Inorganic Chemistry review sheet Exam #1

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Groups (vertical) alkali metals, alkaline earth metals, transition metals.

1 Inorganic Chemistry review sheet Exam #1 Ch. 1 General Chemistry review reaction types: A/B, redox., single displacement, elimination, addition, rearrangement and solvolysis types of substances: elements, ionic, molecular Memorize Periodic Table Periodic Table: metal/metalloid/non-metal Groups (vertical) alkali metals, alkaline earth metals, transition metals., pnictogens, chalcogens, halogens, noble gas Periods (horizontal) Thermodynamics Kinetics 1 st Law: E = q + w Gibbs Free Energy, ΔG = ΔH TΔS Enthalpy, ΔH = qp Entropy, ΔS disorder, S = k lnw Stable (ΔG = +) vs. unstable (ΔG = ) Inert (slow) vs. Labile (fast) Ch. 2 reaction profile: E vs. reaction progress The atom Quantum Theory: Plank and Einstein. E is quantized Rutherford s Au foil experiment: atomic model

Bohr model of the atom: E given to the atom puts the e in an excited state, drops back down to the ground state (a specific orbit; a specific E drop, a specific color).

Standing waves are quantized; quantization a natural result of the model.

The Ψ describes the e in terms of location and E.

finding the e ) Acceptable s mathematically must be: 1. Normalized 2. Single valued at x,y,z 3. Continuous 4.

2 Bohr model of the atom: E given to the atom puts the e in an excited state, drops back down to the ground state (a specific orbit; a specific E drop, a specific color). Visible line spectrum of H2: E is artificially quantized via the orbits from the Bohr model debroglie: e has particle-like and wave-like characteristics. Standing waves are quantized; quantization a natural result of the model. = h / mv e : Particle-like nature: Einstein (photoelectric effect) Wave-like nature: Davisson Germer Schrödinger wave equation uses both properties of e Ψ is the e. The Ψ describes the e in terms of location and E. or simply, H = E where H is the Hamiltonian operator 2 Y/ wrt: x, y, z Goal: Describe an e in an atom via the wavefunction: has no physical meaning, so Born interpretation (Ψ 2 = probability of finding the e ) Acceptable s mathematically must be: 1. Normalized 2. Single valued at x,y,z 3. Continuous 4. Finite is quantized with only certain values (quantum numbers: n, l, ml) Can more easily separate out angle ( ) and distance data (r) if spherical polar coordinates are used instead of Cartesian coordinates. E exactly solvable for H and 1e species: per atom Ψ consists of R(r) (radial function) (R(r) 2 = probability as a function of distance) and Y (angular function; spherical harmonic) (Y 2 = probability as a function of angle). 4 Quantum #s: n: Principle QN; E and size. Any whole # integer from 1 to ( means e is completely removed from atom) l: Orbital angular momentum (azimuthal QN); shape from e movement. All whole # up to n 1

ml : Magnetic QN; orientation, moving e generates a magnetic field.

name, label axes), f orbitals gerade vs. ungerade (i) What is the interpretation of the drawing?

Looking at a one e atom: all orbitals with the same n are degenerate because the one e isn t being shielded by any other e s.

3 ml : Magnetic QN; orientation, moving e generates a magnetic field. Values from l up to +l ms : e can be spin up (+1/2) or down ( 1/2) Wavefunction Equations and Orbital plots Radial - R Radial Density R 2 Radial Probability onion shell 4πr 2 R 2 s, p, d (know shape, name, label axes), f orbitals gerade vs. ungerade (i) What is the interpretation of the drawing? Wavefunction itself (no physical meaning), angular part of wavefunction squared probability at angles (out to infinity), or contour plot 90% probability (includes R 2 and, hence, n). Looking at a one e atom: all orbitals with the same n are degenerate because the one e isn t being shielded by any other e s. Atoms with more than one e show differences in E between orbitals with the same n because of shielding. (s orbitals shield (see below) best, and thus are lowest in E). Can model with Self Consistent Field (SCF) model. E for more than 1e species: per atom Z* Effective nuclear charge Z* = Z S Z; atomic number (# of p + ) S; Shielding (screening) constant s, p: close to nucleus: screened less by inner e. More effective at screening outer e. d, f: screened more by inner e & poor at screening. Ground state e configuration from Periodic Table (Pauli Exclusion Principle, Aufbau and Hund s Rule;, where N, # of e with parallel spin. over all orbitals. K, exchange integral ( 1(1) 2(2) with 1(2) 2(1)) ). Valence e s Exchange Energy maximized with number of parallel spins

Ground state e configuration anomalies (know: Cr (exchange energy) and Cu) TM Anomalous e Configurations Periodic Table should be based on

Diamagnetic, contains paired e s, repelled by a magnetic field.

3d 4s,4p 4d 4f 1. e of interest s or p: a. e s in same group each contribute 0.35 (35%) b. n 1 each contribute 0.85 (85%) c.

