Quantum Chemistry Flashcards
Why was quantum theory developed?
Developed to explain various experimental observations that couldn’t be understood by prevailing ‘classical’ theories of physics
What is quantum theory?
It is based on several principles such as wave particle duality and quantisation.
What were 3 issues which puzzled classical physicists which led to the development of quantum theory?
Black body radiation
Photoelectric effect
Spectroscopic lines
What is a black body?
A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. It does not reflect or transmit any radiation; instead, it absorbs all incoming radiation and re-emits it.
What was the issue with black body radiation?
The issue with understanding black body radiation in the late 19th and early 20th centuries was the failure of classical physics to explain the observed spectral distribution of the emitted radiation. According to classical electromagnetic theory, it was expected that the energy emitted by a black body would increase without bound as the wavelength of the radiation became shorter (known as the ultraviolet catastrophe).
The ultraviolet catastrophe problem arose because classical physics predicted that the intensity of radiation would increase without limit as the wavelength approached zero, leading to an infinite amount of energy. However, experimental observations, particularly the detailed measurements of black body radiation depicted a different behaviour.
Thus, physicists had to find a solution to the black body radiation
What was Planck’s solution to black body radiation?
He proposed that energy is quantised. This means that electroncs can only possess certain discrete energy values, and values between these quantised values aren’t permitted
He suggested that energy is emitted or absorbed in discrete packets or ‘quanta’, which is proportional to the frequency of radiation.
What was the formula to calculate the energy of a system / electron by Planck?
E = hv
E = energy
h = Planck’s constant
v = frequency of oscillation
What is planck’s constant
6.62607015×10^−34 Js-
What is the photoelectric effect? WHat was the issue with it?
Light / electromagnetic radiation can eject electrons from a metal, but only if its frequency is above a threshold frequency which is characteristic for every different metal. The emission of electrons occurs instantaneously and energy of the emitted electrons depends on the frequency of the incident light rather than intensity
However, this contradicted classical wave theories of light, which predicted a gradual increase in the emission of electrons with increasing light intensity, however intensity of light doesnt affect the energy of the emitted electrons.
What did EInstein propose in 1905?
That light has a particle nature as well as a wave nature. Light is quantised.
What is the formula that EInstein developed from Placnk’s formula? (energy of a photon)
E = hv = h x c /λ –> v = c / λ
E = energy
where v = frequency
c = speed of light = 3.0 x 10^8 ms^01
λ = wavelength
h = Planck’s constant
How did Louis de Broglie build on Einstein’s findings of the photoelectric effect
De Broglie built on this to further propose that if light can behave as a wave and a particle, why can’t matter such as electrons also have wave properties –> idea that electrons act as a wave-particle duality
He further suggested that the momentum (mv) of a particle should be related to its wavelength in the same way as a photon
What is the equation of momentum?
Stems from Einsteins special theory of relativity
p = E / c
Where p is momentum, E is energy and c is the speed of light
How can we combine both the equation of momentum and quantum theory?
To form the equation of :
λ = n / p = n / mv
where m = mass
v = velocity
h = planck’s constant
λ = wavelength
What were spectroscopic lines? WHat was the issue with it?
Spectroscopic lines refer to the discrete, well defined lines observed in a spectrum when light is dispersed. These lines represent specific wavelengths or frequencies of light emitted or absorbed by atoms or molecules.
The issue with spectroscopic lines for classical physicists arose when they attempted to explain the observed patterns using classical electromagnetic theory, which treats light as a continuous wave. This means that a heated object would emit radiation continuously across all wavelengths, forming a smooth and continuous spectrum. However, experimental observations showed distinct and well defined lines instead of a continuous spectrum
How did Bohr address the issue of spectroscopic lines
He further developed the quantum model of the atom through using the knowledge of both Einstein (quantised packets of energy for light) and Planck (quantisation of energy).
He suggested that electrons then exist in discrete energies with quantised electron orbits. The electrons in atoms could only exist in certain allowed energy levels, and transitions between these levels resulted in the emission or absorption of photons with specific energies corresponding to the observed spectral lines. This successfully addressed the issue of the defined spectroscopic lines
What was the Bohr model?
Bohr postulates that there is a set of circular orbits for electrons with specific, discrete radii, and energy (quantised) and that electrons could move in each orbit without radiating energy
What was the formula derived for the energy of an orbit ‘n’ in Bohr’s model?
This was derived by looking at the atomic spectra for hydrogen.
En = - (me^4) / (2h^2n^2) = - Er x 1/n^2
En = energy of a particular orbit ‘n’
h = planck’s constant
n is an integer 1,2,3… corresponding to Bohr’s discrete orbitals
Er = Rydberg’s constant - 2.18 x 10^-18 J
This means that only specifc values of E are allowed. Values between Er (n= 1) and Er (n=2) can’t be observed, etc. Has to be only these integers
What’s wrong with Bohr’s model?
According to classical physics, revolving charged particles radiate energy. Thus, electrons should continually lose energy and spiral into the nucleus
Bohr’s model could only explain the emission spectra of single electron atoms such as Hydrogen. It failed to predict the spectra of multielectron atoms
Bohr couldn’t offer a reason as to why an electron should actually have a discrete orbit or energy
How are changes in energy levels achieved?
They are done through the absorption or emission of photons.
Absorption involves increasing an energy level
Emission involves decreasing an energy level
What can electrons be thought of as?
As 3d standing waves, with an amplitude characterised by a wavefunction (𝚿)
A standing wave is also known as a stationary wave, its a combination of two waves moving in opposite directions, each having the same amplitude and frequency.
