chem weeks 1-4

Structure of the atom: 

• Nucleus (less than 0.1% of total volume, made of proton and neutron), and electron.  

Atom posesses mass and occupies volume 

• A=mass number (protons+neutrons) 

• Z=atomic number (protons) 

• In a neutral atom, atomic number=number of electron 

Millikan oil drop experiment

Millikan oil drop experiment discovered elementary charge (charge on e-=-1.6x10 -19 C)

• xray cause molecules to ionise and ejected electrons picked up by oil droplets

• oil droplets become negativly charged, attracted to postive plate

Cathode ray tube experiments

2. Cathode ray tube experiments discovered mass of electrons (originally called corpuscles) 

• Mass to charge (e/m) ratio=1.29x10-7 

• Mass 1000x smaller than H atom 

• measure deflection of electrons via phosphorescent coating

gold foil experiement

Gold foil experiment discovered nucleus 

• Inconsistent with plum pudding model 

• Explained by very small dense centre of positive charge (nucleus) 

• measure deflection through gold foil

discovery of neutron

• James Chadwick devised method for measuring gamma radiation 

• Experiment: bombarded beryllium with alpha particles from radioactive decay of polonium 

• Resulting radiation penetrated lead shields and could not be explained by protons/electrons 

• Interacted with paraffin wax and knocked loose protons that could be detected 

• Conservation of momentum measurement showed that the mass ~=that of proton 

 

• Pathed the way from nuclear fission of uranium-235 

• Unlike charged alpha particle which are repelled by nucleus, neutrons are neutral and therefore able to interact with nucleus 

Isotopes 

atoms of an element with the same number of protons (i.e. atomic number the same) BUT a different number of neutrons (i.e. mass number different) 

• Atomic mass unit (AMU) mass equal to 1/12th of mass of one atom of carbon: 1.66054x10-27 kg 

• Masses of all atom are measured relative to this value

• weighted average accounts for percentage of natural abundance 

Mass spectrometry 

• Detects molecular masses 

• Detects a different mass for every combination of isotopes 

• Can be used to ID molecular formula of a compounds 

How does a mass spectrometer work? 

• Compound must be ionised (charged) 

• if solid / liquid sample, must be VAPORIZED (gas phase) & ionized 

• ions in the gas phase passed through a magnetic field 

• will be deflected according to their mass (i.e. separated) 

• ions detected and a graph (spectrum?) produced 

• can also get very useful information from fragmentation 

steps of mass spectrometry

1. Heating device vaporises the ample entering the spectrometer 

2. Electron beam ionises the sample 

3. Ion beam is accelea=rates by electric feild 

4. Magnetic feild deflects particles according to their mass/charge ration 

1. Ions with smaller mass/charge are deflected more 

2. Ions with larger mass/large are deflected less 

5. This process may cause fragmentation, so mass spectrometer can also detect fragements that have broken off 

 (eg M-CH3 at 63 and 65 on diagram above, differs by 2 units and 3:1 ratio suggests Cl is still there) 

Fragment M-cl at 43 has no chlorine, as no corrosponding peak at 43, so we know the Cl bond is broken off the rest of the molecule 

6. If we have prior knowledge about how the bonds will break, we can find fragments easier 

Radioactive elements 

Elements w/ no stable isotopes 

eg potassium

Three different isotopes: 

39K = 19 protons (& 19 electrons) + 20 neutrons  (93.2581%)----> STABLE 

40K = 19 protons (& 19 electrons) + 21 neutrons (0.0117% or 117ppm) ----> UNSTABLE 

41K = 19 protons (& 19 electrons) + 22 neutrons (6,7302%)----> STABLE 

 

40K: 

• Betadecay to produce 40Ca and a β- particle (~89%) 

• Electron capture to produce 40Ar (~11%) 

• Half-life of 1.25 billion years 

Quantum mechanics (modern Atomic theory) 

explains the structure and behaviour of matter (i.e. atoms, including electrons) and their interaction with radiation (e.g. light) - SPECTROSCOPY 

 Max Planck (1900) 

• studied radiation profiles emitted by solid bodies that were irradiated untilthey emitted light (incandescent matter) 

• demonstrated that e– ONLY ejected once a threshold value had beenobtained (not continually as previously believed) 

• proposed that energy can only be gained / lost in whole number multiples i.e. ENERGY IS QUANTIZED 

•  this means energy is behaving as if it were a particle… 

• Energy (E) is proportional to the frequency (v) 

 Niels Bohr (1913) 

• used the idea of quantized energy to develop an atomic model  

• electrons (X) travel in ‘orbits’ around the nucleus (•) 

•  the energy associated with each orbit has a fixed value  

• determined by distance from the nucleus  

• the chemical properties of each element are largely determined by the number of electrons in the outer orbits of its atoms 

Waves and particles 

• Matter can be considered as both particles and waves 

• Particles: have mass and occupies space 

• Waves: have no mass, carry energy and travel through space 

• Waves have 4 key features associated taht are related to each other: 

• Speed (c= speed of light, constant speed) 

