CHEM 1311A

Course web pagehttp://web.chemistry.gatech.edu/~barefield/1311/chem1311a.html

E. Kent Barefield

Two requests: cell phones to silent/off

no lap tops in operation during class

Bring your transmitter to class on Friday

Outline for first exam period

• Atomic structure and periodic properties• Structures and bonding models for covalent compounds of p-block

elements– Lewis Structures, Valence Shell Electron Repulsion (VSEPR)

concepts and oxidation state– Hybridization– Composition and bond energies in binary p-block compounds– Structure and bonding in organic compounds

First Exam – Wednesday, January 28

Atomic structure and periodic properties

• Early experiments concerning atomic structure and properties of electromagnetic radiation

• Bohr model of the hydrogen atom• Demise of Bohr model• Wave equation and wave model for atom• Wave functions and properties• Orbital representations• Multielectron atoms• Periodic properties and their origin

Properties of Atoms

• Consist of small positively charged nucleus surrounded by negatively charged electrons, some at large distances from the nucleus

• Nucleus consists of positively charged protons and neutral neutrons

• Charges of proton and electron are equal• The atomic number (and nuclear charge) of an atom is

equal to the number of protons in its nucleus.• The mass number of an atom is equal to the number of

protons plus the number of neutrons• Isotopes are atoms with the same atomic number but

different mass numbers, i.e., 1H, 2H, 3H or 12C, 13C, 14C

Atomic SpectraIrradiation from electronically excited atoms is not continuous

Visible region line spectra could be fitted to simple (empirical) formula

1/λ = 1.097 x 107 m-1 (1/22-1/n2)

E = hc/λ = 2.178 x 10-18 J (1/22-1/n2)

Later work showed several series of lines

E = 2.178 x 10-18 J (1/n22-1/n1

2 ) (n2<n1)

> 105> 3 x 1019< 10-9< 0.1γ-Rays103 - 1053 x 1017 - 3 x 101910-7 - 10-910 - 0.1X-Rays3 - 1037.5 x 1014 - 3 x 10174 x 10-5 - 10-74000 - 10Ultraviolet2 - 34.3 x 1014 - 7.5 x 10147 x 10-5 - 4 x 10-57000 - 4000Visible

0.01 - 23 x 1012 - 4.3 x 10140.01 - 7 x 10-5106 - 7000Infrared10-5 - 0.013 x 109 - 3 x 101210 - 0.01109 - 106Microwave

< 10-5< 3 x 109> 10> 109Radio

Energy(eV)

Frequency(Hz)

Wavelength(centimeters)

Wavelength(Angstroms)Region

Spectrum of Electromagnetic Radiation

Wavelength, nm

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Red

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400 500 600 700 800

Color of transmitted light

Complementary color

400 nm4000 Å4x10-5 cm

700 nm7000 Å7x10-5 cm

Visible region of electromagnetic spectrum

Properties of Electromagnetic Radiation

E = hν = hc/λ

With Einstein's relationship E = mc2

hc/λ = mc2

λ= h/mc

c = λν

c = 2.998 x 108 m s-1 (vacuum); λ in meters; ν in cycles per sec or s-I

1 cycle per sec is 1 Hz (Hertz)

Bohr Model

Rule 1. Electron can exist in stationary states; requires fixed energy.

Rule 2. Possible stationary states determined by quantization of angular momentum (mevr) in units of h/2π (mevr = nh/2π)

Rule 3. Transitions between stationary states occur with emission or absorption of a quantum of energy, ΔE = hν

For a stationary state to occur for the electron moving in a planetary orbital about the nucleus, the centripetal force must equal the electrostatic attraction of the electron by the nucleus

Employing the expression for angular momentum from Rule 2:

Note that radius of orbits increase with n2 and decrease with Z

or

ΔE = final energy – initial energy

ΔE = -13.6 Z2 eV (1/nf2 - 1/ni

2)

Total Energy for atom (E) = Kinetic Energy (KE)+ Potential Energy (PE)

Constantsme = 9.10939 x 10-11 kge = 1.60218 x 10-19 Cc = 8.8538 x 10-12 C2 m-1 J-1

h = 6.62608 x 10-34 J s1 eV = 1.6022 x 10-19 J

E = -(2.18 x 10-18 J) Z2/n2

E = -(13.6 eV) Z2/n2

from the previous slide so

Substituting for r :

