ES_chm110_McGill_exam - Chm 110 Equation Sheet ELECTRONIC...

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Unformatted text preview: Chm 110 Equation Sheet ELECTRONIC STRUCTURE Light and Energy c = νλ E = hν Balmer Equation 1⎞ ν = 3.2881 x 1015 s-1 ⎛ 1 ⎜ 2 − 2⎟ n⎠ ⎝2 Radii of the atom r n = n 2a o De Broglie’s Postulate h mu λ=h = p Energy levels of a H-atom En = − Z hcRH 2 n2 ⎞ ∆E = Ef – Ei = hcRH ⎛ 1 ⎜ −1⎟ ⎜ n2 n2 ⎟ f⎠ ⎝i Standing Waves EK = h2 = h2 = n2h2 2 2mλ2 8mL2 2 m( 2 L / n) Heisenberg Uncertainty Principle ∆x•∆p ≥ h 4π RADIOACTIVITY Rate of Decay A = kN Half-Life 0.693 ⎛N ⎞ t1/ 2 = ln ⎜ t ⎟ = − kt ⎜N ⎟ k ⎝ 0⎠ INTERMOLECULAR FORCES/BONDS • • • "London" dispersion forces: temporary dipole moments that develop in molecules as a result of the motion of the electrons. (larger molecules have higher boiling points) Dipole forces: describe the attraction between the negatively charged end of a polar molecule and the positively charged ends of neighbouring polar molecules Hydrogen bonding: involves lone pair of e -s on an electronegative atom (F, O, and N) of one molecule and a polar bond to hydrogen in another molecule Molecular solid: molecules in molecular solids are held in place by the intermolecular forces (dispersion, dipolar, and/or hydrogen bonds) Metallic solid: atoms in metallic solids are held in place be delocalized bonding Network solid: contains an array of covalent bonds linking every atom to its neighbours Ionic solid: contains cations and anions attracted to one another by coulombic interaction Intramolecular Bonds Ionic bonds – generally a bond between a metal and a non-metal; usually very strong Covalent bonds - e -s are shared between 2 nonmetals either equally (non-polar) or unequally (polar) Empirical formula – tells which atoms are involved and in what ratio Molecular formula – tells which atoms are involved and their exact numbers Structural formula – tells which atoms are involved, their exact numbers and arrengement Electronegativity (EN) – ability of an atom in a molecule to attract e -s Dipole moment occurs in molecules with atoms of different EN (e.g. polar covalent bond) Bond length – the separation distance between two atomic centered involved into a chemical bond LEWIS STRUCTURES, VSEPR + VALENCE BOND+ MO THEORIES Hydrogen bond, (in liquids and solids) the strongest of all intermolecular forces. In a molecule where H is bonded to a highly electronegative element (like N,O, or F) and where there are other molecules containing electronegative atoms with lone pairs) we get Hbonds. Increases boiling point and accounts for water’s high boiling point. Covalent Bonding: Lewis Dot Structure Rules (simple rules) 1. Sum the valence electrons of all the atoms. Don’t worry about where the electrons are from, the total number is the thing that is important 2. Dispersion forces: describe the attraction between the negatively charged electron cloud of one molecule and the positively charged nuclei of neighbouring molecules 2. Second-row elements B and Be often have fewer than 8 electrons around them in their compounds (e.g. BeCl2 and BF3). This makes them very reactive. 3. Second-row elements never exceed the octet rule, since their valence orbitals (2s2p) can accommodate only 8 electrons. 4. Third-row and heavier elements often satisfy the octet rule, but can exceed the octet rule by using their empty valence dorbitals (e.g. PCl5) Formal charge When drawing Lewis structures 1) keep formal charges as low as possible 2) try to spread the charge out over a large surface area 3) if you calculate a formal charge of > +1 for an atom in a molecule, the structure is wrong. Formal charge = [# valence electrons an element normally has] – [non-bonded electrons] – ½ [bonded electrons] More rules for Lewis structures: 1. 3. Use a pair of electrons to form a bond between each pair of bound atoms Arrange the remaining electrons to satisfy the duet rule (H) and octet rule (all other elements) around each atom as lone pairs. nd 2 row elements (C, N, O, and F) should always be assumed to follow the octet rule; 2. nd 2 row elements B and Be often have fewer than 8 e -s around them in their compounds (e.g. BeCl2, BF3); Lewis Structures Dipole-dipole interactions: Polar molecules have permanent dipole moments. The force of interaction of these molecules is much stronger than dispersion forces. Increases boiling point over a non-polar molecule. + signs indicate we are short one electron. – signs indicate we need to add one electron. More Rules for Lewis Structures (complicated structures) 1. Second-row elements (C, N, O and F) should always be assumed to follow the octet rule The shorter the bond, the stronger it is: triple bond > double bond > single b0nd All atoms strive to have 8 electrons in their outer (valence) shell. One way to accomplish this is by bonding to other atoms and sharing electrons to make up the magic number of 8. Sharing electrons between atoms makes bonds. STATES OF MATTER 4. 