• Frequency (the number of wave crests that pass over the origin every second, unit s-1 (per second), or Hz, greek letter nu, 𝜈 ) 

• Wavelength (distance between two wave crests/troughs, unit m or nm, greek letter lamda,λ ) 

• Amplitude (displacement from zero, measure of intensity) 

• Relationship C=λν C=𝜆𝜈 

• For electromagnetic radiation, c=speeed of light (2.998x108 ms-1) 

 high frequency 𝜈 --> High energy E,

high frequency 𝜈 --> low wavelength 𝜆 

Low wavelength, low energy 

High wavelength, high energy 

 

Absorption and emission of radiation 

• explore the structure of atoms by examining how they interact with light (or more correctly electromagnetic radiation) 

• Ground State - lowest energy state of an atom 

• Excited State - higher energy state achieved when an atom absorbs a photon of light 

• an energy level diagram depicts the changes of energy of an atom 

• the photon causing the excitement (exciting photon) must have sufficient energy to promote an electron from a lower to a higher energy level or to remove a bound electron from an atom 

• when an atom emits a photon (or radiates heat) the electron returns to a lower energy state 

Atomic emission spectra 

• Measures the energies of the photons emitted by atoms in the excited states 

• Result= EMMISSION SOECTRUM (series of lines) 

• Different elements emit specific lines/colours 

• Suggests energy can only be lost in fixed amounts, as discrete amount of lines= fixed energy levels 

• In a continuous spectrum, all frequencies are emitted, so can see all colours 

• In an atomic spectrum, only discrete frequencies are emitted. The spectrum is different for each element and characteristics of that element (unique set of lines that correspond to unique energy emitted by that element) 

• This type of spectroscopy is mst commonly applied to radiation emitted in the visable region o the spectrum 

atomic absorbtion spectra

• Measures the energies of the photons absorbed by atomons to move to excited states 

• Result= ABSORBTION SPECTRUM (series of black lines in a continuous spectrum) 

• Different elements absorb specific lines/colours 

Bohr (hydrogen) atom model 

• In 1913, neils bohr developed the first ‘quantum’ model for hydrogen 

• It had to explain the discrete emission lines in the hydrogen spectrum 

• Proposed: the electron in hydrogen moves around the nucleus and is only allowed in certain circular orbits 

• Particles made to travel in a circle upon application of a force towards the centre of the circle 

• From classical mechanics: bohr worked out the energy of the electron in the orbit (of hydrogen) 

Emission spectra and the bohr model 

• Electron normally occupies lowest enegry orbit (closest to nucleus) - ground state 

• Ie n=1 

• Incident energy (eg heat) applied 

• Electron absorbs quantised amount of energy and “jumps” to an excited state 

• Ie n=2,3,4... 

• When the electron returns to the ground state, energy is released in the form of light 

• THE ENERGY THAT IS EMITTED IS QUANTISED 

• Energy = light hence light emitted as specific wavelength/colour 

Emission spectra and the hydrogen atom 

• Electrons do not always return directly to the ground state 

• May return to higher energy excited states (n=2, n=3, n=4) 

• Will change the energy associated with the emitted photon, hence the nature of light 

 

lyman, balmer, paschen series

N=1: Lyman series 

• From higher energy level down to n=1 

• Higher energy, lower (shorter) wavelength 

• ultraviolet 

N=2: balmer series  

• From higher enegru level down to n=2 

• Visable lights 

N=3: paschen series 

• From higher energy level to n=3 

• Lower energy, higher (longer) wavelength 

• Infrared 

The rydberg equation 

• Lines in the emission spectrum therefore correspond to transitions between the energy levels 

• Balmer proposed an equation to describe the emission spectrum from a hydrogen atom 

• Used to calculate the frequency of life in the emission spectrum of hydrogen 

Limitations of the bohr model 

• only works for hydrogen 

• in classical physics a charged particle (i.e. the electron) under acceleration should radiate energy and hence spin into the nucleus 

• DOES NOT EXPLAIN WAVE-LIKE PROPERTIES!!! 

intro to spectroscopy

• Interaction of electromagnetic radiation with matter, to obtain information about molecule and materials 

• Molecules have definite three-dimensional structure described by bond lengths and angles  

• Covalent and coordinate bonds hold molecules together 

• Quantum theory fully explains the bonds and in its quantitative form predicts the structures and energy levels of the molecules 

• Yet there is still a need for experimental determination of molecular structure 

• Spectroscopy provides a wide array of structural information 

• Oftens a very fast technique, non-invasive techinique 

• Relevant to all phases of matter AND  mixtures ad well as pure compounds 

• The process of structural elucidation is deductive (doesnt give answer straight away) 

• Often one or more experiments are carried out and structural conclusions ar ereached by analysing the resulting data 

spectroscopy analytical techniques

MASS SPECTROMETRY 

•  molecular formula (and isotopes) 

