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Lecture 2:

More atomsMultielectron atoms, Hunds rulesTrends: Radii (atomic, ionic, Van der Waals),

Ionization Enthalpy (ionization potential)

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+3

Last Lecture: Shielding

Q) Does the 2s valence electron in Li experience the fullattraction of the +3 nucleus, or do the 2 1s electrons fullyshield it (if so it would feel like it was circling a +1nucleus)?

A) Somewhere in between

-

-

-

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Slaters rules for the prediction of

for an electron:

1. Group electron configuration as follows:

(1s)(2s,2p)(3s,3p)(3d)(4s,4p)(4d)(4f)(5s,5p) etc.

2. Electrons to the right (in higher subshells and shells) of an electron donot shield it.

3. If the electron of interest is an ns or np electron:a) each other electron in the same group contributes 0.35 (0.30 for 1s)b) each electron in an n-1 group contributes 0.85

c) each electron in an n-2 or lower group contributes 1.00

4. If the electron of interest is an nd or nf electron:a) each other electron in the same group contributes 0.35

b) each electron in a lower group (to the left) contributes 1.00

Effective Nuclear Z* Charge: Slaters RulesReminder

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Slaters Approximations?

Note that these Rules are brutal by modern standards(but still science!)

A good first approximation for ionization enthalpies ( X

X+)

EZ

nR

n

=

*2

2

Z* =Z -

Z* is the effective nuclear chargeZ is the atomic number is the shielding or screening constant

Of course, all these ionization enthalpy values are allexperimentally known

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Ionization Enthalpy, Hie (ionization potential, IP)

The enthalpy change for ionization by loss of electron(s)E(g) E+(g) + e- Hie First ionization potential

E+(g) E2+(g) + e- Hie Second ionization potential > first

E2+(g) E3+(g) + e- Hie Third ionization potential > second

First Ionization Potentials

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Trends for Atomic Properties in the Periodic Table

Understanding how and why properties change fromelement to element requires us to consider:

1. The electronconfiguration of the atomor ion (the filling order)

2. The type of valenceorbitals involved (size,shape, shielding andpenetration)

3. The effective nuclearcharge felt by electronsin valence orbitals

4. Oddities

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Trends: Orbital Energies for Atoms

Energies change as shells are filled Consequence of penetrating ability of outer orbitals into core

(remember Slater, effective nuclear charge)

For atoms other than hydrogen:Orbital energy depends on n

and l

Ordering of orbital energies:ns

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Building Up the Atoms in the Periodic Table

1) TheAufbau (building up) principle: lowest energyorbitals are filled first 1s, then 2s, then 2p, then 3s, then3p, etc.

2) Remember the Pauli exclusion principle.

3) Hunds rule of maximum multiplicity.

Energ

y

1

2

3

0 1 2

n

l

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Hunds Rule of Maximum Multiplicity

Multiplicity is a measure of the number of unpaired electrons.Multiplicity = number of unpaired electrons + 1It is used because it describes the degeneracy of the state

Hunds rule: Electrons must be placed in the orbitals of asubshell so as to give the maximum total spin.

i.e. put as many unpaired electrons as possible in a subshell toget the most stable arrangement.

# of unpairedelectrons

Total spin(S)

Multiplicity(2S+1)

CommonName

0 0 1 singlet

1 1/2 2 doublet

2 1 3 triplet

3 3/2 4 quartet

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Hunds Rule of Maximum Multiplicity 1: Basis

1. Minimization of electron-electron repulsion- There is less repulsion between electrons in different

orbitals (different regions in space)

Electrons in different orbitals feel a greater Z*, thus they are more stablePart 2, why both same spin?

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Hunds Rule of Maximum Multiplicity 2: Basis

2. Maximization of exchange energy stabilization- This is a quantum mechanical effect that causes systems

with electrons of the same energy and spin to be morestable.-Pauli Exclusion Principle - a wavefunction must beantisymmetric with respect to electron exchange.

- The more exchanges (permutations where electronidentities are changed) possible, the more stable the

electron configuration of the subshell

For an s-orbital (subshell), the spins must are different, sono exchanges are possible.

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Two electrons of the same spin, one exchange is possible:

For a p subshell, there are different orbitals of the same energy

and exchanges are possible.Two electrons of opposite spin, no exchange is possible;configurations after electron exchange must look identical

One exchange

Initial arrangement

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Three electrons of same spin, three exchanges arepossible:

Initial arrangement 123

One exchange 213

Second exchange 132

Third exchange 321

The exchange energy explains whyhalf-filled subshells are unusuallystable.e.g. the electron configuration of Cr:

[Ar]4s13d5 instead of [Ar]4s23d4

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Building up the atoms in the periodic table:Period One

Z Atom Electronconfiguration

para- ordiamagnetic

Hie(first / eV)

1 H 1s1 p 13.6

2 He 1s2 d 24.6

Ene

rgy

1

2

3

0 1 2

n

l

Large!

