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Lecture 1

Lecture 1. Brooklyn College Inorganic Chemistry (Spring 2009). Prof. James M. Howell Room 359NE (718) 951 5458; jhowell@brooklyn.cuny.edu Office hours : Mon. & Thu. 9:00 am-9:30 am & 5:30 – 6:30 Textbook: Inorganic Chemistry, Miessler & Tarr, 3rd. Ed., Pearson-Prentice Hall (2004).

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Lecture 1

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  1. Lecture 1

  2. Brooklyn CollegeInorganic Chemistry(Spring 2009) • Prof. James M. Howell • Room 359NE (718) 951 5458; jhowell@brooklyn.cuny.edu Office hours: Mon. & Thu. 9:00 am-9:30 am & 5:30 – 6:30 • Textbook: Inorganic Chemistry, Miessler & Tarr, 3rd. Ed., Pearson-Prentice Hall (2004)

  3. What is inorganic chemistry? Organic chemistry is: the chemistry of life the chemistry of hydrocarbon compounds C, H, N, O Inorganic chemistry is: The chemistry of everything else The chemistry of the whole periodic Table (including carbon)

  4. Inorganic chemistry Solid-state chemistry Organometallic chemistry Coordination chemistry Bioinorganic chemistry Materials science & nanotechnology Organic chemistry Environmental science Biochemistry

  5. Single and multiple bonds in organic and inorganic compounds

  6. Unusual coordination numbers for H, C

  7. Typical geometries of inorganic compounds

  8. Inorganic chemistry has always been relevant in human history • Ancient gold, silver and copper objects, ceramics, glasses (3,000-1,500 BC) • Alchemy (attempts to “transmute” base metals into gold led to many discoveries) • Common acids (HCl, HNO3, H2SO4) were known by the 17th century • By the end of the 19th Century the Periodic Table was proposed and the early atomic theories were laid out • Coordination chemistry began to be developed at the beginning of the 20th century • Great expansion during World War II and immediately after • Crystal field and ligand field theories developed in the 1950’s • Organometallic compounds are discovered and defined in the mid-1950’s (ferrocene) • Ti-based polymerization catalysts are discovered in 1955, opening the “plastic era” • Bio-inorganic chemistry is recognized as a major component of life

  9. Nano-technology

  10. Hemoglobin

  11. The hole in the ozone layer (O3) as seen in the Antarctica http://www.atm.ch.cam.ac.uk/tour/

  12. Some examples of current important uses of inorganic compounds Catalysts: oxides, sulfides, zeolites, metal complexes, metal particles and colloids Semiconductors: Si, Ge, GaAs, InP Polymers: silicones, (SiR2)n, polyphosphazenes, organometallic catalysts for polyolefins Superconductors: NbN, YBa2Cu3O7-x, Bi2Sr2CaCu2Oz Magnetic Materials: Fe, SmCo5, Nd2Fe14B Lubricants: graphite, MoS2 Nano-structured materials: nanoclusters, nanowires and nanotubes Fertilizers: NH4NO3, (NH4)2SO4 Paints: TiO2 Disinfectants/oxidants: Cl2, Br2, I2, MnO4- Water treatment: Ca(OH)2, Al2(SO4)3 Industrial chemicals: H2SO4, NaOH, CO2 Organic synthesis and pharmaceuticals: catalysts, Pt anti-cancer drugs Biology: Vitamin B12 coenzyme, hemoglobin, Fe-S proteins, chlorophyll (Mg)

  13. Atomic structure A revision of basic concepts

  14. Atomic spectra of the 1 electron hydrogen atom Energy levels in the hydrogen atom Energy of transitions in the hydrogen atom Paschen series (IR) Balmer series (vis) Bohr’s theory of circular orbits fine for H but fails for larger atoms …elliptical orbits eventually also failed! Lyman series (UV)

  15. Fundamental Equations of quantum mechanics Planck quantization of energy h = Planck’s constant n = frequency E = hn • = wavelength h = Planck’s constant m = mass of particle v = velocity of particle de Broglie wave-particle duality l = h/mv Heisenberg uncertainty principle Dx uncertainty in position Dpx uncertainty in momentum Dx Dpx h/4p • H: Hamiltonian operator • : wave function E : Energy Schrödinger wave functions

  16. Quantum mechanics requires changes in our way of looking at measurements. From precise orbits to orbitals: mathematical functions describing the probable location and characteristics of electrons electron density: probability of finding the electron in a particular portion of space Quantization of certain observables occur Energies can only take on certain values.