MICROWAVE (ROTATIONAL) SPECTROSCOPY 

• bond lengths 

INFRARED / RAMAN (VIBRATIONAL) SPECTROSCOPY 

• bond force constants 

•  identification of functional groups 

ULTRA-VIOLET / VISIBLE (UV-VIS) SPECTROSCOPY 

• pathway of energy flow through molecules from electronic excitation 

NUCLEAR MAGNETIC RESONANCE (NMR) SPECTROSCOPY 

•  identification of bonding groups and their interactions through environment of the nuclei within molecules 

X-RAY DIFFRACTION (XRD) 

• molecular structure (3-D atomic coordinates) 

Molecular transitions 

• Molecules have five different transitions that allow us to use spectroscopy to probe their structure 

• These involve different energies and so we use different techniques to study then 

• Nuclear spin is often treated separately  

Molecular vibrations 

• Bond lengths or bond angles change 

Molecular rotations 

• Bond lengths or bond angles DO NOT change 

Energy considerations 

• Born-oppenheimer approximation – recognises that electrocs move much faster than nuclei 

• Can therefore approximate the various forms of energy, such that 

 

• As for atoms, molecular energies are QUANTISED 

• Only certain discrete values are allowed 

• Note: translational energy levels are too close together in enrgy for transitions to be determined 

• Remaining electronic, vibrational and rotational leves are all stacked together 

• fr each electronic enrgy level has own vibrational energy levels which then have their own rotational energy level 

Vibrational modes 

• Symmetrical stretch 

• Scissoring 

• Rocking 

• Anti-symmetrical stretch 

• Twisting 

• Wagging 

vibrational modes rules

• As more atoms ar introduced into the molecule, more VIBRATIONAL MODES become possible  

• For a molecule containing N atoms: 

• Linear Molecule (3N – 5) vibrational modes 

• Non-Linear Molecule (3N – 6) vibrational modes 

• each vibrational mode has its own potential energy curve and series of vibrational energy levels 

Degrees of freedom 

• Position of each atom described by three coordinates (typically x,y,z) 

• For a diatomic model, need x,y,z coordinates of each atom=six pieces of information 

• For triatomic=nine pieces of information etc  

• These ‘pieces of information’ are called degrees of freedom 

degrees of freedom rules

: 

• A  MOLECULE WITH N ATOMS HAD 3N DEGREES OF FREEDOM 

• Every molecule has 3 translational modes (along x,y,z) 

• To find no. Of vibrational modes use 

• Linear Molecule (3N – 5) vibrational modes 

• Non-Linear Molecule (3N – 6) vibrational modes 

• The remainder is no. Of rotational modes (all adds up to no. Of degrees of freedom 

degrees of freedom example

Monoatomic (single atom) 

• N = 1 = 3 degrees of freedom 

• Simply : 3 translational modes (along x, y and z) 

Diatomic (two atoms- must be linear…) 

• N = 2 = 6 degrees of freedom 

• 3 translational modes (along x, y and z) 

• (3N – 5) vibrational modes = 1 (because Linear Molecule (3N – 5) vibrational modes) 

• 2 rotational modes 

Triatomic (three atoms) LINEAR 

• N = 3 = 9 degrees of freedom 

• 3 translational modes (along x, y and z) 

• (3N – 5) vibrational modes = 4 

• 2 rotational modes 

Triatomic (three atoms) NON-LINEAR 

• N = 3 = 9 degrees of freedom 

• 3 translational modes (along x, y and z) 

• (3N – 6) vibrational modes = 3 

• 3 rotational modes 

Infrared spectroscopy 

• used to examine the 𝐸𝑣𝑖𝑏term (along with Raman spectroscopy – not covered CHEM121) 

• both techniques rely on vibrations occurring naturally (but predictably) within molecules 

• allows determination of molecular symmetry (see 200- & 300-level) 

• also gives info on FUNCTIONAL GROUPS within a molecule 

• the IR (and Raman) spectra are unique for each compound 

• useful as vibrations of many functional groups always give rise to features within well-defined ranges in the spectra, regardless of the overall structure of the molecule containing the group 

IR technique 

• Simplest version = single beam 

1. Monochromator selects specific wavelength of electromagentic radiation 

2. Sample absorbs radiation of certain wavelengths 

3. Detector measures and records teh intensity of radiation 

• Radiation absorbed when its enery corresponds to the different in energy levels 

wavenumbers 

• IR spectrum measures the radiation that passes through the sample and compare its to the intensity of radiotion before 

• Typicallly plotted as transmission of radiation (% tTRANSMITTANCE) vs WAVENUMBER 

• Have already seen EM radition can be defined by wavelength or frequency 

• a third parameter is often use din spectroscopy – wavenumber () 

WAVENUMEBR UNIT= cm-1 

• This can be substituted in the previous equation that related frequency, wavelength, speed 

• Same for energy 

• Used to help determine what bonds are in spectroscopy (as above) 

UV-VIS spectroscopy

• Colours are due to electronic transitions that occur due to teh absorbtion of light 

• In general, each/every compound only absorbs certain wavelengths of light which means: 