Further evidence for unique properties of light

Photoelectric Effect

K.E.(ejected electrons) = hν(impinging light) - w(work function)

Compton Effect

Momentum and energy conserved in collisions of light (photons) with electrons

Demise of Bohr Model - Introduction of Wave Model

Heisenberg Indeterminacy (Uncertainty) Principle

Δx•Δ(mv) ≥ h/2π

Exact position and exact momentum cannot both be known simultaneously

De Broglie's Hypothesis

λ = h/mv

Particles have wave lengths; proof came from diffraction of electron beam

Schroedinger's Wave Equation

∂2Ψ/∂x2 + ∂2Ψ/∂y2 + ∂2Ψ/∂z2 + 8π2m/h2(E-V)Ψ = 0 (HΨ=EΨ)

Solution of this equation requires conversion to spherical polar coordinates and the introduction of three constants, which are what we know as quantum numbers, n, ℓ, mℓ

Interpretation of Schrödinger equation solutions

• Each combination of n, ℓ, and mℓ, value corresponds to an orbital• n values relate to the energy and size of the orbitals. n = 1, 2, 3···• ℓ values specify the total angular momentum of the electron and

determines the angular shape of the orbital. ℓ’s have letter equivalents: ℓ = 0 (s), 1 (p), 2 (d), 3 (f), 4 (g), etc. ℓ = 0 ··· n-1

• mℓ, specifies the orientation of the orbitals in space and the angular momentum with respect to direction. mℓ = -ℓ··· 0 ··· +ℓ

• With introduction of the fourth quantum number, ms = +1/2, -1/2 and the Pauli principle, which states that no two eIectrons in a given atom can have the same four quantum numbers, the development of electron configurations for multielectron atoms is straight-forward.

• E = -me4Z2/8εo2n2h2 = -13.6 eV Z2/n2 Same as for Bohr model!!!

Wave Functions Ψn,ℓ,mℓ(r,θ,φ) = Rn,ℓ(r)·Θℓ,mℓ

·Φmℓ

R1,0(r) = 2Z3/2ao-3/2e-Zr/ao

R2,0(r)= (1/2√2)Z3/2ao-3/2(2-Zr/ao)e-Zr/2ao

R2,1(r) = (1/2√6)Z3/2ao-3/2(Zr/ao)e-Zr/2ao

R3,0(r) = (1/4√3)Z3/2ao-3/2(27-18Zr/ao+2Z2r2/9ao

2)e-Zr/3ao

Θℓ,mℓ(θ) = sinmℓ2·Pℓ(cos θ)

Φmℓ(φ) = (1/√2π)e±imℓφ

1/√2π(√5/8)(3cos2θ-1)02

1/√2πe±iφ(√3/2)sin θ±11

1/√2π(√3/2)cos θ01

1/√2π1/√200φΘmℓℓ

12/

2/1

334

3

n,2

])![()!1(4)(R +

+−

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⎛

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⎤

⎢⎢⎣

⎡

+−−

= lll

l

ln

naZr

oo

LenaZr

nannZr o

1s Radial functions

0

5

10

15

20

25

30

0 1 2 3 4 5

r, ao

0

1

2

3

4

5

6

R1,0(r) = 2ao-3/2e-r/ao

R1,02(r) = 4ao

-3e-2r/ao

r2R1,02(r) = 4ao

-3r2e-2r/ao

Representation of the 1s orbital

-0.50

0.51

1.52

2.53

3.5

0 5 10 15

r, ao

-0.100.10.20.30.40.50.60.7

2s Radial functions

R2,0(r)= (1/2√2)ao-3/2(2-r/ao)e-r/2ao

R2,02(r)= (1/8)ao

-3(4-2r/ao+r2/ao2)e-r/ao

r2R2,02(r)= (1/8)ao

-3(4-2r/ao+r2/ao2)r2e-r/ao

Representations of p orbitals

Θℓ,mℓ(θ) = sinmℓ2·Pℓ(cos θ)

Φmℓ(φ) = (1/√2π)e±imℓφ

1/√2π(√5/8)(3cos2θ-1)02

1/√2πe±iφ(√3/2)sin θ±11

1/√2π(√3/2)cos θ01

1/√2π1/√200φΘmℓℓ

Representations of p orbitals

Representations of orbitals

Conical node in dz2 is a sum of two planes:dz2 = dz2–x2 + dz2–y2

Representations of orbitals

(+)