What is the lowest energy level of any standing wave called?
The fundamental
What are the energy levels after the fundamental called?
They are called ‘harmonics’ in order of how many waves it is after the fundamental
I.e. n= 1 –> fundamental –> 1 half wavelength
n = 2 –> First Harmonic –> 2 half wavelengths
n = 3 –> Second Harmonic –> 3 half wavelengths
n = 4 –> Third Harmonic –> 4 half wavelengths
And then the pattern continues
Each harmonic adds a half wavelength
WHat is a half wavelength
It is the distance between each node
What is a node defined by when graphing?
It is defined by the intersections of the standing wave with the x axis
What is the energy of the fundamental of a standing wave dependent on?
Depends on the degree of confinement
WHat confines an electron wave in an atom?
Electrostatic attraction to nucleus
Why does the energy of the electron increase as it gets further away from the nucleus. (I THINK)
(I THINK) This is apparently because of potential energies. It takes more energy to take an electron away when it is close to the nucleus, however the electron only releases a set amount of energy, which is ultimately less than the energy it takes to take it away –> more negative energy, however as it becomes easier to tear the electron away, the amount of ‘potential energy’ increases (?)
Another explain by chatgpt:
So, the basic idea is that electrons have more energy when they’re further from the nucleus because they’ve had to work against the attractive force from the positively charged nucleus to get there.
What is electron density?
It describes an area where the electron is most likely to be in
What is Born’s interpretation?
The probability of finding an electron (i.e. electron density) is given by the square of the wavefunction 𝚿
Because 𝚿^2 is always positive, the probability of finding an electron is always positive regardless of the sign of the wave
WHat is a node?
A node is a point where the probability of finding an electron is zero
How do you determine the number of nodes from the principal quantum number ; n ?
There are n-1 nodes. This means that for n = 1, there are no nodes
WHat is the lobe representation of s orbitals?
It is a sphere around the centre (sphere around the nucleus)
Why does orbital size increase with energy?
This is because electrons with higher energy are found further away from the nucleus. As a result of an increase in energy of electrons, thus, the orbital size also increases (distance to the furthest electron)
How do you identify the principal quantum number, n?
It is the number in front of the letter when listing orbitals, i.e. for 1s, the principle quantum number is 1
What is the equation for energy of an electron?
E = Er (Z^2 / n^2)
WHere E = energy of electron
Er = Rydberg’s constant
Z = Charge (which is normally always 1)
n = principle quantum number
What does the radial probability look at?
Probability of finding a radial/ spherical node
What is a planar/angular node?
Angular node is also referred to as the nodal plane. Angular node refers to a plane that passes through the nucleus.
Does energy increase with the number of nodes?
Yes
WHat does the lobe representation of a p orbital look like?
A dumbbell
How can the 2p orbital exist?
It can exist across 3 planes; x, y and z axis (2px, 2py, 2pz)
What is the angular momentum quantum number , ‘L’, What is its significance
This arises because principal number cant differentiate between 2p and 2s. Thus, the angular moment quantum number determines the shape of the orbital.
L is quantised into different discrete values
S orbital : L =0
p orbital : L = 1
d orbital: L = 2
f orbital: L = 3
L also equals the number of planar/angular nodes. I.e. the p orbital will have 1 planar/angular node, and a 3p orbital would have 1 radial node as well
What is the magnetic quantum number, mL?
mL = -L…, 0,…+L
For example, when L = 1 (i.e. p orbital), mL = -1, 0, 1 –> hence when we see a p orbital it can exist on 3 different planes (x, y, z), and if they’re all used, the 3 different planes are used all together, however if not, it could just be expressed on the x axis or the y axis or the z axis, same continues for others.
Thus, for example, a d orbital will have 5 different orbitals as part of it
It determines the number of orbitals and their orientation
What does the pauli exclusion principle mean?
States that no two electrons in an atom can be in the same quantum state (n, L, mL, and ms)
as a result, electrons in the same orbital must have opposite spins (ms)(application)
What does the Aufbau principle mean?
States that electrons in atoms generally exist in their lowest possible energy state. (Ground state)
Thus, electrons fill lower energy atomic orbitals before filling higher energy ones
What does Hund’s rule state
States that the lowest energy electron configuration in orbitals equals energy t
Thus, before the double occupation of any orbital, every orbital in the sub level must be singly occupied first.
This works because we need to keep electrons as far apart from each other as possible to account for repulsive potential energy between electrons. Thus, the number of unpaid electrons in degenerate orbitals is maximised
What is the significance of Hund’s rule?
What is a degenerate orbital
Electron orbitals having the same energy levels are called degenerate orbitals.
What is the spin quantum number, ms?
Describes the ‘spin’ of an electron which is form of angular momentum of electrons. This arises because an electron behaves like a magnet, so they can be deflected in an inhomogenous magnetic field. A famous example is the Stern - Gerlach experiment demonstration of spin
It states that ms has a spin of +1/2 or -1/2
What are the 2 things we need to consider in a multi electron system?
Electron - electron repulsion
Orbital shielding
What is electron -electron repulsion
When we have more than one electron, the electrons within an orbital will repel each other –> want to maximise distance between electrons
What is orbital shielding and its effects?
