CH164

electronegativity definition

a measure of the tendency of an atom to attract a bonding pair of electrons

oxidation state model

• electrons are fully passed to one molecule

• just a formality

covalent bonding

atoms are held together by a strong electrostatic attraction between the shared pair of electrons and the nuclei of the bonded atoms

• extreme model

factors that increase bond strength of covalent bonding

• short bonds

• large difference in electronegativity between the atoms

  • large degree of polarisation

  • strong ionic contribution to bonding

how strong is a hydrogen bond

• average bond enthalpy = 5-30 kJ/mol

• in water H-bonding is 22x weaker than covalent bond in O-H

dative bonds

atom which donates both electrons becomes positively charged

ionic bonding

• not directional - just need to be close

• good description when Δχ is large

• allows assignment of oxidation states

ionic lattice strength

• 600 - 4000 kJ/mol

• high charges and small ions = strongest lattice enthalpy

metallic bonding melting points

heavier metals = higher melting points

what’s included in intermolecular interactions

combination of permanent dipole-permanent dipole, permanent dipole-induced dipole, temporary dipole-induced dipole

London dispersion forces

1. rate of decrease

2. factors to increase strength

3. ratio of London forces to other forces

• temporary dipole - induced dipole interactions

1. decrease at rate of 1/r⁶ (r = distance between atoms)

2. heavier elements have larger clouds of electron density so are more polarisable, increasing boiling point

3. responsible for 100% of interactions between identical non-polar molecules but roughly 35% if it is a polar molecule

Lennard-jones potential

V( r ) = A/r¹² - B/r⁶

what are intramolecular interactions composed of and their strengths

• electrostatic interactions between charges

  • proportional to 1/r

  • bigger charge = stronger

• dipole-dipole interactions

  • proportional to 1/r³

  • bigger dipole = stronger

• dispersion interactions

  • proportional to 1/r⁶

  • bigger atoms = stronger

• steric repulsion at very short range

  • proportional to 1/r¹²

  • clashes between electrons

examples of exotic bonding

• halogen bonding

• metallophilic interactions

• chalcogen bonding

• quadrupole interaction (pi-pi stacking)

what are robust bonding models able to do

• explain systems

• predict observations

• be consistent across contexts

• be consistent with other scientific models used

lewis theory/valence bond theory

assumes electrons in a bond are localised between two nuclei

dot & cross diagrams rules

• all electrons in a molecule want to form a pair

• a leftover single electron indicates the species is a radical

• aim for octet

negatives of dot & cross diagrams

• drawing double bond suggests that it is 2x single bond when it isn’t

• doesn’t provide shape of a molecule

• all bonds are the same

octet rule

an atom forms bonds in order to lose, gain or share electrons to give an outer shell containing 8 electrons, to achieve noble gas configuration

• useful for s & p block atoms

• heavier elements appear to expand the octet or become hypervalent

lewis structure rules

• make up octets

• draw one covalent bond between connecting atoms

• check formal charge on each atom

• dative bonds make structures formally charged

  • not always entirely accurate but a tool for describing structures

lewis acid/base

• lewis acid has an empty orbital

• lewis base has a lone pair

bond order

number of bonding electrons/2

• can be decimals or fractions

molecular orbital theory

electrons exist in molecular orbitals spread across the molecule

• 2 electrons per molecular orbital

• bonding and anti-bonding possible

resonance

describes delocalised electrons within a molecule, when one single lewis structure cannot express the bonding

• molecule is an average of the resonance forms

electroneutrality principle

each atom in a stable substance has a charge close to 0

draw resonance structures of [NO₃]^-

resonance of SF6 (expanded octet)

bond order < 1

• in this case bond order = 2/3

order of magnitude for different repulsions for VSEPR

• lone pair-lone pair > lone pair-bonding pair > bonding pair-bonding pair

• triple bond > double or single bonds

what causes decrease in repulsion

• greater difference in electronegativity

• longer bonds

• electron density is pulled away from central atom through bonding

negatives of VSEPR

doesn’t account for differing sizes of atoms (steric factors)

steps for predicting shapes using VSEPR

1. draw lewis structures

2. identify central atoms

3. identify number of valence electron pairs on central atom

4. work out parent geometry

5. place lone pairs in least crowded sites

6. place bonds elsewhere

7. assign a name to the shape of the molecule

names:

limitations of VSEPR/lewis theory

• some structures have similar energies

• doesn’t predicted magnetic properties

  • e.g. O₂ is paramagnetic but VSEPR suggests its diamagnetic

• doesn’t work well for when valence pairs = 7

• doesn’t work for d-block compounds

• doesn’t account for steric factors

symmetry

the quality of being made up of exactly similar parts faving each other or around an axis

a symmetry operator

an action that leaves the object apparently indistinguishable

a proper symmetry operation

can be done in real like (only rotational) to a physical shape

a symmetry element

the line or plane about which the symmetry operator is performed

what is C_n and what do the letters stand for

• C = rotation

• _n = how many times you rotate it

• largest n = principle axis (vertical)

what is C_∞

• can rotate it infinite amount

• for all linear molecules

what is σ (point groups)