• The unabsorbed light passes through the sample 

• The colour of the sample is due to the unabsorbed light 

transmittance

• Typically run on solutions in a curvette with a known path length 

• The radiant power of the incidence bea, is I0 

• As the beam passes through the sample some energy is absorbed 

• When the beam leaves the sample the power is I1 

• The amout of radiation absorbed may be measured in a number of ways: 

• Note: T has no units as it involves a ratio of two intensities 

absorbance 

• Note: A also has no units 

• E= MOLAR ABSORBTION COEFFICIANT (or molar extinction coefficient) 

• c= concentration (in mol dm-3 ) 

• L= path length (in cm) 

• If all light passes through the solution 

• If no light passes through the solution 

beer lamber law

• The relationship between absorbance (A) and % transmittance (%T) is: 

•   

• Factors are important in determining rthe amount of radiation absorbed by a sample 

• the concentration (𝑐) (how much 'stuff' is in solution) 

• the pathlength (𝑙) (how far the radiation travels through the sample) 

• the extinction coefficient (𝜖) (how effective a molecule is at absorbing radiation) 

• All brought together in the beer-lambert law

Schrödinger equation

• The wave-like nature of the electron allowed mathematical models to be developed for the atom 

• The most successful is the schrodinger equation 

• Introduced the wavefunction (Ψ) as a function with a value that varies with position 

 

• Tells us what the total energy is (kinetic energy +potential energy) 

• From this, we can work out the enrgy of an electron and the probability of finding it at a particular position 

The born interpretation

• Whiles Ψ contains detailed information on the behaviour of the electron, it cannot be measured and has no physical interpretation 

• Max Born suggested that the square of the wavefunction Ψ2 is proportional to the probabilty of finding the electron within a small vulme of space dπ  

2 solutions to the Schrodinger equation

• The Schrodinger equation can only be solved exactly for one electron systems O(ie H atom, [He]+ 

• Each solution is a wavefunction Ψ characterised by a specific value of energy E 

• The energy is quantised (not all values possible) 

• The region of space define by a wave function is called ATOMIC ORBITAL 

• It shows the electrons are ‘delocalised’ 

• The electron density is the probability of finding an electron in a specific region 

Each atomic orbital has: 

• Characteristic energy 

• Characteristic distribution of electron density =shape 

• A given orientation 

Each electron can be defined by 3 QUANTUM NUMBERS 

• Energy, shape, orientation 

principal quantum number (n) 

• Is a positive interger 

• energy of the orbital

• Can take any value from 1 to infinity (usually between 1 and 7) 

• Correlates with orbital size 

• As n increases the energy of the electron increases, its orbital gets bigger and it gets less tightly bound to the atom 

azimuthal quantum number (ℓ);

• Can be zero, or any postive interger smaller than n 

• shape of the orbital

Each value is assigned a letter 

• spdf orbital notation 

magnetic quantum number (mℓ)

orientation of the orbital 

Can be any interger value fro –ℓ to +ℓ 

summary table (orbital notation)

These quantum numbers appear in orbital notation (eg 1s2, 2s2 etc) where principal quantum number =big number, azimuthal quantum number =letter, magentic quantum number tells number of orbitals (0=1, -1,0,+1=1, -2,-1,0,1,2=3 etc) 

the s orbital

• (n=1,2,3,...; ℓ=0, mℓ=0) 

• These are shown using boundary surfaces (usually plotted at the 90% probability level) 

• s-orbitals are spherical 

• Orbitals get larger as value of n increase 

• (electron density is smaller the further from the nucleus) (peak is nuceus, each side is at boundary of area where liekly to find electron) 

• Whne electron density=zero, it is called a node (no. Of node increases with orbital, as value of n increases) 

• 2s has 1x radial node 

• 3s has 2x radial node

the p orbital (n = 2, 3…; ℓ = 1; mℓ = –1, 0, +1) 

• lowest value of n for which ℓ = 1 is allowed is n = 2 

• i.e. 1p orbitals do not exist, lowest energy = 2p (n = 2) 

 three possible p-orbitals for: 

• mℓ = –1 mℓ = 0 mℓ = +1) 

• Each p-orbital consists of two ‘lobes’ of opposite sign or phase (each side it positive or negative, (+ is coloured blue) important when it comes to combining different orbitals) 

•   Lowest energy p orbital is in 2p 

• The two lobes are separated by a nodal plane called an angular node (where is zero probability of finding electron) 

• Radial node also present for n=3 and higher 

• Shape of 3-p orbital is different (more rounded) 

the d orbital (n = 3, 4…; ℓ = 2; mℓ = –2, –1, 0, +1, +2) 

• lowest value of n for which ℓ = 2 is allowed is n =3 

• i.e. 1d or 2d orbitals do not exist, lowest energy = 3d (n = 3) 

five possible d-orbitals for: 

• mℓ = –2 mℓ = –1 mℓ = 0 mℓ = +1 mℓ = +2 

• four of the five d-orbital consists of four ‘lobes’ (clover leaf pattern) with alternating sign or phase separated by two nodal planes 

