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Lecture 1

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Lecture 1

- Prof. James M. Howell
- Room 359NE
(718) 951 5458; [email protected]

Office hours: Mon. & Thu. 10:00 am-10:50 am & Wed. 5 pm-6 pm

- Textbook: Inorganic Chemistry, Miessler & Tarr,
3rd. Ed., Pearson-Prentice Hall (2004)

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)

Single and multiple bonds in organic and inorganic compounds

Unusual coordination

numbers for H, C

Typical geometries of inorganic compounds

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

Nano-technology

Hemoglobin

The hole in the ozone layer (O3) as seen in the Antarctica

http://www.atm.ch.cam.ac.uk/tour/

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)

Atomic structure

A revision of basic concepts

Energy levels in the hydrogen atom

Energy of transitions in the hydrogen atom

Atomic spectra of 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 failed0

Lyman series (UV)

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

The fundamentals of quantum mechanics

Quantum mechanics provides explanations for many experimental observations

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

- Single valued at a particular point (x, y, z).
- Continuous, no sudden jumps.
- Normalizable. Given that the square of the absolute value of the eave function represents the probability of finding the electron then sum of probabilities over all space is unity.

It is these requirements that introduce quantization.

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

- ½ d2/dx2 X(x) = E X(x)
Standard technique: assume a form of the solution.

Assume X(x) = a ekx

Where both a and k will be determined from auxiliary conditions.

Recipe: substitute into the DE and see what you get.

Substitution yields

½ k2 ekx = E ekx

or

k = +/- i (2E)0.5

General solution becomes

X (x) = a ei sqrt(2E)x + b e –i sqrt(2E)x

where a and b are arbitrary consants

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)

Regrouping

X(x) = (a + b) cos (sqrt(2E)x) + i (a - b) sin(sqrt(2E)x)

Or

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)

We have simply solved the DE; no quantum effects have been introduced.

Introduction of constraints:

-Wave function must be continuous

at x = 0 or x = l X(x) must equal 0

Thus

c = 0, since cos (0) = 1

and second constraint requires that sin(sqrt(2E) l ) = 0

Which is achieved by (sqrt(2E) l ) = n p

Or

In normalized form

Atomic problem, even for only one electron, is much more complex.

- Three dimensions, polar spherical coordinates: r, q, f
- Non-zero potential
- Attraction 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

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

ms

Spin

± 1/2

Describes the orientation of the spin of the electron in space

Quantum numbers

Orbitals are named according to the l value:

Principal quantum number

n = 1, 2, 3, 4 ….

determines the energy of the electron in a one electron atom

indicates approximately the orbital’s effective volume

n = 12 3

s

Angular momentum quantum number

l = 0, 1, 2, 3, 4, …, (n-1)

s, p, d, f, g, …..

determines the shape of the orbital

- Magnetic quantum number
- Determines the spatial orientation of the orbital

ml = -l,…, 0 , …, +l

l = 2

ml = -2, -1, 0, +1, +2

l = 0

ml = 0

l = 1; ml = -1, 0, +1

See: http://www.orbital.com

Electrons in polyelectronic atoms

(the Aufbau principle)

- Electrons are placed in orbitals to give the minimum possible energy to the atom
- Orbitals are filled from lowest energy up

- Each electron has a different set of quantum numbers (Pauli’s exclusion principle)
- Since ms = 1/2, no more than 2 electrons may be accommodated in one orbital

- Electrons are placed in orbitals to give the maximum possible total spin (Hund’s Rule)
- Electrons within a subshell prefer to be unpaired in different orbitals, if possible

Placing electrons in orbitals

5p

E

Approximate order

of filling orbitals

with electrons

4d

5s

3d

4s

4p

3p

3s

2p

2s

1s

5p

E

4d

5s

3d

4s

4p

3p

3s

2p

2s

1s