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Building up the atoms in the periodic table:Period Two

Z Atom Electronconfiguration

para- ordiamagnetic

Hie(first / eV)

3 Li [He]2s1 p 5.44 Be [He]2s2 d 9.3

Ene

rgy

1

2

3

0 1 2

n

l

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Building up the atoms in the periodic table:Period Two

Z Atom Electronconfiguration

para- ordiamagnetic

Hie(first / eV)

5 B [He]2s22p1 p 8.36 C [He]2s22p2 p 11.3

7 N [He]2s22p3 p 14.5

8 O [He]2s22p4 p 13.69 F [He]2s22p5 p 17.4

10 Ne [He]2s22p6 d 21.6

n

E

nergy

1

23

0 1 2 l

Dropped

fromBe (9.3 eV)

???

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c = Coulombic repulsion(destabilizing)

e = exchange energy(stabilizing)

3e

1c + 3e

The Hie Anomaly at Nitrogen and Oxygen

1e

1e

2

e

3e1c

1e

Loss of exchange energy increases value for NLoss of Coulombic repulsion decreases value for O

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Building up the atoms in the periodic table:Period Three

Z Atom Electronconfiguration

para- ordiamagnetic

Hie(first / eV)

11 Na [Ne]3s1 p 5.1

12 Mg [Ne]3s2 d 7.6

Ene

rgy

1

2

3

0 1 2

n

l

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Building up the atoms in the periodic table:Period Three

Z Atom Electronconfiguration para- ordiamagneticHie(first / eV)

13 Al [Ne]3s23p1 p 6.0

14 Si [Ne]3s2

3p2

p 8.215 P [Ne]3s23p3 p 10.5

16 S [Ne]3s23p4 p 10.4

17 Cl [Ne]3s2

3p5

p 13.018 Ar [Ne]3s23p6 d 15.8

n

E

nergy

1

23

0 1 2 l

Only slightlyhigher than H(13.6 eV)

*** repeat***

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Building up the atoms in the periodic table:Period Four

Z Atom Electronconfiguration

para- ordiamagnetic

Hie(first / eV)

19 K [Ar]4s1 p 4.320 Ca [Ar]4s2 d 6.1

Ene

rgy

1

23

0 1 2

n

l

4

Li 5.4 eVNa 5.1 eV

Whoa, what about 3d?!!!

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The 4s orbitals are lowerin energy than the 3d

orbitals for K and Ca.

This is only for the free

atoms! In molecules 3d

are lower in energy than4s!

An accident of nature but it

is consistent throughoutthe table.

An Anomaly of the Periodic Table

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Building up the atoms in the periodic table:Period Four

Z Atom Electronconfiguration

para- ordiamagnetic

Hie(first / eV)

21 Sc [Ar]4s23d1 p 6.522 Ti [Ar]4s23d2 p 6.8

23 V [Ar]4s23d3 p 6.7

24 Cr [Ar]4s13d5 p 6.825 Mn [Ar]4s23d5 p 7.4

26 Fe [Ar]4s23d6 p 7.9

27 Co [Ar]4s2

3d7

p 7.928 Ni [Ar]4s23d8 p 7.6

29 Cu [Ar]4s13d10 p 7.7

30 Zn [Ar]4s2

3d10

d 9.4

exchange E

exchange E

pairing

PrettyconstantWhy?

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Building up the atoms in the periodic table:Period Four

Z Atom Electronconfiguration

para- ordiamagnetic

Hie(first / eV)

31 Ga [Ar]4s23d104p1 p 6.0

32 Ge [Ar]4s23d104p2 p 7.933 As [Ar]4s23d104p3 p 9.8

34 Se [Ar]4s23d104p4 p 9.7

35 Br [Ar]4s23d104p5 p 11.836 Kr [Ar]4s23d104p6 d 14.0

n

E

nergy

1

23

0 1 2 l4

Plummetsfrom 9.4 eV!

***again***

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Building up the atoms in the periodic table:

Period Five:- analogous to period four

Period Six:

- analogous to period five with the introduction of the (4f) lanthanides afterthe 6s elements

Period Seven:

- in theory, analogous to period six with the introduction of the Actinides(5f) after the 7s elements but little is known about the short-lived nucleiafter Z=104 (Rutherfordium).

