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Molecular Geometry and Bonding Theories Quantum Numbers – N 1 Chemistry Lecture 1 Semester One/ Dr. Mohammed Awady Molecular Geometry and Bonding Theories Quantum Numbers – n 1. The Principal quantum number has the symbol – n. n = 1, 2, 3, 4, ...... “shells” n = K, L, M, N, ...... The electron’s energy depends principally on n and tells the average relative distance of the electron from the nucleus. – As n increases for a given atom, so does the average distance of the electrons from the nucleus. – Electrons with higher values of n are easier to remove from an atom. 2. The azimuthal quantum number has the symbol . describes the shape of the region of space occupied by the electron When linked with n defines the energy of the electron, All wave functions that have the same value of both n and l form a subshell = 0, 1, 2, 3, 4, 5, .......(n-1) = s, p, d, f, g, h, .......(n-1) Chemistry Lecture 1 Semester One/ Dr. Mohammed Awady Quantum Numbers – m 3. The symbol for the magnetic quantum number is m. m = - , (- + 1), (- +2), .....0, ......., ( -2), ( -1), • If = 0 (or an s orbital), then m = 0. – There is only 1 value of m. Thus there is one s orbital per n value. n 1 • If = 1 (or a p orbital), then m = -1,0,+1. – There are 3 values of m. Thus there are three p orbitals per n value. n 2 • If = 2 (or a d orbital), then m = -2,-1,0,+1,+2. – There are 5 values of m. Thus there are five d orbitals per n value. n 3 • If = 3 (or an f orbital), then m = -3,-2,-1,0,+1,+2, +3. – There are 7 values of m. Thus there are seven f orbitals per n value, n – Theoretically, this series continues on to g,h,i, etc. orbitals. • Practically speaking atoms that have been discovered or made up to this point in time only have electrons in s, p, d, or f orbitals in their ground state configurations. Chemistry Lecture 1 Semester One/ Dr. Mohammed Awady • Each wave function with an allowed combination of n, l, and ml values describes an atomic orbital, a particular spatial distribution for an electron • For a given set of quantum numbers, each principal shell contains a fixed number of subshells, and each subshell contains a fixed number of orbitals Atomic Orbitals S orbital P Orbital Chemistry Lecture 1 Semester One/ Dr. Mohammed Awady d Orbital f- Orbital Chemistry Lecture 1 Semester One/ Dr. Mohammed Awady 4. Quantum Numbers – ms The last quantum number is the spin quantum number which has the symbol ms. The spin quantum number only has two possible values. ms = +1/2 or -1/2 Quantum Numbers Chemistry Lecture 1 Semester One/ Dr. Mohammed Awady Building up the Periodic Table • The Nucleus: • The Aufbau Process – Used to construct the periodic table – First, Build by adding the required number of protons (the atomic number) and neutrons (the mass of the atom) – Second, Determine the number of electrons in the atoms then add electrons one at a time to the lowest-energy orbitals available without violating the Pauli principle Electrons: Hund’s Rule states that each orbital will be filled singly before pairing begins. The singly filled orbitals will have a parallel spin. – Each of the orbitals can hold two electrons, one with spin up , which is written first, and one with spin down – A filled orbital is indicated by , in which the electron spins are paired Chemistry Lecture 1 Semester One/ Dr. Mohammed Awady – The electron configuration is written in an abbreviated form, in which the occupied orbitals are identified by their principal quantum n and their value of l (s, p, d, or f), with the number of electrons in the subshell indicated by a superscript Pauli’s Exclusion Principle states that paired electrons in an orbital will have opposite spins. Neon - 2p 2s 1s • Valence electrons – It is tedious to keep copying the configurations of the filled inner subshells – The notation can be simplified by using a bracketed noble gas symbol to represent the configuration of the noble gas from the preceding row – Electrons in filled inner orbitals are closer and are more tightly bound to the nucleus and are rarely involved in chemical reactions Now we can write a complete set of quantum numbers for all of the electrons in these three elements as examples. • Na • First for 11Na. – When completed there must be one set of 4 quantum numbers for each of the 11 electrons in Na (remember Ne has 10 electrons) 3s 3p Configuration 1 11Na Ne Ne 3s [Ne] = 1s22s22p6 Chemistry Lecture 1 Semester One/ Dr. Mohammed Awady Electronic Configuration of the Elements Chemistry Lecture 1 Semester One/ Dr. Mohammed Awady Chemistry Lecture 1 Semester One/ Dr. Mohammed Awady Chemistry Lecture 1 Semester One/ Dr. Mohammed Awady A large local charge separation usually results when a shared electron pair is donated unilaterally. The three Kekulé formulas shown here illustrate this condition. In the formula for ozone the central oxygen atom has three bonds and a full positive charge while the right hand oxygen has a single bond and is negatively charged. The overall charge of the ozone molecule is therefore zero. Similarly, nitromethane has a positive-charged nitrogen and a negative-charged oxygen, the total molecular charge again being zero. Finally, azide anion has two negative-charged nitrogens and one positive-charged nitrogen, the total charge being minus one. In general, for covalently bonded atoms having valence shell electron octets, if the number of covalent bonds to an atom is greater than its normal valence it will carry a positive charge. If the number of covalent bonds to an atom is less than its normal valence it will carry a negative charge. The formal charge on an atom may also be calculated by the following formula: Chemistry Lecture 1 Semester One/ Dr. Mohammed Awady VSEPR Theory • Regions of high electron density around the central atom are arranged as far apart as possible to minimize repulsions. • There are five basic molecular shapes based on the number of regions of high electron density around the central atom. • Lone pairs of electrons (unshared pairs) require more volume than shared pairs. • Consequently, there is an ordering of repulsions of electrons around central atom. • Criteria for the ordering of the repulsions: 1 Lone pair to lone pair is the strongest repulsion. 1 Lone pair to bonding pair is intermediate repulsion. 1 Bonding pair to bonding pair is weakest repulsion. • Mnemonic for repulsion strengths lp/lp > lp/bp > bp/bp • Lone pair to lone pair repulsion is why bond angles in water are less than 109.5o. Chemistry Lecture 1 Semester One/ Dr. Mohammed Awady Valence-shell electron-pair repulsion (VSEPR) model predicts the shapes of many molecules and polyatomic ions but provides no information about bond lengths or the presence of multiple bonds Chemistry Lecture 1 Semester One/ Dr. Mohammed Awady .
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