Lecture 1

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)

What is inorganic chemistry?

Organic chemistry is:the chemistry of lifethe chemistry of hydrocarbon compoundsC, H, N, O

Inorganic chemistry is:The chemistry of everything elseThe chemistry of the whole periodic Table(including carbon)

Organicchemistry

BiochemistryEnvironmental

science

Materialsscience &

nanotechnology

Inorganicchemistry

Organometallicchemistry

Coordinationchemistry

Solid-statechemistry

Bioinorganicchemistry

Organic compounds

Inorganic compounds

Single bonds

Double bonds

Triple bonds

Quadruple bonds

Coordination number

Constant Variable

Geometry Fixed Variable

Single and multiple bonds in organic and inorganic compounds

Unusual coordinationnumbers 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 colloidsSemiconductors: Si, Ge, GaAs, InPPolymers: 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 nanotubesFertilizers: 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 drugsBiology: Vitamin B12 coenzyme, hemoglobin, Fe-S proteins, chlorophyll (Mg)

Atomic structureA revision of basic concepts

..

Atomic spectra of the 1 electron hydrogen atom

-RH 1

-1/4RH

-1/9RH

-1/16RH

-1/25RH

0

2

3

45

6

Energy Quantum number n

Lyman series (UV)

Balmer series (vis)

Paschenseries (IR)

Energy levels in the hydrogen atom

1n2E = RH

1nl

2E = RH 1

nh2

Energy of transitions in the hydrogen atom

Bohr’s theory of circular orbitsfine for H but failsfor larger atoms…elliptical orbitseventually also failed!

de Brogliewave-particle duality = h/mv

= wavelengthh = Planck’s constantm = mass of particlev = velocity of particle

Heisenberguncertainty principle x px h/4 x uncertainty in position

px uncertainty in momentum

Fundamental Equations of quantum mechanics

EH

Schrödingerwave functions

H: Hamiltonian operator: wave functionE : Energy

Planckquantization of energy E = h

h = Planck’s constant = frequency

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”.

• 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.

1* dv

It is these requirements that introduce quantization.

How is quantization introduced?

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<lV(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

ork = +/- i sqrt(2E)

There are two solutions depending on the choice of sign.General solution becomesX (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 yieldsX(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 ) = n which is where sine produces 0

Or

lE

n2

)(2

Quantized!!

In normalized form

)/sin(/2)( lxnlxX

n=1

0

0.2

0.4

0.6

0.8

1

1.2

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99

n=2

-1.5

-1

-0.5

0

0.5

1

1.5

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99

Where n = 1,2,3…

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

• Three dimensions, polar spherical coordinates: r, • 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

Atoms

Quantum numbers for atoms

Orbitals are named according to the l value:

l 0 1 2 3 4 5

orbital s p d f g ...

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) andcontributes 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

Principal quantum numbern = 1, 2, 3, 4 ….

determines the energy of the electron (in a one electron atom) and indicates (approximately) the orbital’s effective volume

222

422 2

2 n

k

hn

em

r

eE e

nn

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