Lec 1-5 Matt Flashcards
What are quantum numbers?
- energies of electrons limited to discrete values called energy levels
- Use wave equation to find them
- electrons are wave functions/equations too
What is Heisenbergs uncertainty principle?
- never know the speed and position of electrons at the same time in their orbitals
- consequence of this is that there’s a 95% chance of electron being in a particular space/boundary
What are the 4 quantum numbers?
- Principle QN
- Orbital Angular Momentum QN
- Magnetic QN
- Spin QN
What is principle quantum number?
- describes row of the periodic table
- can be any positive integer from 1 to infinity
- as n increases, energy and size increases also
What is orbital angular momentum quantum number?
- describes the shape of the orbital
- can be positive integer between 0 and n-1
- for s p and d
What is magnetic quantum number?
- describes the direction/orientation of the orbital
- values for mi are all integer values for +-1
- for px , py, pz
- axis are obituary
Summary of orbitals
- shape and size of an orbital = region of space where there is high probability of finding an electron
- size defined by n
- shape defined by I
- orientation defined by mi
- orientation is defined relative to arbitrary axes (x,y,z)
What is spin QN?
- describes spin of electron
- has only two values (+1/2 or -1/2)
- an orbital can contain only two electrons
- represent spin as up or down
Spin QN - diamagnetic
- compounds with paired electrons (opposite spin)
Spin QN - paramagnetic
- compounds with unpaired electrons (parallel spins)
What are the relative energies of orbitals?
1) between shells the orbital energy increases as n increases
2) within shells the orbital energy increases in the order s<p></p>
Can an electron have the same quantum number as another electron? (in an atom)
NO
What is the Pauli Exclusion Principle?
- No two electrons in an atom have the same four QN
- an orbital can only contain 2 electrons
What is the Aufbau Principle?
- electrons fill orbitals from lowest energy orbital upwards
- orbital energy increases as n does
- orbital energy increases as I does
What is Hunds first rule?
- electrons fill orbitals of the same energy to give maximum number of unpaired electrons
- max number of parallel spins
What is wave particle duality?
- every elementary particle exhibits properties of not only particles but also waves
- this is the fundamental concept of quantum mechanics
- the observed properties will depend on the way that you measure the property
What are you interested in regarding electron density of the schrodinger wave equation?
- how far the electron is from the nucleus: i.e. max electron density which is linked to how easily it can react
- in which direction does the maximum electron density lie: informs us what direction bonds are formed
The two parts of the schrodinger wave equation: 1) the radial function
- describes the wave only in terms of distance from the nucleus
The two parts of the schrodinger wave equation: 2) the angular function
- describes how amplitude of the electron varies with direction
What does Ψ² relate to?
- relates wavefunction to a measurable property
- the probability of finding an electron in a very small volume of space
- doesn’t take into account amount of space though
What is radial distribution function?
- equation which is probability of finding an electron in s a spherical shell of thickness (dr) at a distance (r) from around the nucleus
- maximum in the rdf = most probable distance from the nucleus of finding an electron
- is a 3-dimensional electron distribution description
Shielding and penetration explained
- when there is more than one electron
- ability of an electron to shield other electrons from the Zeff of the nucleus
- between shells n=1>n=2>n=3
- within shells s>p>d>f
What would happen if you had 100% shielding?
- every electron in every element would see a charge of +1
What would happen if you had 0% shielding?
- every electron in every element would see +8 charge
What is effective nuclear charge? (Zeff)
- nuclear charge felt by each electron
If shielding of each electron was perfect, then what would a valence electron experience?
- a nuclear charge of +1
Because shielding exists but it is not perfect, what equation is seen?
Zeff = Z - S
s screening constant
What is the impact of Zeff?
- large Zeff means the ion is less extended from the nucleus as the core has a higher charge compared to the no. of electrons, e.g. Li2+ 3 protons vs 1 e-
How does Zeff relate to orbital energies?
- orbital energies become more stable (lower) as you go along the row as Zeff increases
Why is ns orbital lower in energy than np orbital?
- ns orbital penetrates more effectively than np, therefore ns is lower in energy than np orbital
What happens to the gap between ns and np across the periodic table as Zeff increases?
- it increases
What is seen in the orbitals of the Transition metals due to Zeff?
- first row of TM the 4s orbital is lower in energy than the 3d
- 4s penetrates the 3d orbital
- reduction in radial size of atom as d electrons are added in TMs
- d electrons shield badly therefore large increase in Zeff
- this affects the p block
What is ionisation energy?
- energy required to take electron from outer most orbital
- requires energy so is endothermic
- thermodynamically positive
What trends in ionisation energy are seen?
1) Successive IEs increase for each element - removing an electron increases Zeff so harder to remove the next e-
2) IEs decrease down a group - increasing size of electron cloud outweighs increasing nuclear charge (zeff decreases)
3) IEs increase across a period - Zeff increases due to increase in atomic charge
What is electron affinity?
- energy released from gaining an electron
- exothermic
What to consider regarding EA
1) The effect of repulsion of an extra electron in the electron cloud and the size of orbitals
2) Effective nuclear charge (zeff) - depends on a electronic configuration of an atom and anion (EA much larger if adding electron to a filled electronic configuration
Thermodynamically what are first EA and second EA?