00 Periodic Trends: Size, IE, EA, e configurations of ions (and reasoning behind all) Size: Lanthanide contraction makes 3 rd to 4 th row of

4 Ground state e configuration anomalies (know: Cr (exchange energy) and Cu) TM Anomalous e Configurations Periodic Table should be based on atomic numbers (Z) NOT e filling anomalies! Orbital filling: Paramagnetic, contains unpaired e s, attracted to a magnetic field. Diamagnetic, contains paired e s, repelled by a magnetic field. Slater s Rules (Shielding): Screening constant estimated from Slater's Rules: Divide orbitals in groups of n & s,p or d or f: 1s 2s,2p 3s,3p 3d 4s,4p 4d 4f 1. e of interest s or p: a. e s in same group each contribute 0.35 (35%) b. n 1 each contribute 0.85 (85%) c. n 2 & below each contribute 1.00 (100%) 2. e of interest d or f: a. e s in same group each contribute 0.35 b. n 1 & below each contribute 1.00 Periodic Trends: Size, IE, EA, e configurations of ions (and reasoning behind all) Size: Lanthanide contraction makes 3 rd to 4 th row of transition metals smaller than expected IE1 (1 st ionization energy; one e removed), IE2 (2 nd ionization energy; 2 nd e removed) EA1 (1 st e affinity; 1 st e added), EA2 (2 nd e affinity; 2 nd e added) (if adding e is favorable, the EA value will be negative).

5 Ch. 4 Symmetry operation Symmetry elements (point symmetry): 1. Center of symmetry (or inversion) i, point 2. Rotation (or proper) axis Cn, line 3. Mirror, plane Types: h to the principle axis, Cn v containing the principle axis, Cn d s bisecting 2 C2 s 4. Rotation reflection (or improper) axis Sn, line 5. Identity E, no element Group Theory When all the symmetry elements in a molecule are collected, it is found that they have the properties of a mathematical group. 1. Product of 2 elements of a group the same as another element of the group. AB = C 2. There is the identity operator, E. EA = A 3. Every element has an inverse which is an element of the group. A 1 A = E 4. Associative law holds: A(BC) = (AB)C Point Group: All the mathematical operations (symmetry elements) constitute a group; the symmetry elements intersect in at least one point. (If all of the symmetry operations were performed, at least one point remains unchanged). Point groups represented by Schoenflies symbol. Shorthand for all the symmetry of an object (molecule). Some ex.s of point groups: C1 E Ci E, i Cs E, s C2 E, C2 D3 E, 2 C3, 3 C2 C2v E, C2, v(xy), v(yz) C2h E, i, C2, h D2d E, 2 S4, C2, 2 C2, 2 d D4h E, 2 C4, C2, 2 C2, 2 C2, i, 2 S4, h, 2 v, 2 d Td E, 8 C3, 3 C2, 6 S4, 6 d Oh E, 8 C3, 6 C2, 6 C4, 3 C2, i, 6 S4, 8 S6, 3 h, 6 d C v E, 2 C, v D h E, 2 C, v, i, 2 S, C2 Ih E, 12 C5, 20 C3, 15 C2, i, 12 S10, 20 S6, 15 Note: There is no Dnv, Ov or Tv Do not have to find all the symmetry to assign point group:

6 1. Linear? C v or D h 2. High symmetry? Multiple Cn, n > 2 Ix, or Ox 3. Highest Cn Tx, Cnx or Dnx 4. C2 s? Dnx 5. Mirrors? h: Cnh or Dnh ; just v(d): Cnv or Dnd Assigning Point Groups (know how to draw in necessary symmetry elements to validate the Point Group chosen): Character Tables (see Character Tables): Point Group symbol, Mulliken symbol, Symmetry Elements, Irreducible Representations, Characters, orbitals, rotation axes Applications of Symmetry & Group Theory Optical Activity, dipole moments, IR (and Raman) Spectroscopy, NMR, Bonding and Orbitals, Crystallography Can apply the symmetry elements contained in the Group to see what happens to the molecule (orbitals in the molecule): Symmetry operations can leave a vector: unchanged, 1; inverted, 1; or translated, 0 The mathematical result can be used to see if a stretch of a bond will be seen in the IR spectrum, can use results to make MO diagrams, etc Simpler approaches are knowing the point group of a molecule allows the prediction of the number of peaks in an NMR spectrum.

7 IA VIIIA 1 H IIA Periodic Table of the Elements IIIB IVB VB VIB VIIB VIII IB IIB IIIA IVA VA VIA VIIA 2 He Li Be B C N O F Ne Na Mg Al Si P S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc (98) 44 Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po (209) 85 At (210) 86 Rn (222) 87 Fr (223) 88 Ra Lr (262) 104 Rf (267) 105 Db (270) 106 Sg (271) 107 Bh (270) 108 Hs (277) 109 Mt (278) 110 Ds (281) 111 Rg (281) 112 Cn (285) 113 Nh (284) 114 Fl (289) 115 Mc (288) 116 Lv (293) 117 Ts (294) 118 Og (294) 57 La Ce Pr Nd Pm (145) 62 Sm Eu Gd Tb Dy Ho Er Tm Yb Ac Th Pa U Np Pu (244) 95 Am (243) 96 Cm (247) 97 Bk (247) 98 Cf (251) 99 Es (252) 100 Fm (257) 101 Md (258) 102 No (259)

MANY ELECTRON ATOMS Chapter 15

MANY ELECTRON ATOMS Chapter 15 Electron-Electron Repulsions (15.5-15.9) The hydrogen atom Schrödinger equation is exactly solvable yielding the wavefunctions and orbitals of chemistry. Howev er, the Schrödinger