Chapter 7 Atomic Energies and Periodicity

Chapter 7Atomic Energies and Periodicity Department of Chemistry and Biochemistry Seton Hall University

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

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 - 

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

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)

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

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)

Electron configurations • The Pauli Exclusion Principle • No two electrons can have the same four quantum numbers • Hund’s 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

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 • Hund’s 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!!!)

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

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

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

Example • Consider S • Sulfur has 16 electrons • Electronic configuration is therefore1s22s22p63s23p4 • d and f subshells are used for heavier elements • You are expected to do this for any element up to Ar

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

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

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

Electron configuration shorthand • We can then write the electron configuration of S as [Ne]3s23p4 • 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 configuration[core]ns2np4

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

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

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

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

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

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)

The Born-Haber Cycle

Calculating the lattice energy • Coulomb’s 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

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 Coulomb’s law to include the three dimensional ion interactions yields a value for the lattice energy of -781 kJ/mol

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

The overall ionic bonding energy • The energy for the overall process:Na(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

Why not Na2+Cl2-? • 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

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

Chapter 7 Atomic Energies and Periodicity