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Hanadi SLEIMAN CHEM 212 Chapter 1 Hanadi SLEIMAN CHEM 212 Chapter 1 - 1 - I. Lewis Structures 3 • How to write Lewis structures 3 II. VSEPR: The Shape of Molecules 5 III. Bond Polarity & MoleculE Polarity 7 IV. Orbital Theory 8 • Atomic Orbitals 8 • Molecular Orbitals 9 • Hybridization 12 • Summary 14 • Applications 15 V. Acids and Bases 17 • Trends 18 • Lewis Definition of Acids and Bases 20 VI. Exercises 20 VII. Solutions 22 VIII. Suggested Problems from 26 Solomons, 9th edition - 2 - I. Lewis Structures G.N. Lewis: Theory of Bonding based on the octet rule: atoms of C, N, O, F attain stable configurations when they have 8 electrons in their outer = valence shell. How to write Lewis structures Step 1 Count the number of valence electrons available; do not forget to add 1 e- for each (-) charge, and subtract 1 e- for each (+) charge on the molecule. Examples - - - CF4 : C = 4 valence e ; F = 7 valence e ⇒ Total valence electrons = 4174×+ × =32 e - - - - NO3 : N = 5 valence e ; O = 6 valence e ; (-) = 1 valence e ⇒ Total valence electrons = 51×+63 ×+=1 24 e- Step 2 Connect the bonded atoms by a line, representing 2 shared electrons. F O F C F N O F O Step 3 Count the number of shared electrons, and subtract this from the total number of valence electrons; this gives the number of electrons to be added to each atom to complete the structure. - Examples: CF4 = 32 – 8 = 24 NO3 = 24 – 6 = 18 Step 4 Add electrons in pairs to each atom to complete its octet (add 2 electrons for Hydrogen). This is not always possible for all atoms. F O F C F N O O F - - In CF4 all atoms have their octet, whereas in NO3 , the Nitrogen atom has only 6 e . Step 5 If one or more atoms have fewer than 8 electrons, form double or triple bonds to complete their octet. O N O O An electron pair on Oxygen is shared with Nitrogen to form a double bond. - 3 - Step 6 Assigning Formal Charges to atoms; by definition: Formal Charge = # (valence e-) - # (e- assigned to atom) Formal Charge = # (valence e-) – [# (bonds) + #(unpaired e-)] Examples: C = 4 - (4 + 0) = 0 F = 7 - (1+6) = 0 O = 6 - (1+6) = -1 F O = 6 - (2+4) = 0 O F C F O = 6 - (1+6) = -1 N O F O N = 5 - (4+0) = +1 Thus we write: O N O O + 2- Direct Application: Write the Lewis structures of NH4 , CO3 , C2H4 , CH3NO2 , CO2 , C2H5Cl. Solution: H H H O H N H O C CC O H H H H O H H H C N CO O H CCCl O H H H - 4 - II. The Shape of Molecules: VSEPR Method The Lewis structure of a molecule gives no information on the shape of this molecule. VSEPR stands for Valence-Shell Electron Pair Repulsion; the VSEPR theory is a model which helps to predict the geometry of molecules; its premise is that electron pairs on an atom will tend to be as far apart from each other as possible. Coordination Number CN = electron pairs on an atom = bonding pairs + lone pairs. Note that double and triple bonds are counted as 1 “bonding pair”. Basic shapes relevant to Organic Molecules: Coordination Number CN Shape Bond Angles CN = 4 Tetrahedral 109.5° CN = 3 Trigonal Planar 120° CN = 2 Linear 180° Examples: In Methane CH4 , the central Carbon has CN = 4 (4 bonding pairs and 0 lone pairs); thus the molecule has a Tetrahedral geometry. H 109.5° C H H H Dash-Wedge Model Ball-and-Stick Model Space-Filling Model In ammonia NH3 , the central nitrogen has CN = 4 electron pairs(3 bonding pairs, 1 lone pair). The basic geometry is tetrahedral, however the lone pair exercises more repulsion than a bond N pair; therefore bond angles are less than 109.5D (they are 107D ). The shape of the molecule, described according to the position of its atoms, is Trigonal Pyramidal. H H H 107° In water H2O, the central oxygen has CN = 4 electron pairs (2 bonding pairs, 2 lone pairs). D D The basic geometry is Tetrahedral, however the bond angle is less than 109.5 (it is 105 ). O The shape of the molecule is Bent. H H 105° - 5 - - In Boron trifluoride, BF3 , central boron has CN = 3 bonding electron pairs (note that B has only 6 e ). The geometry is Trigonal Planar, with bond angles 120D . F BF F 120° In Carbon dioxide, CO2 , central Carbon has CN = 2 “bonding pairs”. O CO The geometry is Linear, with bond angles of 180D . 