This is when an orbital is occupied, it shields the interaction of the outer orbital with the nucleus. This alters the energy levels of the orbital. Orbital shielding depends on the shape of the orbital
s<p<d<f in terms of orbital shielding
Explain further the significance of orbital shielding
For an atom with more than 1 electron, electrons in orbitals closer to the nucleus shield electrons that are further away. This decreases positive attraction from nucleus, thereby raising energy. Thus lower shells have less shielding
What is the main difference between hydrogen like atoms and multi electron atoms
In hydrogen like atoms (one electron), Energy of electron is the same for a single principal quantum number –> quantum number determines energy, whereas in multi electron atoms due to orbital shielding and electron repulsion, the energies of different orbitals might be different due to these factors –> specific order
What are valence electrons?
These are electrons on the outermost shell of an atom. They are the ones which are important in forming chemical bonds.
What is SPDF notation, and how can we use noble gas configuration
stating how many electrons are in each orbital such as 1s2 2s2 2p3 etc.
However, we could use noble gas configuration, which uses the closest noble gas and then doing the spdf notation afterwards to identify a certain atom:
[He] 2s2 2p2 = Carbon
How many electrons per orbital?
2
What is nuclear charge(z)?
Number of protons in nucleus
WHat is effective nuclear charge (Zeff)
Positive charge felt by an electron in a multi electron atom
Is the effective nuclear charge higher or lower than the nuclear charge? Provide a reason.
Electrons in outer orbitals are partially shielded from the nuclear charge, resulting in weaker attraction between the valence electrons and the protons –> lower Zeff.
Electrons close to a nucleus (i.e. in 1s orbital) feel a nuclear charge close to Z
Outer electrons are considerably shifted from nucleus so Zeff is much lower than Z
What is the trend in atomic radius charge across a period and down a group?
Across a period: effective nuclear charge increases, because number of protons increase and there aren’t that many more electron orbitals being formed –> electrons more tightly held by nucleus –> smaller radius
Down a group: Electrons are added to orbitals further from nucleus –> larger radius. There is also a weaker attraction between the positive nucleus and outside electrons
What is atomic radii?
Distance between nucleus and the furthest electron
Describe anionic radii and the trends associated with it
When forming an anion, electrons are usually added to the same orbital. Because there are more electrons –> more electronic repulsion. Thus, size of anion (how many extra electrons are added), will result in a increase in size of atom because of idea of repulsion
The anion thus has a higher atomic radii compared to the parent atom
Describe cationic radii and the trends associated with it
When forming a cation, electrons are removed from the outer orbital. This reduces electron repulsion, and also allows valence orbitals to be closer to the nucleus (allowing for greater attraction) –> cation is smaller than the atom
The cation thus has a smaller atomic radii compared to the parent atom
What is ionisation energy
It is the amount of energy required to remove an electron completely from an electron
It requires the input of energy. Thus ironisation energy will always be positive
How does effective nuclear charge influence ionisation energy?
Larger Zeff = electrons held more tightly to nucleus –> electrons harder to remove due to increased electrostatic attraction –> higher ionisation energy
What is the trend in ionisation energy across a period?
Across a period Zeff increases. This is because as Zeff increases across a period, electrons are more attracted to the nucleus –> more energy required to pull an electron away –> higher ionisation energy
What is the trend in ionisation energy down a group?
Down a group, electrons are added to orbitals that are further away from the nucleus, and also form electron repulsion with each other. This indicates weaker nuclear attraction –> easier to pull apart this attraction –> lower ionisation energy
What is Electron affinity?
Electron affinity is the energy when an electron is added to an atom in the gas phase
If energy is released when an electron is added, the atom has an affinity for electrons, and it has a negative electron affinity
When energy is required to add an electron, it does not have an affinity for electrons and we cannot directly measure an electron affinity value.
What is the trend for electron affinity?
Periodic trends for electron affinity aren’t too clear.
CHeck books on equilibrium bond distance and covalent bonds
What is bond length?
Separation distance at which the molecule has the maximum energetic advantage
What is bond energy?
Energy required to break the covalent bond
What is the unit for bond length?
Angstrom (Å) = 0.1nm
What is the bohr radius
Most probable distance between the nucleus and electron in a H atom. The Bohr radius is 0.53 Å
What is the total number of atomic orbitals in the component atoms equal to?
Equal to the number of molecular orbitals
Overlap of N atomic orbitals = formation of N molecular orbitals
What is molecular orbital theory
Considers the formation of molecular orbitals from the overlap of atomic orbitals on all of the individual atoms in the molecule
What are the 2 ways that atomic orbitals can overlap?
Through in-phase overlapping (both orbitals having the same phase (wave function)), or out of phase overlapping (both orbitals having opposite phases)
In-phase overlapping is constructive overlaps and gives a bonding molecular orbital, in which electron density is maximised –> minimises internuclear repulsion. (This has lower energy)
Out-of-phase overlapping is destructive overlaps, and gives an antibonding molecular orbital, in which electron density is minimised between the nuclei and is zero at the node between the nuclei (it forms a node). (This has higher energy due to presence of node)
LOOK AT EXAMPLES OF MOLECULAR ORBITAL DIAGRAMS IN BOOK
LOOK AT EXAMPLES OF MOLECULAR ORBITAL DIAGRAMS IN BOOK
LOOK AT EXAMPLES OF MOLECULAR ORBITAL DIAGRAMS IN BOOK
CHECK WHAT bonding and antibonding SIGMA AND PI MO BONDS LOOK LIKE
What are paramagnetic molecules?
Paramagnetic molecules have unpaired electrons and a net magnetic moment. Such substances will be drawn into magnetic fields
What are diamagnetic molecules?
Diamagnetic molecules do not have unpaired electrons, and have no magnetic moment. They are weakly repelled by magnetic fields
WHat is HOMO?
Refers to the ‘Highest Occupied Molecular Orbital’–> highest orbital which has an electron
What is LUMO?
