Vapor Pressures and Thermodynamic Properties of Mg(BH4)2, KBH4 and RbBH4 Using Torsion-Effusion and Thermogravimetric Method
AuthorNgwa Nforbi, Lum-Ngwegia
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The aim of this research was to study the total vapor pressures and vapor molecular weights of magnesium borohydride (Mg(BH4)2), potassium borohydride (KBH4) and rubidium borohydride (RbBH4). The torsion-effusion method was used to obtain the vapor pressures of effusing gases. The molecular weights of these gases were obtained by the gravimetric method which involved monitoring the rate of weight loss of the material in mg/h. Values of the molecular weights in g/mol gave an indication of the type of gases that were predominant in the effusing gas. The partial pressures of various species, equilibrium constants for the vaporization reactions, their enthalpies, entropies and Gibbs energies have been determined. The first set of experiments involved independently studying the vaporization behavior of Mg(BH4)2 measuring within the temperature ranges 225 °C to 263 °C, and 165 °C to 216 °C, and using two molybdenum Knudsen cells with orifice diameters of 0.3 mm and 0.6 mm respectively. Moderate pressures of 10-5 torr were employed in these experiments. Based on our measurements between 165 °C - 263 °C, we propose that Mg(BH4)2 disproportionates to form predominantly H2 gas (~ 95 %) with a small amount of Mg(BH4)2(g) (~ 5%). The combined measured molecular weight from this first set of experiments is 4.16 g/mol and indicates that mostly H2 gas is present in the vapor phase. The total vapor pressure for the disproportionation of Mg(BH4)2 is given by logP(bar) = 9.2303 - 7286.2/T. The partial vapor pressures for the Mg(BH4)2 and H2 gases are given by the equations logP(bar) = 8.2515 - 7286.2/T and logP(bar) = 9.1821 - 7286.2/T respectively. The partial pressures of the gaseous species were determined as PH2(g)/PT = 0.895 and PMg(BH4)2(g)/PT = 0.105. Enthalpies of reaction for the effusing gases in this temperature range were calculated to be ΔH = +558.0 kJ/mol H2 and and ΔH = +135 kJ/mol Mg(BH4)2. The standard Gibbs free energy changes, ΔG°(kJ/mol), for the complete decomposition reaction (Mg(BH4)2(s) → Mg(s) + 2B(s) + 4H2(g)), sublimation reaction (Mg(BH4)2(s) → Mg(BH4)2(g)) and the disproportionation reaction for Mg(BH4)2 were calculated. An intensive study of the decomposition pathway of Mg(BH4)2 was carried out in the temperature range of 115.2 °C - 439.8 °C. Results of this experiment show that Mg(BH4)2 desorbs via a multi-step process. This research work carried out on Mg(BH4)2 indicates how different results can be obtained using different starting materials. Different reaction products were obtained depending on the method used in the vaporization experiment. The total vapor pressure and average vapor molecular weight of potassium borohydride (KBH4) and rubidium borohydride (RbBH4) were determined. Total vapor pressures of KBH4 and RbBH4 were measured using two Mo Knudsen effusion cells with 0.3 mm (P1 cell) and 0.6 mm (P2 cell) orifice diameters. Measurements with KBH4 were done over the pressure range of 10-7 - 10-5 bar, between 651 K and 740 K. Measurements with RbBH4 were done over the same pressure range but within a temperature range of 616.3 K and 695.1 K. Both starting powders were cubic and similar vaporization behaviors were expected for these alkali metal borohydrides. The measured average molecular weight of KBH4 is 23.5 g/mol for P1 cell and 23.3 g/mol for P2 cell. These values were very close to the calculated molecular weights of effusing gases of 22.5 g/mol but much less than the theoretical molecular weight of KBH4 which is 53.94 g/mol indicating that KBH4 does not sublime but decomposes. In the case of RbBH4, the measured average molecular weight of is 50.9 g/mol for P1 cell and 47.1 g/mol for P2 cell. Both of these are much less than the molecular weight of RbBH4, which is 100.3 g/mol, hence RbBH4 does not sublime but disproportionates. The calculated molecular weight of effusing gases for RbBH4 was 54.9 g/mol respectively. Vapor pressures for RbBH4 show dependence on the orifice size of the Knudsen cell. The Whitman - Motzfeldt zero-extrapolation method is used to calculate the equilibrium pressure (Peq) for the RbBH4 measurements using the P1 and P2 cells. The average vapor pressure equation for KBH4 was determined as: log P(bar) = (8.134 ± 0.041) - (9557.7 ± 28.7)/T The equilibrium vapor pressure equation for RbBH4 was determined as: log Peq(bar) = (10.053 ± 0.037) - (9591 ± 24)/T. Vapor pressure equations for KBH4 and RbBH4 using the P1 and P2 cells each were also obtained. The partial pressures of K(g) and H2(g) that were evolved during vaporization of KBH4 sample were determined as PK/PT = 0.688 and PH2/PT = 0.312 for both P1 and P2 cells. The partial pressures of Rb(g) and H2(g) from RbBH4 vaporization from the high pressure data were determined as PRb/PT = 0.765 and PH2/PT = 0.235 for the P1 and P2 cells. These partial pressure values are used to obtain standard Gibbs energy changes (ΔGº) as well as standard enthalpies and entropies of reaction for the decomposition of KBH4 and RbBH4. Extensive work has been done on determining the thermodynamic properties of Mg(BH4)2. Some thermodynamic constants of KBH4 have also been determined but these values do not seem reliable since they were obtained via an auto-compilation process. The vapor pressures and thermodynamic properties of RbBH4 have never been determined. The use of the torsion-effusion method for determining the vapor pressures and thermodynamic properties of Mg(BH4)2, KBH4 and RbBH4 has never been reported. The work presented in this document is the first of its kind. We have experimentally obtained thermodynamic data for Mg(BH4)2, KBH4 and RbBH4 using the torsion-effusion thermogravimetric method. Thermodynamic constants for KBH4 and RbBH4 have been obtained with very little uncertainty and are therefore reliable. This data will be tabulated on thermodynamic constants tables.