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Ionization Potential Summary

First Ionization Potentials

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Further Ionization Enthalpies, Hie

Some examples:

Na(g) Na+(g) + e- Hie = 502 kJ /mol

Al(g) Al+(g) + e- Hie = 578 kJ /mol

Al+(g) Al2+(g) + e- Hie = 1817 kJ /mol

Al2+(g) Al3+(g) + e- Hie = 2745 kJ /mol

Thus:Al(g) Al3+(g) + 3e- Hie = 5140 kJ /mol

l ffi i ( ) d l

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Electron Affinity (EA) and ElectronAttachment Enthalpy (Hea)

The enthalpy change for the gain of an electron, E(g) + e-

E-

(g)

EA ~Hea (note ve sign)

Cl(g) + e- Cl-(g) Hea = 349 kJ /mol

O(g) + e- O

-(g) Hea = 142 kJ /molfirst attachment is usually exothermic

O-(g) + e- O2-(g) Hea = 844 kJ /mol

second attachment is usually endothermic

O(g) + 2e- O2-(g) Hea = 702 kJ /mol

Other factors favour the presence of O2- when it is found in molecules andionic solids.

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Na: [Ne]3s1 additionalelectron makes [Ne]3s2

which is a full subshell. Si: [Ne]3s23p2 additional electron makes[Ne]3s23s3 which is a more

stable half-filled subshell soEA is high.

P: [Ne]3s23p3

additional electron makes[Ne]3s23p4 which requireselectron pairing so EA islow.

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In general:

- radii decrease across a period because of increasing Z*.

-radii increase down a group because of the increasing distance of theelectrons from the nucleus.

- increasing distance from the nucleus outweighs effective nuclear charge foratomic radii down a group.

The Size of Atoms and Ions

Radii of neutral atoms

The atomic radius of an atom is not really an exact scienceGoal: predict bond lengths within a reasonable error

Element Bond Length (pm) Atomic Radius

F2 142 F = 71

Cl2 199 Cl = 100

Br2

228 Br = 114

I2 267 I = 133

C (diamond) 154 C = 77

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0.1 nm = 1 = 100 pm

Remember that the maximum probability for an orbital movesfurther away from the nucleus with increasing n.

The d-blockcontraction causesGa to be about thesame size as Al. This

is caused by theintroduction of the 3delements whichcause a vastly largerZ* for Ga.

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This is a self-consistent scalebased on O-2 = 1.40 (or 1.38).

Positively charged ions aresmaller than their neutralanalogues . Increased Z*.Lower n.

Negatively charged ions arelarger than their neutralanalogues because ofdecreased Z*.

Radii of ions

Same periodic trends as atomicradii for a given charge

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Example: Utility of Covalent and Ionic RadiiThe radii tabulated in various books allow us to predict the bond length

(distance between nuclei) we would expect to see for a new bond. Forcovalent radii, the predictions will be the best for atoms that have similarelectronegativities. If the electronegativities are very different, thepredicted distance will be too long.

Li OAtomic 1.52 0.73 d = 2.25 AngstromsIonic 0.68 1.40 d = 2.08 AngstromsWhy the difference?

Example:What is the expected bond length for a single Sb-N bond ?

For N, rcov = 0.70 and for Sb, rcov = 1.41

Using these values, an Sb-N bond should be 2.11 .

The experimental distance is 2.05 .

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Van der Waals radii are established from contact distances between

non-bonding molecules in crystals rVDW decreases

rVDWincreases

Van der Waals radii

VDW radii allow us todetermine whether therecan be a bondinginteraction between twoatoms:

If the distance betweenthe nuclei is larger thanthe sum of the VDW radii,

then the atoms areprobability not bonded.

H 1.2

N 1.5 O 1.4 F 1.35

P 1.9 S 1.85 Cl 1.80

Sb 2.2 Te 2.2 I 2.15 Angstroms

http://images.google.com/imgres?imgurl=ntri.tamuk.edu/cell/chapter3/waals1.gif&imgrefurl=http://ntri.tamuk.edu/cell/chapter3/bonds.html&h=362&w=558&prev=/images%3Fq%3D%252Bvan%2Bder%2Bwaals%2B%252Bradius%26svnum%3D10%26hl%3Den%26sa%3DG

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Summary

Hunds rules

Trends:Ionization Enthalpy (ionization potential)

Electron attachment enthalpy (-electronaffinity)

Radii (atomic, ionic, Van der Waals)

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Next Class

Lecture 3

Redox Frost Diagrams

Electronegativity Polarizability, hard and soft