Lowest Unoccupied Molecular orbital –> lowest orbital which doesn’t have an electron
What is the lowest energy electronic transition of a molecule?
The lowest energy electronic transition of a molecule is the HOMO-LUMO transition
CHECK BOOKS AND TEXTBOOK AND THE SLIDES
What are core electrons?
These are electrons not affected by the presence of neighbouring atomic nuclei
What is the difference in sigma and pi bonds?
Sigma bonds are formed by direct head to head overlap between orbitals while pi bonds are formed by side by side overlap, typically from the p orbitals
Can sigma bonds be from p orbitals?
Yes, even though p orbitals are shaped like a dumbbell, if it is direct head to head overlaps, it can cause a sigma bond to form. However, if they are side by side then it forms a pi bond.
Do all sigma and pi bonds look the same?
No they won’t, for example the resulting sigma bond will look different depending on which orbital is overlapping (s, p, d, f). However, generally for sigma bond it is just one horizontal clump
Similar for other pi bonds as well
The resulting sigma bonds will look different depending on which orbi
What are sigma bonds?
Sigma bonds are a result of the head-to-head overlapping of atomic orbitals
What are pi bonds?
whereas pi bonds are formed by the lateral overlap of two atomic orbitals.
What are non bonding orbitals?
Localised on only one atom and do not affect bonding
A non-bonding orbital, also known as non-bonding molecular orbital (NBMO), is a molecular orbital whose occupation by electrons neither increases nor decreases the bond order between the involved atoms
These are energetically not favoured
Sigma star and pi star bonds
Will a chemical molecule favour the production of a substance which has less or more energy
Less energy –> hence, favouring the bonding MO which is below the antibonding MO
How many electrons in a single atomic orbital?
2 electrons max
How many electrons in a single molecular orbital?
2 electrons max
What is the total number of molecular orbitals equal to?
Equal to the total number of atomic orbitals
What is the equation for bond order?
1/2 (No. of bonding electrons - No. of antibonding/nonbonding electrons)
How do valence and conduction bands form?
They form through a large amounts of orbitals being mixed together , and eventually there are so many orbitals that it can just be treated as a ‘continuous band’
What is a valence band?
The band of occupied orbitals is called the valence band. (occupied with electrons)
Typically formed by interactions of sigma bonds
What is a conduction band?
The band of unoccupied orbitals is called the conduction band (electrons don’t occupy this band)
Typically formed by interactions of sigma star bonds
What is the band gap?
It is the energy gap between the conduction and valence bands.
It is the minimum energy that a network solid must absorb to promote an electron from the valence to the conduction band
Does the band gap of a network solid determine its colour?
Yes. The reason for this is because different band gaps require different amount of energy to be absorbed. These different amounts of energy absorbed will lead to the display of different colours –> band gap determines colour
WHat is conductivity caused by?
Caused by electrons having access to an unoccupied energy level
The conductivity depends on the number of charge carriers ( electrons in n-type semiconductors or holes in p-type) and the size of the band gap.
Explain why the conductivity of semiconductors increases with temperature
In semiconductors, there is a small band gap, which prevents electrons from the valence band to freely move to the conduction band. Thus, heat can be used to provide energy to excite these electrons from the valence band to the conduction band. The more heat there is (greater temperature), the more the electrons can be excited to the higher conduction band, thereby increasing flow of electrons, and thus increasing the conductivity
Explain conduction in metals
Metalls don’t have a band gap. This is because valence and conduction bands overlap, so metals can conduct electricity freely
Explain conduction in insulators
In insulators, there is a large band gap - electrons can’t be promoted to conduction bands
What are the different types of ideas which control conductivity of solids
Insulator, semiconductor, metal
What is the band gap in semiconductors?
SMall/moderate band gap, but not enough to freely move electrons across the bands
What are the two types of semiconductors
Intrinsic and extrinsic semiconductors
What are intrinsic semiconductors?
When band gap is small, electrons can be promoted to the conduction band, leaving electrons in the conduction band, and holes in the valence band (e.g. silicon, germanium)
What are extrinsic semiconductors?
These are semiconductors which require the use of doping to allow for conductivity
What is doping?
Doping involves the substitution of some atoms in the original semiconductor with other atoms.
There are two types of doping; n-type and p-type doping
What is n-type doping
In n-type doping, there is are extra negative charge carriers (i.e. more electrons)
This is achieved through substituting with an element to the right of the periodic table, which has more electrons (i.e. substituting Si with P)
Extra electrons reside in DONOR levels, just below the conduction band. This makes it easy for electrons to be promoted to the conduction band –> carriers which contribute to conductivity
As the material is heated, these electrons are promoted to the conduction band, and vastly outnumber any holes in the valence band
Charge carriers are electrons. Electrons free to move around the semiconductor
WHat is a donor level?
This is a level right below the conduction band, and this makes it easy for electrons to be promoted to the conduction band (small band gap between that and the conduction band)
What is p - type doping
Here, the ‘charge carriers’, are the holes in the valence band
There are fewer electrons, and more positive charge carriers (i.e. holes)
Achieved by substituting with an element to the left of the periodic table with less electrons (i.e. substituting Si with Al)
Electron poor atoms generate acceptor levels, just above the valence band
As the semiconductor is heated, valence bond electrons are promoted to the acceptor levels, leaving holes in the valence bond
The creation of this lower acceptor level is small enough to allow electrons to flow from valence band to the acceptor level, thus also creating one form of conductivity
What are holes? How do they promote conductivity? (NEED TO DOUBLE CHECK)
A hole can be seen as the “opposite” of an electron.
they are the absence of an electron in an atom
Holes are formed when electrons in atoms move out of the valence band (the outermost shell of the atom that is completely filled with electrons) into the conduction band (the area in an atom where electrons can escape easily), which happens everywhere in a semiconductor.