• lie - between (dxy dyz dxz) or along (dx2y2) the axes 

• dark is +, light is - 

• dz2 is a combination of two valid solution of the Schrödinger equation (dz2y2 and dz2x2) 

• two lobes of the same phase projected along the z-axis 

• torus (ring / belly –band) of opposite phase around the centre 

• two NODAL CONES rather than nodal planes (in yellow) 

• If has square in name, lobes are pointing along axis

the spin quantum number (ms)

• All electrons have a property called ‘spin’ 

• They behave in one of two possible ways in the magnetic fields: spin up or spin down 

• This is described by the spin quantum number 

• two possible values of ms +½, –½  

pauli exclusion principle

No two electrons can have the same set of four quantum numbers (n, ℓ, mℓ , ms) 

• Each electron in an atom has a unique set of quantum numbers which must meet the folllowing requirements: 

• Thus all orbitals can contain and maximum of two electrons with opposite spin

the aufbau principle

• In the hydrogen atom, the energy of an orbital depends only on the principal quantum number n 

• Therefore 

• 2s orbital is same energy as 2p 

• 3s orbital is same energy as 3p same as 3d 

• degenerate=same energy 

• For many electron systems, the lower the value of ℓ, the lower the enrgy of the orbital 

• Ie 2s<2p 

• 3s<3p<3d etc 

• Each electron in an atom occupies the most stable orbit available 

hunds rule

The ground state (lowest energy configuration) will have the maxium number of unpaired (parallel) electrons (ie maximum number of electrons in the same spin state) 

• Electrons are as ‘spread out’ as possible 

Orbital capacities: 

•  s=1 orbital, 2 electrons

• p= 3 orbital, 6 electrons

• d=5 orbital,10 electrons

• f=7 orbital, 14 electrons

• For each principal quantum number:

ionisation energy Ei

• The energy of an orbital can be measured by the amount of energy required to remove an electron from the atom 

• Values measured un the gas phase 

sheilding

• For multi-electron systems Ei depends on the size of the nuclear charge and the distance of the electron from the nucleus 

• Also need to consider electron-electron reulsion, which will cancel out some of nucleus-electron attraction 

• This partial cancellation of nuclear chagre is called shielding 

• An electron with a given value of n (principal quantum number) will provide effective shielding for orbitals with a larger value of n 

• There is also a small amount of shielding by electrons with the same value of n as these will occupy the same region in space 

• The greater the shielding the lower the Ei 

 

• also need to consider the shapes of the orbitals 

•  for the 1s orbital most electron density is between the nucleus and the 2s orbital 

• so an electron in the 1s orbital shields an electron in the 2s orbital from nuclear charge 

• this reduces the attraction between the nucleus and an electron in the 2s orbital, thus raising the energy 

• Note: screening is incomplete as some of the 2s density is located ‘inside’ the 1s (known as penetration) 

• The 2s orbital penetrates more than the 2p orbital (remember p-orbital has an angular node at the nucleus) 

• The 2p orbital is therefore more effctivly shielded 

• Result is the 2p orbital is higher in energy 

the fundamentals of chemical bonding

• Three types of interaction within a molecule 

• Nucleus/electron (+/-) ATTRACTIVE 

• Electron/election (-/-) REPULSIVE 

• Nucleus/nucleus (+/+) REPULSIVE 

• When atoms are closer together, there is increasingly destabilisation and repulsion between nuclei dominates 

• When atoms get further apart, stabilisation increases and attraction dominates. There is a minimum distance where a stable bond is formed 

• For larger distance, atoms are so far apart they don't interact and potential energy is 0 

key parameters of chemical bonding

• minimum of the potential energy curve is where the molecule has the maximum energetic advantage over the separated atoms  

• i.e. is most stable 

• mean distance between the two atom centres at the minimum in the potential energy curve = BOND LENGTH 

• units = pm (10–12 m), although commonly see the ‘old’ unit, Å (10–10 m) 

• i.e. H–H bond length = 74.1 pm or 0.741 Å 

• the energy required to break the bond = BOND DISSOCIATION ENTHALPY (D) 

• units = kJ mol–1 (always positive) 

• e.g. H–H bond dissociation energy = + 435.8 kJ mol–1 (as below) 

diatonic: two same atoms 

• bond length gets bigger due to spd orbitals, so dissociation energy is lower, as atoms less close together so less tightly held 

types of bonding

• Covalent (formed between identical atoms) 

• Polar covalent (formed between atoms that ahve unequal sharing of electron) 

• Ionic (electrons transferred from cation to anion 

• ‘pure’ ionic or covalent bonds are the ends of a bonding continuum 

• Most bonds are between these extremes 

the lewis model 

• simplistic model based on tendency of atoms to achieve an octet (i.e. obtain 8 electrons) in their outer shell 

• related to filled ‘s’ (2e–) and ‘p’ (6e–) orbitals 

• corresponds to the ‘closest’ Group 18 element (noble gas) 

• works for small molecules and can be used to provide information on likely coordination and formal charge 

• can achieve octet by ‘sharing’ electrons (i.e. a BOND!) 

