Kinetic Study of the Bromine-Catalyzed Isomerization of Methyl- and Chloro-Maleic Acids in Aqueous Ce(IV)-Br -H2SO4 Medium

Methylmaleic (citraconic, CTA) acid and methylfumaric (measaconic, MSA) acid in aqueous sulfuric acid solution undergo bromine-catalyzed reversible cis-trans isomerization in the presence of ceric and bromide ions. The positional isomerization of CTA or MSA to itaconic acid (ITA) is not observed. The method of high performance liquid chromatography (HPLC) was applied to study the kinetics of this catalyzed isomerization. The major catalytic species is best expressed as the Br^?₂ · radical anion. Under suitable catalytic conditions, there is a tendency for the [MSA]/[CTA] ratio to reach an equilibrium value of 4.10 at 25° for the CTA+Br^?₂ · ? MSA+Br^?₂ · reaction. Chloromaleic (CMA) and chlorofumaric (CFA) acids undergo similar isomerization with an equilibrium [CFA]/[CMA] ratio of 10.3 at 25°. The isomerization of maleic acid (MA) to fumaric acid (FA) is essentially irreversible with 50 as the lower limit of the equilibrium [FA]/[MA] ratio. The substituent has an important effect on the reversibility of this catalyzed isomerization of butenedicarboxylic acids. The thermodynamic parameters ΔH° and ΔS° at 25° for the CTA+Br^?₂ · ? MSA+Br^?₂ · reaction were found to be ?5.1±0.7 kj/mol and ?6.0±3.3 J/mol K, respectively. The present method gives a plausible way to measure the differences in enthalpy and entropy between the trans- and cis-isomers of butenedicarboxylic acids (CRCO₂H=CR'CO₂H) in aqueous solution.     

Preparation and Crystal Structure of PrNb_5O_(14)

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Synthesis and Crystal Structure of a New Mixed Orthovanadate-Pyrovanadate Series: MBa2V3O11 or MBa2V2PO11 with M = Bi, In, or a Rare Earth

A new series of vanadates with the general formula M Ba₂V₃O₁₁, where M may be Bi, In, or a rare earth, has been synthesized and structurally characterized by single crystal X-ray diffraction and powder X-ray diffraction. The general formula may be rewritten as M Ba₂(VO₄)(V₂O₇) to emphasize that there is one orthovanadate group and one pyrovanadate group in each formula unit. Up to one-third of the vanadium may be replaced by phosphorous, leading to the general formula M Ba₂V₂PO₁₁. However, phosphorous shows no preference between the ortho and pyro groups. Both M Ba₂V₃O₁₁ and M Ba₂V₂PO₁₁ crystallize in the monoclinic system with the space group P2₁/_c and Z = 4. The cell parameters from single crystal X-ray data of BiBa₂V₃O₁₁ are a = 12.332(4) Å, b = 7.750(4) Å, c = 11.279(4) Å, β = 103.22(3)°, V = 1049(1) ų; and for BiBa₂PO₁₁ are a = 12.266(2) Å, b = 7.615(2) Å, c = 11.312(2) Å, β = 103.32(2)°, V = 1028.2(2) ų. The Bi atom coordinates to six oxygen atoms forming a distorted octahedron, and the edge sharing of BiO₆ octahedra results in a BiO₄ chain along the b axis. There are two types of Ba atoms with coordination numbers of 10 and 11. There are three types of tetrahedral (T) atoms in these structures. The nonequivalent T atoms of the pyro group give T-O-T angles of 167 and 171° in BiBa₂V₃O₁₁ and BiBa₂V₂PO₁₁, respectively. Isostructural M Ba₂V₃O₁₁ compounds were prepared in which M is In, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Yb, or Lu.     

The stability of RDDE\ddot x(t) + p_1 (t)\dot x(t) + q_1 (t)x(t) + p_2 (t)\dot x(t - r(t)) + q_2 (t)x(t - r(t)) = O

In this paper, the author considered the stability of zero solution of linear RDDE $$\begin{gathered} \ddot x(t) + p_1 (t)\dot x(t) + q_1 (t)x(t) + p_2 (t)\dot x(t - r(t)) + q_2 (t)x(t - r(t)) = O, \hfill \\ \ddot x(t) + p_1 (t)\dot x(t) + q_1 (t)x(t) + p_2 (t)\dot x(t - r(t)) = O \hfill \\ \end{gathered} $$ using Liapunov-Razumikhin functional and transformations and obtained some sufficient conditions for the stability of Eqs.(1) and (2). These results are suitable both for boundedp _i (t),q _i (t) andr(t).i=1,2.     

BRST quantization of a scalar particle in a curved background

The BRST formalism is employed to quantize a scalar particle and interactions with an external scalar field (x ) and vector gauge fieldA (x ) in the background of an arbitrary gravitational field. The second-quantized actions are obtained.