These are positive charge carriers and can be used to promote conductivity
These positive charged holes can move as electrons leave their positions, and are able to thus carry the charges. They act as positive charges, and the flow of these can create electricty
Additionally, allows formation of the acceptor level and the electrons jump to acceptor level and this creates energy
What is an acceptor level?
The acceptor level lies above the valence band
From the energy gap viewpoint, such impurities “create” energy levels within the band gap close to the valence band so that electrons can be easily excited from the valence band into these levels, leaving mobile holes in the valence band. These holes can act as positive charge carriers –> conductivity
They create “shallow” levels, levels that are very close to the valence band, so the energy required to ionize the atom (accept the electron that fills the hole and creates another hole further from the substituted atom) is small. As electrons are exxcited, there are more holes –> conductivity
What are solar cells?
These can be generated by combining an intrinsic semiconductor with both p - type and n - type extrinsic semiconductors
Electrons travel to the conduction bands of the n-type semiconductor
Absorption of light promotes electron from valence to conduction band of the instrinsic semiconductor
As electrons move, the holes left by electrons in the balence band also changes position
What is spectroscopy?
Study of the interaction of matter with electromagnetic radiation
The type of electromagnetic radiation used, instruments and sample preparation determines the information that will be obtained
Do white materials absorb visible light
No, they don’t absorb any visible light.
Do black materials absorb visible light
Yes, they absorb all visible light shone on them
What causes colour
It is due to the wavelengths of light a material absorbs
What is Newton’s colour wheel
It is a circle with the main colours, and allows for interpretation of what colour would be emitted given a certain wavelength of colour absorbed
How do we interpret the Newton colour wheel
If an object absorbs a certain colour on the colour wheel, then it will emit another colour, which is opposite to the colour being absorbed on the colour wheel
What are transparent materials
Allow light to pass through (e.g. air, water, clear glass)
What are translucent materials
Allow some light to pass through, but the light is scattered (e.g. frosted glass, some plastics)
What are opaque materials
Don’t let any light pass through. Light is either reflected or absorbed (e.g. wood, stone, metals)
What is the equation for wavelength?
1 / λ = Er ( 1 / m^2 - 1 / n^2)
m = level of lower energy orbit (final energy level)
n = level of higher energy orbit (initial energy level)
What is the energy of one electron atoms given by?
En = -Er Z^2 / n^2
Z = no of protons
n = principal quantum number
What is the beer-lambert law?
A = εcl
A = absorbance. (This is related to how much light can pass through a solution. High absorbance –> less light gets through –> darker solution)
c = concentration (A more concentrated coloured solution will absorb more light)
ε = molar extinction coefficient (for a given molecule, this is a constant - it is a measure of how strongly a chemical species or substance absorbs light at a particular wavelength.)
l = path length. (How far the light has to travel. If the light has to travel through more solution, then more is absorbed)
How does atomic absorption spectroscopy (AAS) work?
- Sample must be in atomic form, as bonding will change energy levels
- A hollow cathode lamp containing atom of interest will release light that will be specifically absorbed by that atom
- Some of the light will be absorbed by the atomised sample, according to its concentration
- the monochromator ensures that only light of interest is measured, and the detector measures absorbance
Describe how the hollow cathode lamp operates
Cathode Design: The hollow cathode lamp consists of a cylindrical tube made of a suitable metal (such as tungsten or tantalum) with a hollow core. One end of the tube is sealed, and the other end is open.
Filling with Inert Gas: The tube is filled with an inert gas, typically argon or neon, at low pressure.
Cathode Material: The inner surface of the hollow cathode is coated with a thin layer of the metal of interest. For example, if you’re analyzing for calcium, the cathode might be coated with calcium metal.
Electrical Discharge: When a high-voltage electrical discharge is applied between the cathode (the metal coating) and an anode (typically made of the same metal as the cathode), the inert gas within the tube becomes ionized.
Excitation of Atoms: The high-energy electrons from the discharge collide with the atoms of the cathode material, causing them to become excited or even ionized.
Emission of Light: As the excited atoms return to their ground state, they emit photons of characteristic wavelengths. These photons represent the elemental signature of the metal being analyzed.
Why is the hollow cathode lamp important for sensitive AAS measurements?
Importance in Sensitive AAS Measurements:
Narrow Line Width: The emission lines produced by the hollow cathode lamp are relatively narrow, which is essential for precise and accurate measurements in AAS. This narrow line width helps in reducing interference from other elements, thus enhancing sensitivity.
Stable Emission: The emission intensity from the hollow cathode lamp remains stable over time, allowing for consistent and reproducible measurements. This stability is crucial for achieving reliable analytical results, especially in trace analysis where minute changes in concentration matter.
Low Background Signal: The background signal from the hollow cathode lamp is low, which means that the signal-to-noise ratio of the measurement is high. This is critical for detecting low concentrations of analytes accurately.
Selectivity: The specific metal coating on the cathode ensures that the lamp emits light predominantly at the wavelengths corresponding to the element of interest. This selectivity enhances the specificity of the analysis, reducing the likelihood of interference from other elements present in the sample
Identify constraints on analysis by atomic absorption spectroscopy (AAS)
Use of hollow cathode lamps is expensive (and it can’t be reusable for all elements)
Sensitivity: AAS may have limited sensitivity for certain elements, especially at low concentrations. This can be a constraint when analyzing trace levels of elements in complex matrices.