• reflectional symmetry

• σ_h = reflection horizontal to principle axis

• σ_d = reflection dihedral between the corners (between atoms)

• σ_v = reflection vertical to the principle axis (through atoms)

what is S_n

• improper rotation

• C_n followed by σ reflection

  • same n as C_n

what is .i

• inversion

• S₂ improper rotation

• turns molecule inside out

point group

when two molecules possess the same set of symmetry elements

how to label a point group

• Number = order of principle axis

• Capital letter

  • D = n C₂ axes at right angles to principle axis

    • E.g. for benzene there are 6xC₂  which are horizontal to the principle axis so it is D

  • C = no n C₂ axes at right angles to principle C_n axis

• Small letter

  • h = horizontal mirror plane

  • d, v = no h but n vertical mirror planes

  • d goes with D

  • v goes with C

polar molecule

has a dipole moment caused by non-symmetric polar bonds

a dipole moment

• a property of the molecule

• unchanged by symmetry operation

• cannot be perpendicular to any C_n axis

• cannot occur if it has a centre of inversion

chiral compounds

• non-superimposable on their mirror image

• rotates the plane of polarised light

• does not possess axis of improper rotation

what are symmetry adapted linear combinations (SALCs) used for

• important in molecular orbital theory

• calculated for the orbitals on the non central atoms

what is the speed of light

c = 2.998 × 10⁸ ms^-1

equation for speed of light

c = fƛ

• c = speed of light

• ƛ = wavelength (m)

  • f = frequency (Hz or s^-1)

what is the photoelectric effect

when light hits a metal surface, electrons can be ejected and you can measure their kinetic energy

what happens if light behaves like a wave

• increasing intensity of light, increases energy of electrons

• changing frequency or wavelength of light has no effect on energy

how to calculate energy of a photon with frequency

E = hf = hc/ƛ

• h = 6.626 × 10^-34 J

what is planck’s constant

h = 6.626 × 10^-34 J

how electrons behave

• act like particles or waves

• when electrons fired at gold film, causes an electron diffraction pattern, which can only be explained by assuming electrons are waves

how to calculate De Broglie wavelength of a particle moving with speed v

ƛ = h / mv

• ƛ = wavelength

• h = planks constant

• m = mass

• v = speed

what does energy being quantised mean

there is only a certain set of possibilities: discrete set of energy levels (the change between them = quanta)

how to move a molecules energy up or down

absorption or emission of light can move up from the ground state or back down

draw out what happens when a photon is emitted

equation to calculate wavelength of photon emitted

|E_f - E_i| = hf = hc / ƛ_em

• E_i = initial energy

• E_f = final energy

• ƛ_em = wavelength of photon emitted

(same for absorbed)

draw what happens when a photon gets absorbed by an atom

what can you see in atom emission spectra

• certain frequencies

• each line is a different emission wavelength of a photon

what is the Rydberg equation

1/ƛ = R_H (1/n₁² - 1/n₂²)

• R_H = 109,677.581 cm^-1

• n₁, n₂ = integers where n₂ > n₁

• same as E = hc/ƛ = E(n₁) - E(n₂)

what did Schrödinger suggest

the electron in a hydrogen atom is described by a wave function that must obey an equation:

what does the wave function depend on

(x, y, z) coordinates of the electron

• every electron position has a corresponding wave function value

what does schrodingers equation tell us

energy is quantised as only some wave functions obey the equation so there must be discrete energy levels

what are quantum numbers

the shapes of the allowed wave functions are characterised by 3 quantum numbers

name the 3 different quantum numbers and what they describe

principle quantum number

• n

• n = 1, 2, 3…

• Same as the energy

  • i.e. in 1s, n=1 vs in 2p, n=2

angular quantum number

• l

• l = 0, 1, …, n-1

• Same as the shape

  • i.e. in 1s, l represents the s and l=0

  • In 2p, l represents the p and l=1

magnetic quantum number

• m_l

• m_l = -l, -l-1, …, 0, …, l-1, l

• Represents orientation

what do radial parts graphs show

• wave function decays to 0 as we move away from the nucleus

• shows where the electron likes to sit

• have n - 1 - l radial nodes

what does radial nodes tell about the shape of an orbital

the wave function is 0 so the number of radial nodes = number of nodal planes where electron density is 0