  17. How is quantization introduced? By demanding that the wave function be well behaved. Characteristics of a “well behaved wave function”. • Single valued at a particular point (x, y, z). • Continuous, no sudden jumps. • Normalizable. Given that the square of the absolute value of the wave function represents the probability of finding the electron then the sum of probabilities over all space is unity. It is these requirements that introduce quantization.

  18. Example of simple quantum mechanical problem. Electron in One Dimensional Box Definition of the Potential, V(x) V(x) = 0 inside the box 0 <x<l V(x) = infinite outside box; x <0 or x> l, particle constrained to be in box

  19. Q.M. solution (in atomic units) to Schrodinger Equation • ½ d2/dx2 X(x) = E X(x) X(x) is the wave function; E is a constant interpreted as the energy. We seek both X and E. Standard technique: assume a form of the solution and see if it works. Standard Assumption: X(x) = a ekx Where both a and k will be determined from auxiliary conditions (“well behaved”). Recipe: substitute trial solution into the DE and see if we get X back multiplied by a constant.

  20. Substitution of the trial solution into the equastion yields ½ k2 ekx = E ekx or k = +/- i sqrt(2E) There are two solutions depending on the choice of sign. General solution becomes X (x) = a ei sqrt(2E)x + b e –i sqrt(2E)x where a and b are arbitrary constants Using the Cauchy equality: eiz = cos(z) + i sin(z) Substsitution yields X(x) = a cos (sqrt(2E)x) + b (cos(-sqrt(2E)x) + i a sin (sqrt(2E)x) + i b(sin(-sqrt(2E)x)

  21. Regrouping X(x) = (a + b) cos (sqrt(2E)x) + i (a - b) sin(sqrt(2E)x) Or with c = a + b and d = i (a-b) X(x) = c cos (sqrt(2E)x) + d sin(sqrt(2E)x) We can verify the solution as follows -½ d2/dx2X(x) = E X(x) (??) - ½ d2/dx2 (c cos (sqrt(2E)x) + d sin (sqrt(2E)x) ) = - ½ ((2E)(- c cos (sqrt(2E)x) – d sin (sqrt(2E)x) = E (c cos (sqrt(2E)x + d sin(sqrt(2E)x)) = E X(x)

  22. We have simply solved the DE; no quantum effects have been introduced. Introduction of constraints: -Wave function must be continuous, must be 0 at x = 0 and x = l X(x) must equal 0 at x = 0 or x = l Thus c = 0, since cos (0) = 1 and second constraint requires that sin(sqrt(2E) l ) = 0 Which is achieved by (sqrt(2E) l ) = np which is where sine produces 0 Or Quantized!!

  23. In normalized form Where n = 1,2,3…

  24. Atoms Atomic problem, even for only one electron, is much more complex. • Three dimensions, polar spherical coordinates: r, q, f • Non-zero potential • Attraction of electron to nucleus • For more than one electron, electron-electron repulsion. The solution of Schrödinger’s equations for a one electron atom in 3D produces 3 quantum numbers Relativistic corrections define a fourth quantum number

  25. Quantum numbers for atoms Symbol Name Values Role n Principal 1, 2, 3, ... Determines most of the energy l 0 1 2 3 4 5 l Angular momentum 0, 1, 2, ..., n-1 Describes the angular dependence (shape) and contributes to the energy for multi-electron atoms orbital s p d f g ... ml Magnetic 0, ± 1, ± 2,..., ± l Describes the orientation in space relative to an applied external magnetic field. ms Spin ± 1/2 Describes the orientation of the spin of the electron in space Orbitals are named according to the l value:

  26. Principal quantum number n = 1, 2, 3, 4 …. determines the energy of the electron (in a one electron atom) and indicates (approximately) the orbital’s effective volume n = 1 2 3

  27. Angular momentum quantum number l = 0, 1, 2, 3, 4, …, (n-1) s, p, d, f, g, ….. determines the number of nodal surfaces (where wave function = 0). s

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