Due to the way they interact with light, most non-metals cannot be readily detected through AAS.
Limited sensitivity
Can only measure on element at a time
Linearity Range: AAS instruments have a finite linear dynamic range, beyond which the instrument response may become non-linear. This can limit the range of concentrations that can be accurately measured without dilution or sample preparation.
Describe the process of molecular spectroscopy
Follows same principle as AAS but doesnt need to be atomised. It is also encompassing various spectroscopies such as:
UV-Visible Spectroscopy:
Light Source: Typically uses a UV-Visible light source, such as a deuterium lamp for the UV range and a tungsten filament lamp for the visible range.
Monochromator: Light passes through a monochromator, which selects a narrow range of wavelengths for measurement.
Sample Compartment: The sample is placed in a cuvette or cell in the sample compartment. The cuvette may be made of quartz or other suitable materials transparent to UV-Visible light.
Detector: Light transmitted through the sample is detected by a photodetector, such as a photodiode array or a photomultiplier tube.
Infrared (IR) Spectroscopy:
IR Source: Uses an IR source, such as a heated filament or a ceramic source, which emits IR radiation.
Interferometer: Often employs a Fourier-transform infrared (FTIR) spectrometer, where IR radiation passes through an interferometer to modulate the wavelengths.
Sample Compartment: The sample is placed in a sample holder, typically made of sodium chloride (NaCl) or potassium bromide (KBr), which is transparent to IR radiation.
Detector: IR radiation transmitted through the sample is detected by a detector, such as a thermal detector (e.g., thermocouple) or a photon detector (e.g., mercury-cadmium-telluride detector).
Compare and contrast atomic and molecular spectroscopy
Similarity:
Beer Lambert’s Law applies
Molecules absorb specific wavelengths of light according to orbital energies as well (both molecular and atomic)
Both molecular and atomic spectroscopy involve the interaction of matter with electromagnetic radiation, such as ultraviolet, visible, and infrared light, as well as radiofrequency and microwave radiation in some cases.
Both molecules and atoms have quantized energy levels associated with their electronic, vibrational, and rotational motion
Differences:
Molecular spectroscopy doesn’t need atoms to be atomised because it is measuring energy of electrons in molecules not atoms
molecular spectroscopy is less sensitive to atomic spectroscopy
What does Beer Lambert law tell us about the calibration curve (Absorbance vs concentration)
It should be a linear function - straight line.
Calibration curve constructed using a number of solutions of different concentrations
What is electronegativity?
Ability for an atom to attract electrons to itself
WHat are the trends in electronegativity and why?
Electronegativity increases across a period, because the effective nuclear charge increases and the atomic size decreases –> more likely to attract electrons
Electronegativity decreases down a period because the effective nuclear charge decreases, and the large atomic size also provides lots of electron and orbital shielding –> less attraction from +ve nucleus to the electrons –> lowering electronegativity
Is a high or low electronegativity difference going to form an ionic compound?
A high electronegativity difference >1.5 will form an ionic compound
What does isoelectronic mean?
Same number of electrons / same electronic structure
Where are the electron donors and acceptors on a periodic table?
Electron donors on the left of the periodic table
Good electron acceptors on the right of the periodic table
Are cations larger or smaller than their parent atoms? Why?
Cations are smaller. Electrons are removed from the highest energy, outermost orbitals. The remaining orbitals also contract due to reduced electron - electron repulsion
Are anions larger or smaller than their parent atoms? Why?
They are larger than parent atoms
Electrons are added to the highest energy, outermost orbitals, which expand due to electron electron repulsion
What is ionic bonding?
The long range electrostatic attraction between cations and anions, together with short range repulsion between electrons in adjacent ions
How do we know what equilibrium distance is?
Occurs when the potential energy is a minimum. (I.e. when the attractive and repulsive forces are equal and opposite)
What does isotropic mean? Are electrostatic interactions isotropic?
Isotropic means that they are the energy is the same in all directions and that they are long ranged - this is what electrostatic interactions are
How does ionic bonding work? Why do they exist as crystals/lattices and not as molecules?
Shell of oppositely charged ions (counterions) is attached to a central ion. This in turn attracts another shell of the counterions counterions to surround the counterions. The structure continues to grow leading to ionic crystals rather than small molecules.
This attraction between oppositely charged ions makes the crystal stable
Oppositely charged ions are nearest neighbours
What are the two different packing arrangements?
Face centred cubic array
Primitive cubic array
(look at slides for lecture 15 to visualise)
How does ionic radii influence face centred cubic array?
If the ionic bond has a large difference in ionic radii, the fcc is formed
How does ionic radii influence primitive cubic array?
If the ionic bond has a small difference in ionic radii , the pca is formed
Packing is less stable here than fcc array
How does ionic radii influence the packing arrangement?
Ionic radii influence close-packing by determining the optimal distance between adjacent ions. Larger ions require more space, while smaller ions can be packed more closely together.
The coordination number of an ion in a crystal lattice refers to the number of nearest neighbor ions that surround it. The coordination number is influenced by the size of the ions and their ionic radii.
Larger ions typically have higher coordination numbers because they can accommodate more neighboring ions within their vicinity without significant repulsion or distortion of the lattice structure.
What is the lattice energy? Give an example
It is the energy charge when gas phase ions combine to form a crystal lattice.
