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9A.Valence-bond theory; 9B.Molecular orbital theory: the hydrogen molecule-ion, 9C.Molecular orbital theory: homonuclear diatomic molecules; 9D.Molecular orbital theory: heteronuclear diatomic molecules; 9E.Molecular orbital theory: polyatomic molecules).
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E9A.6(a) Describe the bonding in methylamine, CH 3 NH 2 , using hybrid orbitals. E9A.6(b) Describe the bonding in pyridine, C 5 H 5 N, using hybrid orbitals. Answers: (a) Considering the Lewis structure of the molecule, the electron-pair geometry around and nitrogen is attached to the remaining hydrogen. The nitrogen atoms have three half filled sp^3 orbital and one filled with a lone pair and electronic configuration method shown below. Complete(spdf) notation of N=7[N]1s^2 2s^2 2p^3 ↑↓ ↑↓ ↑↑↑ filled one loan pair: ↑↓ ↑ ↑↓↑↑ 1s^2 2s^2 2p^3 1s^2 2s^1 2p^4 The methylamine molecule, the electron-pair geometry around both the C and N atoms in CH 3 - NH 2 is a tetrahedral. Then we assign sp^3 hydridization to each atoms and C-N bond is formed by trigonal overlap of sp 3 orbital on these atoms. Each C-H bond is formed by overlap of a carbon sp^3 orbital with a hydrogen 1s orbital and the N-H bond if formed by overlapping of oxygen sp^3 orbital with hydrogen 1s orbital. The one lone pairs on nitrogen occupy the remaining sp^3 orbital on the atom. (b) The lone pair in sp2 orbital is perpendicular to the p orbitals and pi bond in the molecule. The electron pairs from the nitrogen that participates in aromaticity is the one in the C=N bond. D9B.2 What feature of molecular orbital theory is responsible for bond formation? Answer: In molecular orbital theory atomic orbitals of combining atoms are mixed/overlap with each other to form new orbitals known as molecular orbitals. That is two atoms come closer to each other interaction takes place and they form the bond. The energy of combining orbitals should be same. P9C.2 Before doing a calculation, sketch how the overlap between a 1s orbital and a 2p orbital directed towards it can be expected to depend on their separation. The overlap integral between an H1s orbital and an H2p orbital directed towards it on nuclei separated by a distance R is
. Plot this function, and find the separation for which the overlap is a maximum. Answer: The equation x 3 - 3x-3=0 has one real positive root. The overlap is maximum at R=2.1a 0. P9E.3 Suppose that a molecular orbital of a heteronuclear diatomic molecule is built from the orbital basis ψA, ψB, and ψC, where ψB and ψC are both on one atom (they can be envisaged as F2s and F2p in HF, for instance). Set up the secular equations for the optimum values of the coefficients and set up the corresponding secular determinant.