3. nd 2 row elements never exceed the octet rule; 4. rd 3 row and heavier elements often satisfy the octet rule but can exceed the octet rule by using their empty valence d-orbitals (e.g. PCl5) Resonance structures Found when molecules have more than one possible Lewis structure VSEPR Theory VSEPR describes the 3-D shape of a molecule. 1. draw Lewis dot structure 2. count bonded atoms and lone pairs located around central atom and arrange them We’ve helped over 50,000 students get better grades since 1999! Need help for exams? Check out our classroom prep sessions - customized to your exact course - at around the central atom so that interactions are minimized 3. 4. 5. double/triple bonds are counted as 1 electron pair only!! determine positions of atoms (maximize separation of lone pair e ) name the molecular structure based on the position of the atoms only. The placement of all electron pairs (bonding and lone pairs) determines the structure of the molecule, but the actual shape name we assign depends on the positions of the atoms only. E.g. H2O has tetrahedral geometry as it has 4 electron pairs around it, but its shape is called “bent”. Vsepr Theory: Describes 3D shape of molecule 1. draw LS 2. e -s, or double or triple bond. (see bonding in AO Valence Bond Theory atomic orbitals centered on the same atom # atomic orbitals (AOs) = # hybrid orbitals s+p s+p+p 3 sp 2 # MO = # AO Since light can act as a wave (with amplitude and wavelength) and as a particle (photon), particles (electron, alpha particle, etc.) can act as waves. λ = h/mv e -s with opposite spins each MO can hold 2 w Bond order tells how strong the bond is: Bond order = # bonding e − # antibonding e 2 Diamagnetic – all wavelength (particle) = Plank’s constant/mass×speed e -s are paired (no magnetic Bond angles (ideal) 180° Geometric family Linear Trigonal planar 120° s+p+p+ 3 4 sp 109.5° p s+p+p+ 3 5 sp d p+d s+p+p+ 32 6 sp d p+d+d Molecular Orbital Theory Tetrahedral Trigonal bipyramidal Octahedral Paramagnetic – unpaired e -s (align with a magnetic field) QUANTUM MECHANICS Atomic structure Electromagnetic radiation -1 -1 keeping atoms together) or anti-bonding (not involved in bonging). If # bonding h = hν = cλ e -s > anti- e -s, then we have a molecule formation. For MOs, add up all (core + valence) e -s that belong to both atoms in the molecule and find Quantum number Principal quantum number (n) Angular momentum quantum number (l) Magnetic quantum number (m) Photoelectric effect and Work function WORK FUNCTION for a particular metal is the energy of the photon that will cause an electron to “escape” from the metal surface. KEelectron escaping = hv-φ, where φ is the energy that binds the electron to the metal (BE, Binding energy) Bohr atom, particles and wave equations 2 orbital shape (s, p, d, f) l = 0, to …n-1 orbital orientation (px, py, pz) m = -l to +l Electronic Configuration How to write electronic configuration – order of subshells Three rules: 1. 2. Hund’s rule - e -s pair up only after Pauli Exclusion principle – no e -s have the same 4 quantum numbers ∆E = energy of a photon released as you go from excited back to ground state Noble gases have fully filled subshells (the last element in a period) Transition elements – d-block in the periodic The Bohr atom and theory H e occupy the lowest filling subshell 3. Z (atomic number) =R Aufbau rule - available energy first RH (Rydberg constant = 2.18×10-18J) final energy level Possible values n=1, 2, 3…. describes spin m s = + ½ or Spin quantum of electron number (ms) -½ Each electron has a unique set of quantum numbers. 2 En=-RH(Z /n ) The energy of an electron at n energy level is calculated from ∆ E = E initial − E Description -34 where h is Plank’s constant or 6.6261×10 Js n (energy level); n=1, 2, 3 etc e -s are characterized as bonding (involved in Orbitals and electrons Quantum numbers descriptions effect) E photon Important fact: the number of atomic orbitals added to make hybrids is equal to the number of hybrids formed. s + p → 2 sp orbitals Hybrid orbital – mathematical combination of # and type of hybrids 2 sp DeBroglie # σ = # σ* Speed(ms )= frequency(s ) × wavelength (m) Table 1 on the last page) Hybridized AOs notice that Z has been replaced by 1 (atomic number for H = 1). This equation only holds true for hydrogen. Anti-bonding MO (σ*) is higher in energy than count bonded atoms and lone pairs Electron group – pair of both bonding and non- bonding Bonding MO (σ) is lower in energy than in AO ⎛1 1 −2 ⎜2 ⎜n n initial ⎝ final ⎛Z2 ⎞ En = −R H ⎜ 2 ⎟ ⎝n ⎠ ⎞ ⎟ ⎟ ⎠ table; starts from period #4 e -s: ns e -s are removed first and only then (n-1)d e -s in case of removing places for them Our Course Booklets - free at prep sessions - are the “Perfect Study Guides.” Need help for exams? Check out our classroom prep sessions - customized to your exact course - at more positive EA – unfavorable configuration PERIODIC PROPERTIES (metals, Periods – horizontal rows in the table Groups (families) – vertical columns in the table Valence e -s - e -s in an outermost shell; # of val. e -s is the same for elements in the same group val. Na + Complex ion – a central metal ion bonded to several molecules or anions ); metals & noble gases Non-metal properties metal ↑ propertie s↓ - Lewis acid – any species that accepts an e pair EA negativity ↑ Lewis base – any species that donates an e pair EA negativity ↑ e -s when covalent bond is formed properties & chemical behavior Electronegativity ≡ EA e -s; ns2np6 Nuclear shielding - e -s on filled shell protect electronegative ≡ EA more negative Octet – 8 val. valence More F > O > N > Cl > Br > I >S > C > H positively charged protons in a nucleus from e -s Acidity – how well proton is donated or e is accepted, or pH is lowered High acidity ⇒ strong acid ⇒ weak (H-X) bond & Effective nuclear charge, Zeff – reduced positive nuclear charge by e -s in the filled shell Move across the period (left to right) – add # of — stable anion X− high electronegativity of X ⇒ stable X− val. e s bigger R of X ⇒ longer (H-X) bond ⇒ weaker Move down in the group (top to bottom) – add (H-X) extra filled shell EN↑ Electrostatic forces: R↑ shield and positive protons Molecular Orbital Theory e -s in both Repulsion – between filled shell and valence shell Atomic & ionic radius: Z↑ e attraction ↑ # val s↑ # shells ↑ Z↓ R ↓ shielding ↑ R ↑ X+ < X < X− Ionization energy, IE – energy needed to remove the least-tightly bound # val e - ↑ # shells ↑ Z↓ e (val. shielding ↑ addition of an Spectrochemical series – the relative ability of ligands to split the d orbitals of a metal ion I < Br < Cl < F < H2O < SCN < NH3 < en < NO2 < CN < CO 1) bond order tells us how strong a bond = ½ (bonding e - antibonding e ) Weak field ligands – give a small crystal field Table 1. paramagnetic is when you have electrons with unpaired spins (always occurs if there is an odd number of electrons, like for NO) Linear 2 sp Trigonal planar 3 2 0 1 4 sp3 Tetrahed -ral 4 3 2 0 1 2 5 4) when diagramming the molecular orbitals, add up all (core + valence) electrons that belong to both atoms in the molecule and find places for them!! # lone pairs on central atom 0 sp3d Trigonal bipyrami dal 5 4 3 2 0 1 2 3 6 sp3d2 Octahedr al 6 5 4 0 1 2 # electr on grou ps 2 3 Hybridiz ation of central atom sp 2 diamagnetic is when you have electrons with paired spins COORDINATION CHEMISTRY Geometr ic family # bond ing pairs e more negative EA – favorable configuration (halogens, Crystal field splitting energy – difference in energy between two sets of metal-ion d orbitals as a result of electrostatic interactions with bonded ligands splitting energy IE ↓ Electron affinity, EA – energy associated with Crystal field theory – a model that explains the colour, magnetism, and bonding of co-ordination compounds based on the effects of ligands on metal-ion d-orbital energies Four things to know about MO theory 3) IE ↑ Coordination isomers – Structural isomers where the ligand and counter-ion switch positions Strong field ligands – give a large crystal field splitting energy e) attraction ↑ Coordination number – the number of bonds formed between a metal ion and its ligands, the most co-ordination numbers and geometries are: 2 – Linear (least common) 4 – Tetrahedral 4 – Square Planar 6 – Octahedral (most common) Electrons are categorized as bonding (involved in keeping atoms together) or anti-bonding (not involved in bonding). If the # of bonding electrons>antibonding, then we have the formation of a molecule. 2) Cation - add e -s ⇒ repulsion ↑ ⇒ R ↑ Anion - remove e -s ⇒ attraction ↑ ⇒ R ↓ Z↑ acidity ↑ acidity ↑ e -s in filled Attraction – between Ligand – neutral molecule or ion that has a lone pair of e that can be shared in a coordinate covalent bond, monodentate: one bond, bidentate: two bonds w Electronegativity, EN – ability of an atom to pull e -s responsible for Cl − ); non-metals - Transition metals – members of the d-block of the periodic table Coordination compounds – substances that contain at least one complex ion Our Course Booklets - free at prep sessions - are the “Perfect Study Guides.” Shape Linear Trigonal planar Bent Tetrahedral (tetrahedron) Trigonal pyramid Bent Trigonal bipyramidal See-saw (distorted tetrahedron) T-shaped Linear Octahedral Square pyramid Square planar ...
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This note was uploaded on 09/29/2010 for the course SCIENCE 120 taught by Professor Frenser during the Spring '10 term at McGill.

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