exist while for Ba2I4 only two isomers, C3v and C2h, were confrmed. For all halides, the bipyramidal C3v isomers possessed the lowest energy. The structural parameters and vibrational frequencies were employed in calculation of thermodynamic func tions and enthalpies of dissociation reactions of the species. The enthalpies of formation ∆fH(0) of the C3v isomers were obtained (in kJ mol−1):−1874 ± 2 (Ba2F4);−1236 ± 7 (Ba2Cl4);−1023 ± 8 (Ba2Br4);−787 ± 11 (Ba2I4). The relative abundance of the isomeric forms was evaluated for a broad temperature range, between 200 and 2000 K. It was shown that the concentrations of different isomers appeared to be comparable in saturated vapors at temperatures close to experimental conditions.