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Lecture 1
Brooklyn College
Inorganic Chemistry
(Spring 2009)
• Prof. James M. Howell
• Room 359NE
(718) 951 5458; [email protected]
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)
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)
Inorganic
chemistry
Organometallic
chemistry
Organic
chemistry
Coordination
chemistry
Biochemistry
Bioinorganic
chemistry
Environmental
science
Solid-state
chemistry
Materials
science &
nanotechnology
Organic
compounds
Inorganic
compounds
Single bonds


Double bonds


Triple bonds


Quadruple bonds


Coordination
number
Geometry
Constant
Variable
Fixed
Variable
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, MnO4Water 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
.
.
Atomic spectra of the 1 electron hydrogen atom
Quantum
number n
Energy
-1/25R H
-1/16R H
-1/9R H

0
Paschen
series (IR)
6
5
4
3
Energy levels in the hydrogen atom
E = RH 12
n
Balmer series (vis)
-1/4R H
2
Energy of transitions in the hydrogen atom
E = RH 12 1 2
nl nh
Lyman series (UV)
-RH
1
Bohr’s theory
of circular orbits
fine for H but fails
for larger atoms
…elliptical orbits
eventually also failed!
Fundamental Equations of quantum mechanics
Planck
quantization of energy
E = hn
h = Planck’s constant
n = frequency
de Broglie
wave-particle duality
l = h/mv
l = wavelength
h = Planck’s constant
m = mass of particle
v = velocity of particle
Heisenberg
uncertainty principle
Dx Dpx  h/4p
Schrödinger
wave functions

H   E
Dx uncertainty in position
Dpx uncertainty in momentum
H: Hamiltonian operator
: wave function
E : Energy
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.
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.

 *dv  1
It is these requirements that introduce quantization.
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
- 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.
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: e i z = 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 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/dx2 X(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, 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 )
Or
(np )
= np which is where sine produces 0
2
E
2l
Quantized!!
In normalized form
X ( x )  2 / l sin( npx / l )
Where n = 1,2,3…
n=1
1.2
n=2
1.5
1
1
0.8
0.5
0.6
0
1
-0.5
0.4
-1
0.2
-1.5
0
1
8
15 22 29 36 43 50 57 64 71 78 85 92 99
8
15 22
29 36 43 50 57 64
71 78 85 92 99
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
Quantum numbers for atoms
Symbol
Name
Values
Role
n
Principal
1, 2, 3, ...
Determines most of the energy
l
Angular
momentum
0, 1, 2, ..., n-1
Describes the angular dependence (shape) and
contributes to the energy for multi-electron
atoms
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:
l
0
1
2
3
4
5
orbital
s
p
d
f
g
...
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
2p 2 me e 4
e2
k
En  

 2
2 2
2rn
nh
n
n=1
2
3
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