Chapter 7 Atomic Energies and Periodicity

1
Chapter 7Atomic Energies and Periodicity

• Department of Chemistry and Biochemistry
• Seton Hall University

2
Nuclear Charge

• n - influences orbital energy
• Z - nuclear charge also has a large effect
• We can measure this by ionization energies (IE)
• A ? A e-
• Consider H and He
• H ? H e- 2.18 ? 10-18 J
• He ? He e- 8.72 ? 10-18 J
• Orbital stability increases with Z2

3
Electron-electron Repulsion

• Negatively charged electron is attracted to the
  positively charged nucleus but repelled by
  negatively charged electrons
• Screening, ?, is a measure of the extent to which
  some of the attraction of an electron to the
  nucleus is cancelled out by the other electrons
• Effective nuclear charge
• Zeff Z - ?

4
Screening

• Complete screening would mean that each electron
  would experience a charge of 1
• Consider He
• w/o screening the IE would be the same as for He
• Complete screening the IE would be the same as
  for H
• Actual IE is between the two values

5
Screening

• Screening is incomplete because both electrons
  occupy an extended region of space, so neither is
  completely effective at screening the other from
  the He2 nucleus
• Compact orbitals (low values of n) are more
  effective as screening since they are packed
  tightly around the nucleus
• Therefore, ? decreases with orbital size (as n
  increases)

6
Screening

• Electrons in orbitals of a given value n screen
  the electrons in orbitals with larger values of n
• Screening also depends on orbital shape (electron
  density plots, ?2 vs r, help show this)
• Generally, the larger the value of l, the more
  that orbital is screened by smaller, more compact
  orbitals
• Quantitative information about this can be
  obtained from photoelectron spectroscopy

7
Structure of the periodic table

• The periodic table is arranged the way it is
  because the properties of the elements follow
  periodic trends
• Elements in the same column have similar
  properties
• Elemental properties change across a row (period)

8
Electron configurations

• The Pauli Exclusion Principle
• No two electrons can have the same four quantum
  numbers
• Hunds rule
• The most stable configuration is the one with the
  most unpaired electrons
• The aufbau principle
• each successive electron is placed in the most
  stable orbital whose quantum numbers are not
  already assigned to another electron

9
Orbital diagrams and rules

• The Pauli Exclusion Principle - no two electrons
  may have the same four quantum numbers.
• Practically, if two electrons are in the same
  orbital, they have opposite spins
• Hunds Rule - when filling a subshell, electrons
  will avoid entering an orbital that already has
  an electronic in it until there is no other
  alternative
• Consider the dorm room analogy (I suggested this
  to the author!!!)

10
Summary of the rules

• Each electron in an atom occupies the most stable
  orbital available
• No two electrons can have the same four quantum
  numbers
• The higher the value of n, the less stable the
  orbital
• For equal values of n, the higher value of l, the
  less stable the orbital

11
Shell designation

• The shell is indicated by the principle quantum
  number n
• The subshell is indicated by the letter
  appropriate to the value of l
• The number of electrons in the subshell is
  indicated by a right superscript
• For example, 4p3

12
Electronic configurations

• We use only as many subshells and shells as are
  needed for the number of electrons
• The number of available subshells depends on the
  shell that is being filled
• n 1 only has an s subshell
• n 2 has s and p subshells
• n 3 has s, p and d subshells

13
Example

• Consider S
• Sulfur has 16 electrons
• Electronic configuration is therefore1s22s22p63s2
  3p4
• d and f subshells are used for heavier elements
• You are expected to do this for any element up to
  Ar

14
Core and valence shells

• Chemically, we find that the electrons in the
  shell with the highest value of n are the ones
  involved in chemical reactions
• This shell is termed the valence shell
• Electrons in shells with lower n values are
  chemically unreactive because they are of such
  low energy.
• These shells are grouped together as the core