(-)

(+)

(+)

(-)

(+)

(-)

(-)

(-)(+)

(+)

(+)

(+)

(+)

(-)

(-)

(-)(-)

(+)

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14 16 18

r, ao

Comparison of ns radial distribution functions

1s

2s

3s

Comparison of 1s, 2s and 2p radial distribution functions

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12

r, ao

1s

2p 2s

• Radial nodes

• Angular nodes

• Relative size

Angular functions as contour maps

Contour plots of H 2p and C 2p

Contour lines are set at 0.316 of maximum values of Ψ2(r,θ,φ)

-3

-2

-1

0

1

2

3

-1.5 -1 -0.5 0 0.5 1 1.5

Multi-electron atoms; Aufbau Principlen=1

s

[He]

[He]

[He]

[He]

[He]

[He]

n=2

s p

[He]

[He]

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12

r, ao

H

He

Li

Be

B

C

N

O

F

Ne

• Electron configurations in the third period (n=3) mirror those for the second period

• In the fourth period (n=4) the 3d orbital energies are lower than the 4p so that these orbitals fill before the 4p. The elements with d electrons are referred to as transition elements.

• Electron configurations of the first transition element series are 4s23dn except for Cr and Cu, which are 4s13d5 and 4s13d10, respectively. These irregularities are a result of lower electron-electron repulsion energies.

• All transition metal cations with + 2 or greater charge have dn

electron configurations.

More on multi-electron atoms

Mn: [Ar]4s23d5 Mn2+: [Ar]4s03d5

Ti: [Ar]4s23d2 Ti3+: [Ar]4s03d1

Ni: [Ar]4s23d8 Ni2+: [Ar]4s03d8

The Periodic Table and the Aufbau Principle

n =1

2

3

4

5

6

7

(n)s

(n)p

(n–1)d(n–2)f

Periodic properties

• Ionization energy• Atomic and ionic radii• Electron Affinity• Electronegativity

Ionization energy

Ionization energy is the minimum energy required to remove an electron from a gaseous atom (or other species). E = E+ + e-

0

500

1000

1500

2000

2500

0 20 40 60 80

Z

IE/k

J m

ol-1

0

500

1000

1500

2000

2500

0 4 8 12 16Z

IE/e

V

Effective nuclear charge

-60

-50

-40

-30

-20

-10

0

Li Be B C N O F

E/eV

sp

s & p orbital energies vs Z

Zeff = Z – shielding constant

2s2p

1sNe

5.765.76

F5.135.10

O4.494.45

N3.853.83

C3.223.14

B2.582.42

Be1.91

Li1.28

He1.69

H1.0

Effective nuclear charges

Atomic radii as function of Z

Atomic and ionic radii

Tl3+

0.88Ba2+

1.36Cs+

1.70

I-

2.20In3+

0.79Sr2+

1.16Rb+

1.49

Br-

1.96Se2-

1.98As3-

2.22Ga3+

0.62Ca2+

1.00K+

1.38

Cl-

1.81S2-

1.84P3-

2.12Al3+

0.53Mg2+

0.72Na+

1.02

F-1.33

O2-

1.40N3-

1.71Be2+

0.27Li+

0.59

Radii of some common ions, Å

Fe2+ 0.75, Fe3+ 0.69

Radial distribution functions foralkali metal ions

Electron affinity

Electron affinity is the energy change associated with addition of an electron to a atom or ion. E + e- = E-

-200

-100

0

100

200

300

400

H Li Be B C N O F Na Mg Al Si P S Cl K Ca

EA/k

J m

ol-1

Note that EA’s have been historically recorded as the negative of the energy associated with the electron attachment reaction.

Electronegativity

Electronegativity is the ability of an atom to attract electron density to itself in a chemical bond

Ba0.89

Cs0.79

I2.66

Te2.10

Sb2.05

Sn1.96

In1.78

Sr0.95

Rb0.82

Br2.96

Se2.55

As2.18

Ge2.01

Ga1.81

Ca1.00

K0.82

Cl3.16

S2.58

P2.19

Si1.90

Al1.61

Mg1.31

Na0.93

F3.98

O3.44

N3.04

C2.55

B2.04

Be1.57

Li0.98

H2.20

Pauling electronegativities