180° + 2- + Direct Application: Determine the shape of NH4 , C2H4 , C2H2 , CO3 , NO2 . Solution: + H H H CC H CCH N H H H H H Tetrahedral, CN = 4 Trigonal Planar, CN = 3 Linear, CN = 2 2- O + CO O NO O Linear, CN = 2 Trigonal Planar, CN = 3 - 6 - III. Bond Polarity and Molecule Polarity Electronegativity measures the ability of a bonded atom to attract the shared electrons in a covalent bond. In the periodic table, electronegativity increases from left to right, and decreases down a group. The red arrows indicate an increase in electronegativity. Thus we have the following ranking of electronegativities: Li < Be < B < C < N < O < F and I < Br < Cl < F When 2 atoms of different electronegativities form a covalent bond, the bonding electrons are unequally distributed. The more electronegative atom draws these electrons closer to it, and thus acquires a partial negative charge (-δ); the less electronegative atom acquires a partial positive charge of equal magnitude (+δ): an electrical dipole μ is thus created. This covalent bond is termed polar. A molecule is polar if the resultant of its bond dipoles is non-zero. Molecule polarity depends on: 1. The individual bond polarities 2. The geometry of the molecule 3. The lone pairs (large contribution to dipole moment) Examples: CCl4 is unpolar, μ = 0 Cl Cl C Cl Cl Similarly, perfectly trigonal planar (e.g. BF3) and linear (e.g. CO2) molecules are unpolar. Consider NH3 vs. NF3 : N vs. N H F H F H F The net dipole moment in NH3 is larger than in NF3. - 7 - IV. Orbital Theory Although the Lewis and VSEPR models can be used for many applications, they do not explain what a bond really is. This is because electrons do not just behave as particles localized between nuclei. A large number of experiments show that the electrons also behave like waves. Atomic Orbitals The wave-particle duality of matter was expressed mathematically by Louis de Broglie as hh λ == p mv where λ = wavelength of the particle, m = mass of the particle, v = velocity of the particle, and h = Planck’s constant. Note that mv = momentum of the particle = p. Basically, the wave nature of a particle (expressed by λ) is important only when the particle is very small, e.g. the electron. The Heisenberg Uncertainty Principle states that we cannot simultaneously know the position and the momentum of a particle with absolute accuracy. Thus, when the energy (or momentum) of the electron is known with high accuracy, we cannot be certain of the position of this electron; we can only define regions of space where this electron is most likely to be found, the orbitals. The Schrodinger equation is a mathematical expression which describes the motion of an electron, the latter treated as a wave. Its solutions are called wavefunctions (Ψ). Each solution defines a certain region of space where the electron is most likely to be found, called orbital, and each of these orbitals is associated with a certain energy: (Ψ1,E1), (Ψ2,E2), (Ψ3,E3) and so on. An electron in an atom is only allowed these energies (E1, E2, E3 etc.). The energy of an atom is therefore quantized (hence the name quantum mechanics). The square of the wavefunction, Ψ2, represents the probability of finding an electron in a certain region of space, or electron density. The 3D plot of Ψ2 generates the shape of atomic orbitals. The orbitals relevant to Carbon are the 1s, 2s, and 2p orbitals. The 1s and 2s orbitals are spherical in shape. The 2s orbital contains a nodal surface – area where Ψ = 0, and the probability of finding the 2s electron is Ψ2 = 0. A node defines a change in sign of the wavefunction Ψ. There are three 2p orbitals, 2px, 2py, and 2pz. Each is dumbbell-shaped, and possesses a nodal plane perpendicular to its direction (e.g. the 2px node is the yz plane). The sign of the wavefunction is positive in one lobe and negative in the other lobe of the orbital; the energies of these orbitals are E(1s) < E(2s) < E(2p); the three 2p orbitals have the same energy, thus they are called degenerate. - 8 - z z - + y y + + x x Node 1s 2s z z z + - y - + y y + - x x x 2px 2py 2pz Now that we have the regions of space where the electrons are most likely found in the atom, we need some rules to place the electrons in these orbitals: 1. The Pauli Exclusion Principle: a maximum of 2 electrons can occupy one orbital, and these electrons must have paired spins. 2. The Aufbau Principle: orbitals are filled with electrons in order of increasing energy. 3. Hund’s Rule: when electrons are added to degenerate orbitals, one electron is added to each orbital with their spins unpaired, until each degenerate orbital contains 1 electron. Then a second electron – paired with the first – is added to each orbital.
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