• always shared in pairs, represented by a single line joining the two atoms 

• electron pairs not involved in bonding = LONE PAIRS 

drawing lewis structure

Step 1:  

• obtain the number of electron pairs: count the number of valence electrons on each atom and divide by 2 

Step 2: 

• predict the most likely geometric arrangement of atoms using common patterns and assemble the bonding framework using single bonds 

Step 3: 

• place three non-bonding pairs of electrons on each outer atom (except hydrogen) 

Step 4: 

• assign the remaining electrons to the inner atoms 

• (in this case already used all 12 electrons) – skip Step 4 

Step 5: 

• if a central atom does not have at least 8 electrons, convert a lone pair to a double bond 

resonance

• Some molecules have structures not expressed correctly by single lewis structures 

• experimental measurement of the N–O bonds however show that all are equal (124 pm) 

• shorter than N–O single bonds (140 pm) 

• longer than N=O double bonds (120 pm) 

• considered as a blending of all these RESONANCE STRUCTURES 

• the blended (average) structure is called the RESONANCE HYBRID 

if valence electrons can be represented in more than one sensible way then neither is an accurate representation, and the actual structure is intermediate between them

benzene

• Kekulé proposed a cyclic structure with alternating double and single bonds 

• Does not explain the chemistry (no colourisation of Br2 solution) 

• All bonds the same length (139pm 

• C–C single (154 pm) 

• C=C double (134 pm) 

• RESONANCE lowers energy (diffuses electron density over greater volume - reduces e–:e– repulsions) 

• resultant HYBRID has lower energy than any of its components 

formal charge

• Often more than 1 way to draw a lewis structure for a specific moleule 

• The msot reasonable aswer (most stable) can be determined by examing the FORMAL CHARGES on the atoms 

Formal charge: 

The difference between the number of valance electron in a free atom and the number of assigned to the atom in the lewis structure 

NOTE: assumes electrons in a bond are shared equally between the two atoms 

formal charge steps

• Looks at the extent to which atoms have gained tr lost electron in each arrangement 

• The most likely structure has the lowest formal charge 

• if an atom has more electrons than the free atom ---> Formal NEGATIVE Charge 

• if an atom has fewer electrons than the free atom ---> Formal POSITIVE Charge 

 

• for a neutral molecule, the sum of the Formal Charges must add up to zero 

• for a charged ion, the sum of the Formal Charges must add up to the charge on the ion 

 

• atoms in molecules ‘try’ to achieve Formal Charges as close to zero as possible 

• any negative Formal Charges are expected to reside on the most electronegative element (a measure of tendency to attract electrons in a bonding pair) 

problems with the Lewis model

• many stable molecules exist that do not obey the octet rule 

• e.g. nitrogen dioxide, NO2 

• perform Steps 2 & 3 (section 5.2.2) 

• 2. predict the most likely geometric arrangement of atoms using common patterns and assemble the bonding framework using single bonds 

• 3. place three non-bonding pairs of electrons on each outer atom (except hydrogen) 

• also need to consider that central atoms in the third period (and beyond) can have more than 8 electrons 

• e.g. PF5 : phosphorus = 5 e–, each fluorine = 1 e– TOTAL @ P = 10 e– 

valence shell electron pair repulsion theory

• uses valence shell electrons to predict the shapes of molecules 

• negatively charged electron pairs repel each other and prefer to be as far apart as possible in 3-dimensional space 

• also need to consider LONE PAIRS (these also occupy space) 

Disphenoidal=seesaw

valence bond theory

• Lewis model assumes each bonding electron pair is located between the two bonded atoms (i.e. a localized electron model) 

BUT 

• from the wave-particle duality of the electron we know that it’s location in an atom cannot be described in terms of a precise position, but only in terms of the probability of finding it somewhere in a region of space defined by its orbital 

• same principle applies for the electrons in molecules, only over larger regions 

• led to the VALENCE BOND THEORY (or VB THEORY) 

• the first quantum mechanical model of bonding, developed (in part) by Linus Pauling 

• deals with covalent bonds between atoms in terms of the interaction between two atomic orbitals on the two atoms 

• result is a bonding orbital located between the two atoms, containing two electrons 

 

• must remember Hund’s rule and the Aufbau principle 

• only consider the valence orbitals in this model 

valence bond description of H2

• each hydrogen atom has an electron in a spherical 1s orbital 

• the VB approach considers how these atomic orbitals interact to give a wavefunction for the H2 molecule as a whole 

NOTE: accurate descriptions need to consider ioninc form H+H- and H-H+) as well as covalent (H-H), but for hydrogen the ionic form is small so it can be ignored 

• he combination of the 2 × 1s orbital results in a cylindrical electron distribution  

• called a 𝜎 -BONDING ORBITAL 

• the electron density is concentrated between the two hydrogen nuclei 

hybridisation and methane, CH4

• experimentally: methane contains a tetrahedral carbon with internal angles of 109.5° 

• 4 × identical C–H bonds (same bond length, bond energy) 