For example:
Li+ (g) + F- (g) –> LiF (s) , lattice energy is -1050kJ mol^-1
negative lattice energy denotes that energy of crystal lattice is lower than that of ions. This is the same idea as the -ve potential energy that binds a negative electron to a positive nucleus (indicates a favourable formation as well)
What is the equation of lattice energy?
Total energy of lattice = attraction between nearest neighbors + repulsions between next - nearest neighbours + …
OR (not in the powerpoints)
Fₑ = k(q₁q₂)/r².
F = electric force
q1, q2 = charges
r = distance of separation
k = Coulomb’s constant
What factors affect the next - nearest, next-next nearest, etc. neighbour distances?
Depends on the geometry of the lattice (i.e. square, triangular, hexagonal…, which includes no. of neighbours), and the nearest neighbour distance
What factors affect the lattice energy?
1) sum of the anion and cation radii (a smaller combined radii has more energy than a larger combined radii)
2) Charge of the ions (More charge (either +ve or -ve) has a higher lattice energy)
3) Arrangement of ions (Face centred cubic has more energy than primitive cube)
What is the simpler model of bonding that we use to model polyatomic molecules?
Lewis model of bonding
What is the octet rule?
Suggests that atoms share bonds to achieve a full valence electron shell (8 electrons)
What is the Lewis model of bonding
diagrams that show the bonding between atoms of a molecule, as well as the lone pairs of electrons that may exist in the molecule.
When was Lewis model of bonding developed?
In 1916, before nuclear structure of the atom was understood, before wave nature of electron was discovered and before molecular orbital theory was developed
What are the rules for Lewis structures/models?
1) Count the total no. of valence electrons in the molecule
2) Draw single bonds between the atoms (assume 2 electrons each)
3) Count how many electrons are left, and then assign them as lone pairs to fill valence shells to complete octet rule
4) If incomplete valence shells, form multiple bonds to complete them
5) If there are more than one plausible structures, we consider all of the structures to be resonance structures
6) Minimise the formal charges on all atoms
How do we know what the centre atom normally is in a polyatomic molecule?
It is normally the one that needs to share the greatest number of electrons
What are resonance structures?
Resonance structures are a set of two or more Lewis Structures that collectively describe the electronic bonding of a single polyatomic species including fractional bonds and fractional charges.
Equivalent representations of bonds that can exist in polyatomic molecules
What is the symbol for resonance?
Double ended arrow ( <—–> )
How do we know what the favoured resonance structure is?
It will have the lowest formal charge
When we say lowest formal charge we don’t mean average, we mean the lowest charge of all (i.e. even if all structures have an added formal charge of 0, if one structure has a highest FC of 3 , and another of 1, the favoured one would be the one with FC of 1)
WHat is the formal charge
It is the difference between the no. of valence electrons in a neutral atom, and the number assigned to it in a Lewis structure
FOrmal charge is the charge assigned to an atom in a molecule, assuming electrons are equally shared between atoms
What is the formal charge equation?
Valence electrons of free atoms (overall VE of the atom) - 2x no. of lone pair electrons of atom (Lone electrons in an atom) - 1/2 (shared electrons)
What happens if you’re trying to figure out which resonance structure is favoured using formal charges, but the formal charges are the same?
(i.e. when formal charges are 1, 0, 0 for 2 different structures)
We can use electronegativity. We determine which parts of the molecule are more electronegative than the other, and then we can say that it is most likely that that part of the molecule has more electrons associated with it
Can we break the octet rule?
Octet rule suggests a max of 4 electron pairs (8 electrons) surrounding them. However, this can be broken?
(important to note that even tho graphically it looks like its broken, in reality it isn’t, but it could still be considered a ‘break’)
What elements might be able to breatk the octet rule
Elements below the 2nd period may bind to more than 4 other atoms. If these rules are followed, the octet may have to be broken.
How do you find bond order of multiple resonance structures?
Average number of bonds across the resonance structures
What can be used to show the 3D structure of the molecule?
VSEPR theory. It allows us to find 3D arrangement of electron groups, and 3D arrangement of atoms(i.e. when lone pairs ignored) –> shape of molecule
what does VSEPR theory suggest?
We need to consider all groups of electrons; bonding groups (single, multiple and partial bonds) and lone pairs
As electrons are -ve charged, the electron pairs will repel each other. To minimise potential energy of repulsive interactions, electron groups are arranged so they are as far as possible from each other
VSEPR suggests geometry corresponds to minimum potential energy, and gives sets of rules which describe observed geometries of molecules
What are the rules for VSEPR?
Write correct Lewis structure
Choose atom interested in (usually central atom) and count no. of electron groups. This determines arrangement (linear, trigonal planar, tetrahedral, trigonal pyramidal or octahedral)
Focus on atoms: what is the shape that the atoms occupy
What are the different arrangements for molecules with different numbers of electron groups ?
2 electron groups: Linear arrangement
3 electron groups: trigonal pyramidal arrangement
4 electron groups: Tetrahedral arrangement
5 electron groups: Trigonal bypyramidal arrangement
6 electron groups: Octahedral arrangement
What are the bond angles of the different numbers of electron groups?
2 electron groups: 180 degrees
3 electron groups: 120 degrees
4 electron groups: 109.5 degrees
5 electron groups: 90 degrees and 120 degrees
6 electron groups: 90 degrees
What is the difference between the arrangements and the shape
Molecular shape is used to describe a molecule with only the atoms present whereas molecular geometry is used to describe the molecule taking into account how unbonded valence electrons affects the overall structure.
Even if there are lone pairs etc they will adjust to look like the different arrangements, but then after the lone pairs are accounted for, they will form the shapes
What do the different shapes look like?