1) exothermic 2) endothermic
Trend in EA
- down groups decreases
- across rows increases
What is electronegativity?
- ability of an atom to attract electron density towards itself
- qualitative
What does electronegativity depend on?
- atomic number
- distance of its valence electrons from the nucleus
- oxidation state
- atoms bonded to the element
- state of hybridisation
What is Pauling Electronegativity scale?
- A relative scale running from 0.7 (Fr) to 3.98 (F)
- H = 2.20
- all bonds have some degree of iconicity and some degree of covalency
Trends in EN…
1) Increases from left to right due to increasing Zeff
2) Metallic character (sblock) - down each group 1&2 EN decreases
3) D-block contraction and TMs - EN increases across row Sc to Cu (explains why you get metals in p block)
4) Flattening in atomic size of p-block due to d-block contraction
Ionicity - to determine whether bond is ionic or covalent
- if there is a large difference then bond is ionic
- small then covalent
Problems in determining atomic size
1) size of isolated atom has no real meaning
2) there are a vast range of structures and bonding
3) errors in experimental methods
What does a covalent radii consist of?
- valence electrons involved in overlap
- size of electron cloud depends on Zeff
- radii observed internuclear distances should be constant
How could you establish a set of covalent radii?
- by trail and error for a variety of molecules
- from X2 bond lengths
What does an ionic radii consist of?
- determine internuclear distance in ionic crystal
- apportion radii A+ and B- so charges balance
What does ionic radii assume?
- that ions are hard spheres - they touch but don’t merge
What is metallic radii?
- half the nearest metal-metal distance in solid state
What is Van der Waals radii?
- is half the distance between the closest approach of two atoms of the same element in different molecules
- contact distances between non-bonded atoms
- larger than covalent radii
- uses neighbour-molecule distances in crystals and critical volumes in gases
Bonding models - The Lewis Model
- shares electrons to attain electronic configuration of the closest noble gas
- octet rule: each atom shares electrons to acquire 8 electrons in its valence shell, refers to filling outer s and p orbitals
- unshared electrons called lone pairs
Features of the Valance Bond Model
- atoms are brought together and allowed to interact
- interactions localised between pairs of atom involving pairs of electrons
- useful in IR spectroscopy
- expresses Lewis’ ideas of covalent bonding in terms of wavefunction and resonance
Features of Molecular Orbital Model
- nuclei put into position and electrons placed into multicentre MOs
- electrons are delocalised over the whole molecule
- useful for small molecules, UV spec
- combines atomic orbitals to form in and out of phase molecular orbitals
What is the Valence bond theory?
- localised bonding - electrons within a molecule are associated with a particular bond
Two situations for a covalent bond -
1) interaction between two orbitals each containing one electron
2) one atom donating a lone pair in one orbital to a vacant orbital on another atom = dative bond
What is resonance?
- electrons in molecules are not always localised to specific bonds
- resonance used to explain this
- actual structure is hybrid of all possible forms
- double headed arrows
What is Valence Shell Electron Pair Repulsion (VSEPR)?
- used to predict structures of main group covalent molecules
- arrangement of electron pairs used to predict geometry
- assumes that electron pairs (bonding and non-bonding) arrange so as to be as far apart as possible to minimise electronic repulsion
5 rules of VSEPR
1) Valence shell electron pairs (lone and bonding) arrange to minimise repulsions
2) Basic geometry controlled by number of sigma bonding electrons pairs (pie bonds support)
3) Order of repulsive power (lp-lp>lp-db>lp-bp>db-bp>db-bp>bp-bp>)
4) The ideal structure which allow valence shell electron pairs to be as far apart as follows are linear, trig plan, tet, trig by, ocht
5) In the trigonal bipyramidal structure (n=5) not all vertices are equal (equatorial and axial environments are different)
In a trigonal bipyramidal structure where do lone pairs of electrons prefer to go to?
- equatorial positions as they have more space
What is molecular orbital theory? LEC 5
- delocalised
- all atomic orbitals combine to provide a new set of molecular orbitals (associated with the molecule not individual atoms)
- use linear combination of atomic orbitals method (same no. of MO as AO that you started off with)
Linear combination of atomic orbitals is…
- consider only valence electrons
- must combine these atomic orbitals to give a new set of molecular orbitals
LCAO Rules
1) Must have the same number of Molecular orbitals as atomic orbitals
2) Only orbitals of the same symmetry combine
3) Only orbitals of similar energy combine
4) For every bonding MO there is a corresponding antibonding MO (one lower one higher in energy)
5) Bonding MOs are lower in energy that the constituent Aos and antibonding MOs are correspondingly higher in energy
Bond orders
- gives indication of the strength and length of a bond
- BO = (no. of bonding e-) - (no. of antibonding e-) / 2
- BO = no. of bonds between two atoms
- the higher the BO the stronger the bond and the shorter the bond length
- if a BO is lower the bone is weaker and hence lower
LCAO for 2p elements
- use same principles but include p orbitals
- O2 valence electrons are 2s2 2p4
- two 2s orbitals combine to give sigma bonding and sigma star (antibonding) MOs
- three 2p orbitals to consider in O2
Combining 2p orbitals
- z axis defined as internuclear axis
- px/y and pz don’t combine as not correct orientation for overlap
- pz and pz combine to give sigma and sig star
- px/y and px/y combine to give pie bonding and pie star antibonding