• valence electrons on carbon = 2s2 2p2  

BUT.. ‘s’ and ‘p’ electrons = different energies, not arranged tetrahedrally 

• the carbon atom is sp3-hybridized 

• each sp3-hybrid orbital contains 1 × electron 

• spatially arranged to be as far apart as possible in 3-D space (i.e. tetrahedral) 

small is -, big is + 

each sp3-hybrid orbital is able to overlap with the 1s atomic orbital of hydroge to form a 𝜎 -orbital corresponding to a C–H bond 

• ie Carbon atoms hybridise but H atoms dont, therefore can overlap to form C-H bond 

milikan oil experiment:

discovered elementary charge/charge on an electron

Xray ionise molecule in air, ejected e- picked up by oil droplets, which are then repelled from positively charged plate.

cathode ray tube experiment:

discovered mass of electrons by putting e- through electric field and seeing how much they deflected

gold foil experiment

discovered nucleus, by directing alpha particles at gold film, and see that some were deflected and fewer reflected straight back, most went through.

discovery of neutron

james chadwick measured gamma radiation by bombarding beryllium with alpha particles from radioactive decay of polonium 

Resulting radiation penetrated lead shields and could not be explained by protons/electrons 

Mass spectrometry 

Detects molecular masses: peaks correspond to molar weight of isotopes and compounds.

height of peak corresponds to percentage of isotope in molecule. fragmentation means compound will break into fragments/functional groups which can then be detected.

how does mass spectrometry work?

• Compound must be ionised (charged) by electron beam

• if solid / liquid sample, must be VAPORIZED (gas phase) & ionized 

• ions in the gas phase is passed through a magnetic field and will be deflected according to their mass (i.e. separated) 

• ions detected and a graph produced. can also get very useful information from fragmentation 

 Max Planck (1900) E=hv

• demonstrated that e– ONLY ejected once a threshold value had been obtained

• energy can only be gained / lost in whole number multiples (QUANTIZED) energy is behaving as if it were a particle… 

• Energy (E) is proportional to the frequency (v) E=hv

 Niels Bohr (1913) 

developed atomic model based off idea of quantized energy

• electrons (X) travel in ‘orbits’ around the nucleus (•) 

•  the energy associated with each orbit has a fixed value determined by distance from the nucleus  

• the chemical properties of each element are largely determined by the number of electrons in the outer orbits of its atoms 

electron: wave or particle

both:

• Particles: have mass and occupies space 

• Waves: have no mass, carry energy and travel through space

• key features of wave: speed, wavelength, frequency, amplitude

c=λv can be rearranged to E=hc/λ

Bohr (hydrogen) atom model 

• first ‘quantum’ model for hydrogen: had to explain the discrete emission lines in the hydrogen spectrum 

• Proposed: the electron in hydrogen moves around the nucleus and is only allowed in certain circular orbits 

• Particles made to travel in a circle upon application of a force towards the centre of the circle 

• From classical mechanics: bohr worked out the energy of the electron in the orbit (of hydrogen) 

Emission spectra and the bohr model 

• Electron normally occupies lowest enegry orbit (closest to nucleus) (ground state)

• Incident energy (eg heat) applied; electron absorbs quantised amount of energy and “jumps” to an excited state 

• When the electron returns to the ground state, energy is released in the form of light  THE ENERGY THAT IS EMITTED IS QUANTISED 

limitations:

• only works for hydrogen 

• in classical physics a charged particle (i.e. the electron) under acceleration should radiate energy and hence spin into the nucleus 

• DOES NOT EXPLAIN WAVE-LIKE PROPERTIES!!! 

emission spectra series

N=1: Lyman series 

• From higher energy level down to n=1 

• Higher energy, lower (shorter) wavelength 

• ultraviolet 

N=2: balmer series  

• From higher enegru level down to n=2 

• Visable lights 

N=3: paschen series 

• From higher energy level to n=3 

• Lower energy, higher (longer) wavelength 

• Infrared 

The rydberg equation 

• Lines in the emission spectrum therefore correspond to transitions between the energy levels 

• Used to calculate the frequency of life in the emission spectrum of hydrogen

• v=Rh*(1/n1^²) - 1/n2^²)

• n2 must be greater than n1

spectroscopy

• measuring interaction of electromagnetic radiation with matter, to obtain information about molecule and materials 

• Molecules have definite three-dimensional structure described by bond lengths and angles  held together by covalent and coordinate bonds

• Spectroscopy provides a wide array of structural information, often a very fast technique, non-invasive technique 

• Relevant to all phases of matter AND mixtures ad well as pure compounds 

• The process of structural elucidation is deductive (doesnt give answer straight away) 

• Often one or more experiments are carried out and structural conclusions are reached by analysing the resulting data 

molecular transistions

five, but only 2 are considered in chem 121

Molecular vibrations 

• Bond lengths or bond angles change 

Molecular rotations 

• Bond lengths or bond angles DO NOT change 

Born-oppenheimer approximation

• Born-oppenheimer approximation – recognises that electrocs move much faster than nuclei (translational, vibrational, and rotational levels)

