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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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brooklyn college inorganic chemistry spring 2009
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)
slide3

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)

slide6

Inorganic

chemistry

Solid-state

chemistry

Organometallic

chemistry

Coordination

chemistry

Bioinorganic

chemistry

Materials

science &

nanotechnology

Organic

chemistry

Environmental

science

Biochemistry

slide9

Unusual coordination

numbers for H, C

slide11

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
slide15

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)

slide16

Atomic structure

A revision of basic concepts

slide17

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)

slide18

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

slide19

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.

by demanding that the wave function be well behaved characteristics of a well behaved wave function

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.

example of simple quantum mechanical problem electron in one dimensional box
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

q m solution in atomic units to schrodinger equation
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.

slide23
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)

slide24

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)

slide25

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!!

slide26
In normalized form

Where n = 1,2,3…

slide27

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

slide28

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:

slide29

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

slide30

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