what do the 3d orbitals look like

what do the 3p orbitals look like

why can schrodingers equation not be used for atoms with many electrons

repulsion between electrons makes solving it impossible but can still use atomic orbitals to explain structure/properties of many electron atoms

what is electron spin

• an intrinsic property (cannot remove/destroy it)

• spin quantum number = m_s can be +1/2 or -1/2

what is the Pauli exclusion principle

• no 2 electrons can occupy the same orbital and spin state

• no 2 electrons can have the same set of 4 quantum numbers

  • can only have 2 electrons per orbital

what is the Aufbau principle

• when placing electrons in atomic orbitals, you fill from the lowest energy and continue upwards

• molecules tend to adopt their lowest electron configuration

• changes in orbital penetration and shielding makes it more complex for many electron atoms as energy ordering of atomic orbitals changes

what is Hunds rule

electrons fill degenerate orbitals to maximise the number of electrons of parallel spin as electrons with parallel spins repel each other less

what does the wave function tell us

the born interpretation: the value of |ψ|² tells us the probability of finding an electron at that point (electron density)

what do radial distribution functions tell us

the probability of seeing an electron anywhere on a shell at distance r from the nucleus

draw radial distribution functions for 1s, 2s+2p, and 3s+3p+3d orbitals

how does shielding effect the electrons in 2s/2p orbitals

• 1s electrons shield attraction between nucleus and electrons

  • effective nuclear charge is less than actual nuclear charge

how does penetration affect 2s and 2p electrons

• 2s electrons penetrate 1s orbital (less so for 2p orbital)

• 2s feels greater effective nuclear charge than 2p so 2s is more stabilised

• 2s electrons close to nucleus

• energy of 2s is lower than 2p so it can be closer to the nucleus

equation for effective nuclear charge

Z_eff = Z - S

• Z_eff = effective nuclear charge

• Z = actual nuclear charge

• S = shielding constant

what affects effective nuclear charge

• electrons added to a shell increases Z_eff

• Z_eff drops when electrons go into a shell with new principle quantum number due to shielding

trends in atomic radii and why

1. increase down the groups

   • outermost electrons sit in larger orbitals

   • maximum in radial distribution function moves outward as n increases

2. decrease across the periods

   • Z_eff increases so electrons are drawn closer to nucleus

ionisation energy definition

energy required to remove an electron from an atom (endothermic)

first and second ionisation energy equations

A _(g) → A⁺_(g) + e^-

A⁺_(g) → A²⁺_(g) + e^-

how does ionisation energy change for each subsequent ionisation

energy required is greater as removing an electron from a charged species is harder than removing one from a neutral species

how does ionisation energy change across a period/down a group

across a period, ionisation energy increases with some dips

• second period ionisation energies are higher than third periods ionisation energies dow to more tightly bound electrons

down a group, ionisation energy decreases as atoms get larger

electron gain energy definition

energy required to add an electron to an atom or ion

equations for first and second electron energy gain

A_(g) + e^- → A^-_(g)

A^-_(g) + e^- → A^2-_(g)

when is electron gaining favourable

when electron gain energy value is negative

electronegativity trends

• increases across a period as Z_eff increases

• decreases down a group as size increases

what is the LCAO approximation

approximate that MOs are a linear combination of atomic orbitals

• AOs represent one-electron wave functions (have wave characteristics)

• combine consecutively or destructively

what does it mean if AOs combine destructively

anti bonding occurs

how many MOs form from n AOs

n

what do the different symbols stand for in 1σ_g or 1σ_u*

1 = lowest energy σ_g or σ_u MO

σ = MO is spherically symmetric when viewed down inter-nuclear axis

_g = MO looks same after inversion

_u = MO changes sign after inversion

* = anti-bonding

draw MOELD for Li₂

bond order equation

Bond order = 1/2[(electron count for bonding MOs) - (electron count for antibonding MOs)]

what is Born-Oppenheimer approximation

electrons are much lighter than nuclei so when a nuclei changes position, electrons instantaneously rearrange themselves into lowest energy MO

general rule for MOs

only AOs of the correct symmetry will interact to give MOs