• Can therefore approximate the various forms of energy (Etotal= Eelec+Evib+Erot+Etrans)

molecular energies are QUANTISED only certain discrete values are allowed 

translational energy levels are too close together in enrgy for transitions to be determined 

• Remaining electronic, vibrational and rotational leves are all stacked together 

• for each electronic enrgy level has own vibrational energy levels which then have their own rotational energy level 

Vibrational modes 

• Symmetrical stretch 

• Scissoring 

• Rocking 

• Anti-symmetrical stretch 

• Twisting 

• Wagging 

 

• As more atoms are introduced into the molecule, more VIBRATIONAL MODES become possible  

degrees of freedom rules

• Position of each atom described by three coordinates (for a diatomic model, need x,y,z coordinates of each atom=six pieces of information, for triatomic=nine pieces of information etc)

rules:

• A  MOLECULE WITH N ATOMS HAD 3N DEGREES OF FREEDOM 

• Every molecule has 3 translational modes (along x,y,z) 

To find no. Of vibrational modes use 

• Linear Molecule (3N – 5) vibrational modes 

• Non-Linear Molecule (3N – 6) vibrational modes 

The remainder is no. Of rotational modes (all adds up to no. Of degrees of freedom 

Infrared spectroscopy 

examine vibrational energy (Evib)

• allows determination of molecular symmetry (see 200- & 300-level) 

• also gives info on FUNCTIONAL GROUPS within a molecule and spectra are unique for each compound 

• useful as vibrations of many functional groups always give rise to features within well-defined ranges in the spectra, regardless of the overall structure of the molecule containing the group 

IR technique

• Simplest version uses single beam 

1. Monochromator selects specific wavelength of electromagentic radiation 

2. Sample absorbs radiation of certain wavelengths 

3. Detector measures and records teh intensity of radiation 

• Radiation absorbed when its energy corresponds to the different in energy levels 

wavenumbers ~v (v with ~hat)

IR spectrum measures the radiation that passes through the sample and compare its to the intensity of radiotion before 

~v=1/λ can be substituted into E=hc~v

Used to help determine what bonds are in spectroscopy

UV-VIS spectroscopy

• colours are due to electronic transitions that occur due to the absorption of light 

• In general, each/every compound only absorbs certain wavelengths of light which means: 

• The unabsorbed light passes through the sample 

• The colour of the sample is due to the unabsorbed light 

transmittance

• The radiant power of the incidence bea, is I0 

• As the beam passes through the sample some energy is absorbed 

• When the beam leaves the sample the power is I1 

The amout of radiation absorbed may be measured in a number of ways: 

• T=It/Io and %transmittanceT=100T

absorbance (beer lambert law)

A=ecl

• E= MOLAR ABSORBTION COEFFICIANT (or molar extinction coefficient) 

• c= concentration (in mol dm-3 ) 

• L= path length (in cm) 

If all light passes through the solution 

•  Io=It T=1 %T=100% A=0

If no light passes through the solution 

• It=0 T=0 %T=0 A=infinity

the born interpretation of Schrödinger equation

wavefunction Ψ² is proportional to the probabilty of finding the electron within a small vulme of space dπ  

high Ψ² is high probability of finding e-.

low Ψ² is low probability of finding e-

solutions to Schrödinger equation

• Each solution is a wavefunction Ψ characterised by a specific value of energy E 

• The energy is quantised (not all values possible) 

• The region of space define by a wave function is called ATOMIC ORBITAL (electrons are ‘delocalised’)

• The electron density is the probability of finding an electron in a specific region 

Each atomic orbital has: 

• Characteristic energy 

• Characteristic distribution of electron density =shape 

• A given orientation 

• Each electron can be defined by 3 QUANTUM NUMBERS 

n=principle quantum number: energy of the orbital

l=azimuthal quantum number: shape of the orbital

ml= magnetic quantum number: orientation of orbital

ms: spin

These quantum numbers appear in orbital notation (eg 1s2, 2s2 etc) where principal quantum number =big number, azimuthal quantum number =letter, magentic quantum number tells number of orbitals (0=1, -1,0,+1=1, -2,-1,0,1,2=3 etc) 

principle quantum number

energy of orbital

• positive interger (can take any value from 1 to infinity (usually between 1 and 7) 

• Correlates with orbital size 

• As n increases the energy of the electron increases, its orbital gets bigger and it gets less tightly bound to the atom 

azimuthal quantum number (ℓ)

shape of the orbital

• Can be zero, or any positive integer smaller than n 

• Each value is assigned a letter 

magnetic quantum number (mℓ)

orientation of the orbital

Can be any interger value fro –ℓ to +ℓ 

the s orbital

(n=1,2,3,...; ℓ=0, mℓ=0) 

s-orbitals are spherical, Orbitals get larger as value of n increase 

• (electron density is smaller the further from the nucleus) (peak is nucleus, each side is at boundary of area where likely to find electron) 

(no. Of node increases with orbital, as value of n increases) 

• 2s has 1x radial node 

• 3s has 2x radial node