Check the book
How do we know if a polar bond will form?
If two atoms form bonds with high difference in electronegativity –> polar bonds –> dipoles
Here, the electrons would be more attracted to the electronegative atom creating a polar bond
Is their polarity in a symmetric molecule?
No, this is because dipoles add together to cancel out
Is there polarity in an asymmetric molecule
Yes, this is because the dipoles dont completely cancel out –> finite dipole –> polar
What is the molecular shape of a molecule with 2 electron groups, 0 lone pairs
Linear
What is the molecular shape of a molecule with 3 electron groups, 0 lone pairs
Trigonal Planar
What is the molecular shape of a molecule with 3 electron groups, 1 lone pairs
Bent
What is the molecular shape of a molecule with 4 electron groups, 0 lone pairs
Tetrahedral
What is the molecular shape of a molecule with 4 electron groups, 1 lone pairs
Trigonal pyramidal
What is the molecular shape of a molecule with 4 electron groups, 2 lone pairs
Bent
What is the molecular shape of a molecule with 5 electron groups, 0 lone pairs
Trigonal bipyramidal
What is the molecular shape of a molecule with 5 electron groups, 1 lone pairs
See saw
What is the molecular shape of a molecule with 5 electron groups, 2 lone pairs
T shaped
What is the molecular shape of a molecule with 5 electron groups, 3 lone pairs
Linear
What is the molecular shape of a molecule with 6 electron groups, 0 lone pairs
Octahedral
What is the molecular shape of a molecule with 6 electron groups, 1 lone pairs
Square pyramid
What is the molecular shape of a molecule with 6 electron groups, 2 lone pairs
Square planar
What is the molecular shape of a molecule with 6 electron groups, 3 lone pairs
T shaped
What is the molecular shape of a molecule with 6 electron groups, 4 lone pairs
Linear
Why might we prefer certain molecule representations over others?
Some representations are more informative than others.
Also, as molecules get bigger, some representations become time consuming to draw –> need to think of new ways to represent molecules
What are the advantages of line representations (i.e. skeletal drawings)
SImple to draw but still full of structural info
Quick to draw
Bond angles and heteroatoms(non carbons) represented
What are the disadvantages of line representations?
Determining molecular formula takes time for beginners
How does line drawing work? Steps.
1) Lines represent bonds - 1,2, or 3 lines for single, double, triple bonds respectively
2) C is basis of structure:
Carbon atoms arent shown and are assumed to be at the intersections/ends of lines
C-H bonds omitted
All heteroatoms are shown (and the H’s bonded to the heteroatom)
3) Valence:
4 for C, 3 for N, 2 for O, 1 for H or Cl or Br or I
4) Geometry:
Use VSEPR. and indicate bond angles(~120 degrees or 180 degrees)
5) In condensed formulae, atoms bonded to a C atom are listed after it
i.e. CH3COCH2CH2CH3
How are the different bonds shown in 3D?
C-H bond in the plane of the page
Triangle wedge between C and H, shows bonds coming towards you
Several lines between two atoms are bonds going away from you
What are the advantages of traditional representation of molecules?
All atoms and bonds drawn
All molecules represented as 2D images
What are the disadvantages of traditional representation of molecules?
Bond angles aren’t 90 degrees which is whats depicted here
Tedious to draw
What are the advantages of condensed formulas?
Indicates connectivity
Easily written
Enables naming of constitutional isomers
What are the disadvantages of condensed formulas?
No stereochemistry representation
No indication of molecular shape
Slightly tedious
What are the advantages of structural formulae?
Indicates 3D structure
Atomos and bond angles represented
Allows accurate names of molecules
Advanced mechanistic understanding
What are the disadvantages of structural formulae?
Takes time to draw
What are the advantages of ball and stick model?
Bond angles represented
Some indication of space occupied
stereogchemistry indicated where applicable
What are the disadvantages of ball and stick model?
Requires computers/models
What are the advantages of space filling models
Gives indication of ‘extent of molecule
Indicates perspective (3D image)
What are the disadvantages of space filling models
Needs computers
Bond angles hidden
Difficult to use to study for mechanisms
What is hybridisation?
In chemistry, hybridization is defined as the process of combining two atomic orbitals to create a new type of hybridised orbitals.
For the different types of bonds (single, double, triple) , just count how many bonds will be created from the atom, and then you can see whether it is sp3, sp2 or sp hybrid orbitals
What is a sp3
This is a common form of hybridisation in tetrahedral environments
Here, the hybrid is formed by combining a s orbital, and 3 p orbitals, forming 4 hybrid orbitals
These four sp3 hybrid orbitals are oriented in a tetrahedral arrangement, with angles of approximately 109.5 degrees between them.
FOrmed with single bonds (most of the time)
What is a sp2
This is a common form of hybridisation in planar trigonal environments
Here, the hybrid is formed by combining a s orbital, and 2 p orbitals, forming 3 hybrid orbitals
These three sp2 hybrid orbitals are oriented in a trigonal planar arrangement, with angles of approximately 120 degrees between them
Formed with double bonds (most of the time)
What is a sp
This is a common form of hybridisation in linear environments
Here, the hybrid is formed by combining a s orbital and a p orbital, and forming 2 hybrid orbitals
These two sp hybrid orbitals are oriented in a linear arrangement, with an angle of 180 degrees between them.
Formed with triple bonds (most of the time)
How many total bonds does a C want?
4
How many total bonds does a N want
3
How many total bonds does a O want
2
How many total bonds does a H, Cl, Br or I want?
1