15
Electron configurations and the periodic table

• We develop a shorthand for the electron
  configuration by noting that the core is really
  the same as the electron configuration for the
  noble gas that occurs earlier in the periodic
  table
• E.g. for S (1s22s22p63s23p4), the core is
  1s22s22p6 which is the same as the electron
  configuration for Ne

16
Atomic properties

• Ionization energy (IE)A(g) ? A(g) e-
• Electron affinity (EA)A(g) e- ? A-(g)
• Ion sizes
• Cations are smaller than the neutral atom
• Anions are larger that the neutral atom

17
Electron configuration shorthand

• We can then write the electron configuration of S
  as Ne3s23p4
• We note that the valence shell electron
  configuration has the same pattern for elements
  in the same group
• For S (a chalcogen) all the elements have the
  valence electron configurationcorens2np4

18
Periodic trends

• Atomic radii decrease across a period
• Atomic radii increase down a group
• Ionization energies increase across a period
• Ionization energies decrease down a group

19
Near degenerate orbitals

• degenerate orbitals are those that have the same
  energy
• normally, certain orbitals will be degenerate for
  quantum mechanical reasons
• near degenerate orbitals have close to the same
  energy for a variety of reasons

20
Ion electronic configurations

• Electronic configurations for ions involves
  adding or subtracting electrons from the
  appropriate atomic configuration
• Example Na ? Na
• 1s22s22p63s1 ? 1s22s22p6
• Example Cl ? Cl-
• 1s22s22p63s23p5 ? 1s22s22p63s23p6

21
Magnetic properties

• The spin of electrons generates a magnetic field
• Two types of magnetism
• Diamagnetism - all electrons are paired
• Paramagnetism - one or more electrons are
  unpaired
• In solids, two types of condensed phase magnetism
  results in bulk magnetic properties -
  ferromagnetism and antiferromagnetism

22
Energetics of ionic compounds

• Ions in solids have very strong attractions
  (ionic bonding)
• Due mostly to cation-anion attraction, and
  includes a component termed lattice energy
• We can calculate this energy from a Born Haber
  cycle

23
Path yielding a net reaction

• Vaporization ?Evaporization 108 kJ/mol
• Ionization ?E IE 495.5 kJ/mol
• Bond breakage ?E ½(bond energy) 120 kJ/mol
• Ionization ?E EA -348.5 kJ/mol
• Condensation - includes all ion-ion attractive
  and repulsive interactions (the lattice energy)

24
The Born-Haber Cycle
25
Calculating the lattice energy

• Coulombs law allows us to calculate the
  electrical force between charged particles
• q1,q2 are the electrical charges of the particles
• k 1.389 ? 105 kJ pm/mol
• r interionic distance in pm

26
Calculating the lattice energy

• Result of calculation yields a value of -444
  kJ/mol
• This includes only part of the lattice energy,
  since the coulombic interactions do not stop at
  the individual ions pairs.
• An expansion of Coulombs law to include the
  three dimensional ion interactions yields a value
  for the lattice energy of -781 kJ/mol

27
3 D interaction in crystal

• Note that NaCl extends in all directions
• Each ion experiences attractions and repulsions
  from other ions past the ones directly in contact

28
The overall ionic bonding energy

• The energy for the overall processNa(s) ½Cl2
  (g) ? NaCl(s)
• Calculated -406 kJ/mol
• Actual -411 kJ/mol
• This treatment assumes the interaction between
  Na and Cl- is only ionic. The slight
  discrepancy is ascribed to a small degree of
  electron sharing

29
Why not Na2Cl2-?

• Main reason is the very large ionization energy
  of the core of NaNa ? Na IE1 495.5
  kJ/molNa ? Na2 IE2 4562 kJ/mol
• EA2 for Cl is expected to be large and positive
• Basic point is that it costs way too much energy
  to ionize the core of Na

30
Ion stability

• Group 1 and 2 ions will lose all of their valence
  electrons
• Above Group 2, removal of all valence electrons
  is generally not observed
• Anions will generally add enough valence
  electrons to fill the valence shell