The VSEPR Model 10.33 Predict the shape or geometry of the following mole- cules‚ using the VSEPR model. a. SiF4 b. SF2 c. COF2 d. PCl3 10.34 Use the electron-pair repulsion model to predict the geometry of the following molecules: a. GeCl2 b. NF3 c. SCl2 d. XeO4 10.35 Predict the geometry of the following ions‚ using the electron-pair repulsion model. a. ClO3? b. PO43? c. SCN? d. H3O? 10.36 Use the VSEPR model to predict the geometry of the fol- lowing ions: a. N3? b. BH4? c. SO32? d. NO2
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+ to – or from – to +; and as many false [negative] roots as the number of times two + signs or two – signs are found in succession.” Analytic Geometry Descartes’ greatest contribution to mathematics was developing analytic geometry. The most basic definition of analytic geometry is applying algebra to geometry. Descartes established analytic geometry as “a way of visualizing algebraic formulas”. He developed the coordinate system as a “device to locate points on a plane”. The coordinate system
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mechanical explanations (Wozniak). Most of the contributions were in the category of philosophy and reasoning‚ but a lot of the important ones had to deal with math and science. Out of all the contributions Rene Descartes has made‚ the idea of analytic geometry is one of his most famous works and contributions to today’s mathematical world. Descartes was born on March 31‚ 1596 in the town of La Haye‚ which was renamed Descartes‚ in France. He was the son of an intellectual and Councilor in the French
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outstanding genius who studied geometry as a child. At the age of sixteen he stated and proved Pascal’s Theorem‚ a fact relating any six points on any conic section. The Theorem is sometimes called the "Cat’s Cradle" or the "Mystic Hexagram." Pascal followed up this result by showing that each of Apollonius’ famous theorems about conic sections was a corollary of the Mystic Hexagram; along with Gérard Desargues (1591-1661)‚ he was a key pioneer of projective geometry. He also made important early
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these molecules can be predicted from their Lewis structures‚ however‚ with a model developed about 30 years ago‚ known as the valence-shell electron-pair repulsion (VSEPR) theory. The VSEPR theory assumes that each atom in a molecule will achieve a geometry that minimizes the repulsion between electrons in the valence shell of that atom. The five compounds shown in the figure below can be used to demonstrate how the VSEPR theory can be applied to simple molecules. There are only two places in the
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© Drs. XO‚ PHB‚ CWR Crystal & Ligand Field Theory (10.2.1‚ 10.3) CHEM 241 Fall 2014 TM − p.1 Ligand field theory (the MO version of crystal field theory) includes two main components: 1. What holds the complexes together: The set of ligands are held to a metal ion by largely electrostatic forces (although there really is a high degree of covalency). The forces arise from the positive charge on the metal ion and the electric dipoles of the ligands‚ whose negative ends are associated
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di Pisa. There he was taught by Dini and Bianchi‚ who quickly influenced Guido to undertake research in geometry. He presented his doctoral thesis Clifford’s Parallelism in Elliptic Spaces in 1900. Most young doctoral students take a few years to make themselves well know in their area. However‚ Guido was lucky for his teacher Bianchi was about to publish an important work on differential geometry. Bianchi discussed the results of Guido’s thesis in his treatise‚ which appeared in 1902. Guido remained
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Alexander Grothendieck Alexander Grothendieck is a prominent mathematician who is well known for his theories in algebraic geometry‚ homological algebra and functional analysis. He was born in the capital of Germany‚ Berlin‚ in 1928‚ one year before the Wall Street Crash of 1929. Grothendieck’s parents were Sascha Shapiro and Hanka Grothendieck. Shapiro was a Russian anarchist of Jewish decent‚ prosecuted by the Czar and later by the Bolsheviks. He’d lost his left arm during an attempted prison
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amateur mathematician. He became known because of the contribution he made in mathematics and physics in the twentieth century. Hilbert is well remembered for landmark researches he conducted in algebra. He also left an indelible mark in axiomatic geometry and mathematics. Hilbert also profoundly contributed in other areas such as invariant theory and mathematical physics. Hilbert studied at the university of Konigsberg‚ and during his studies‚ he made several trips to abroad. He visited Europe on
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occupy a lot of space. Scientists use VSEPR Theory to determine the molecule’s geometry by counting the number of electron domains that surround the central atom. Electron domain can be described as a lone pair‚ single‚ double and triple bond‚ and also even free radical. Lone pairs tend to occupy a lot of space and lower the angle of a bond‚ which gives molecular geometry. Lewis structure help determine the molecular geometries‚ 3D structure‚ and distribution of electrons in order to understand the chemical
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