Volumetric Properties of Ethylbenzene with Ethyl Acrylate,Butyl Acrylate,Methyl Methacrylate,and Styrene at 298.15 K

Densities of the binary systems of ethylbenzene with ethyl acrylate, butyl acrylate, methyl methacrylate, and styrene have been measured as a function of the composition, at 298.15 K and atmospheric pressure, using an Anton Paar DMA 5000 oscillating U-tube densitometer. The calculated excess volumes were correlated with the Redlich-Kister equation and with a series of Legendre polynomials. The excess volumes are positive for the systems ethylbenzene + (methyl methacrylate, ethyl acrylate) and negative for the systems ethylbenzene + (butyl acrylate, styrene).     

Ultrasonic and viscometric studies of molecular interactions in binary mixtures of tetrahydrofuran with some aromatic hydrocarbons at temperatures from 288.15 to 318.15 K

Densities of the binary systems of 2,2′-oxybis[propane] with ethyl acrylate, butyl acrylate, methyl methacrylate, and styrene have been measured as a function of the composition, at 298.15 K and atmospheric pressure, using an Anton Paar DMA 5000 oscillating U-tube densimeter and used to calculate the partial and excess volumes. The latter were correlated with the Redlich-Kister equation and with a series of Legendre polynomials. The excess volumes are negative for all the systems reported here.     

Solution properties of octyl β-D glucoside. Part 1: Aggregate size. shape and hydration

Aqueous solutions of octyl--D-glucoside have been examined in a wide concentration range. By combining information from density, viscosity and dielectric permittivity, the transition from molecular to micellar state has been evidentiated. Classical equations for the viscosity colloidal dispersions have been reexamined and applied to get information on micelle shape. A combined analysis of dielectric and viscosity findings indicates a slight and continuous dependence of micellar shape on surfactant content. The role of hydration on micellar stability is significant.     

Ultrasonic vibration potentials,apparent molal volumes,and apparent molal heat capacities of 1:1 electrolytes in acetonitrile

The ultrasonic vibration potentials and apparent molal volumes for many inorganic and organic electrolytes were measured in acetonitrile at 25°C and combined to obtain ionic contributions to the standard partial molal volumes V°(ion). Monatomic cations and anions of the same size essentially have the same V°(ion). Their size dependence can be interpreted through Hepler's equation. The apparent molal heat capacities were also measured in acetonitrile and used to derive standard values. Various methods of estimating C _p ⁰ (ion) were investigated and an ionic scale is proposed. It is concluded that C _p ⁰ (ion) of large organic ions are very close to the intrinsic heat capacities of the ions, and the solvation contribution to monatomic ions is positive for both cations and anions.     

Complete Formulas for the Volumes of Tubes about Curves in a Riemannian Manifold

By using the Taylor expansions of the solutions of Jacobi equations, we obtain the complete formulas for the volumes of tubes about curves in a Riemannian manifold. This unifies the known results and simplifies the computations involved in this direction. In the special case of surfaces, we also obtain the corresponding complete formulas which generalize the known results. Received July 23, 1998, Accepted January 14, 1999     

On students' understanding of volumes of solids of revolution: An APOS analysis

We apply Action-Process-Object-Schema theory (APOS) to (1) examine the textbook used by students in the study to infer mental constructions the book proposes that students could do to understand solids of revolution, (2) use semi-structured interviews with nine students to find out which of the textbook’s proposed constructions students actually do, and what unconjectured or unexpected constructions students do, and (3) use the results of the interviews and the research literature to inform and set forth an alternative proposal for constructing volumes of revolution. Results suggest that many students have not constructed processes to visualize solids of revolution and to relate Riemann sums to the corresponding definite integrals. Implications for curriculum and instruction are discussed.