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CHEM170 > Equations And Theory > Flashcards

Equations And Theory Flashcards

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1
Q

What does phase velocity = ?

A

Phase velocity = frequency x wavelength

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2
Q

Convert radians to degrees

A

Radian = 2Pi / 360

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3
Q

What equation relates energy, h and frequency?

A

E = h v

(h = Planck’s constant)

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4
Q

How can E = hv also be written as?

A

E = h (c / lamda)

(As v = c / lamda)

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5
Q

What equation gives the energy of the rotational quantised levels?

A

E = BJ(J+1)

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6
Q

What is the equation of I - moment of inertia?

A

I = u r^2

Where r = bond length in m, and u = reduced mass

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7
Q

What are the selection rules for rotational spectroscopy?

A

For a pure rotational spectrum to be excited by microwave radiation, the molecule MUST possess a permanent dipole moment

E.g. HCl or CO

J (rotational quantum number) can only change by + or - 1.

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8
Q

How does vibrational spectroscopy differ to rotational spectroscopy?

A

Molecular vibration requires more energy than rotation

Pure vibration spectra occur in infrared region of EM spectrum (5000-100cm^-1)

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9
Q

What is the units of Joules and how can you remember this?

A

Kg m^2 s^-2
1 joule = 1 Nm

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10
Q

What is the units of Newtons and how can you remember this?

A

Kg m s^-2

F = m x a

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11
Q

How can molecules execute different types of vibrations?

A

By changing bond lengths or bond angles

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12
Q

What must happen to carry out vibrational spectroscopy?

A

Molecular vibration must give rise to a CHANGE in dipole moment

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13
Q

What’s the potential energy contribution in the PiB model?

A

0 - so there is only kinetic energy

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14
Q

What is the De Broglie formula?

A

Lambda = h / p

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15
Q

What expression can be used to describe the wavelengths that fit in the PiB model?

A

n(lambda / 2) = r

Where r = box length

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16
Q

How can the De Broglie formula be used to find the kinetic energy from momentum?

A

Rearrange de broglie for p

Rearrange PiB expression for lambda
- sub this into de broglie to get p = hn / 2r

Sub p = hn / 2r into kinetic energy of electron from momentum

Should get E = (h^2 n^2) / 8me r^2

n can only be a whole number, therefore E can only take certain specific quantised values. Hence th energy is quantised.

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17
Q

Why is the energy in PiB model quantised?

A

Because only certain, very specific wavelengths are allowed as n can only be an integer.

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18
Q

What is the lowest energy level in PiB model? Why is this?

A

E = 1 - as E1 is the energy of 1 half wavelength in the box, so E0 cannot exit as this would mean you have 0 half wavelengths in the box

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19
Q

Why is an absorption spectrum missing only special wavelengths? How does this relate to the Planck formula?

A

Because the electrons can only be in energies determined by the energy levels

Absorbing a particular wavelength = absorbing a particular energy - Planck formula

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20
Q

How do you find the number of vibrations a linear/non-linear molecule has?

A

Non-linear = 3N - 6 vibrations

Linear = 3N - 5 vibrations

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21
Q

How do you convert cm^-1 to m^-1?

A

X 100

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22
Q

How do you determine degeneracy?

A

2 J + 1 = degeneracy

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23
Q

What does degeneracy’s actually mean?

A

Degeneracy - in terms of QM - means the number of energy levels / sub-orbitals at a specific energy level.

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24
Q

What is the reduced mass equation?

A

u = ( m1m2 ) / ( m1 + m2 ) x 1.661x10^-27

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25
Is the lowest energy in HO model 0? Why is this?
It’s not 0, its E0 = 1/2 h v
26
What is the name given to the energy present at absolute zero in the HO model?
Zero-point energy
27
What is the difference between the spacing of energy levels of HO and PiB models?
PiB has level spacing = (h^2 (2n+1) ) / 8me r^2 Harmonic oscillator has level spacing = hv
28
What does the harmonic oscillator model not allow? Why?
Molecule dissociation - when V > 0 molecule is not bound, HO shows any energy is possible after dissociation occurs - impossible
29
How can a full electron orbit about an atom be show in PiB model?
1 full wavelength - Wavefunction must be periodic
30
What is the equation for the moment of inertia for an electron orbiting a nucleus?
I = me r^2 (Where me = mass of electron)
31
What is the lowest possible energy of rotations? Why?
E = 0 - the electron is not rotating This is because a straight line is the same at start and beginning - hence no zero-point energy.
32
When n = 0 what orbital does it produce and why? How many nodes?
S-orbital No change of sign - no nodes
33
When n = 1 what orbital does it produce in 3D and why? How many nodes?
P-orbital One sign change produced from single wavelength - also results in 1 node
34
When n=2 what 3D orbital does it produce and why? How many nodes?
D-orbital Two wavelengths produce 2 sign changes - results in 3 nodes
35
What are l and m?
l is orbital angular momentum number - determines shape of orbital ( l = number of nodes ) ml is magnetic quantum number - determines the number of orbitals and their orientation ( ml is an interval from -l to +l )
36
What is the quantum rotation number?
J
37
How do atoms reach a favourable bond length?
Repulsive force pushing atoms apart if too close An attractive potential - making atoms in bond move closer when too far apart These forces result in a ‘well’ being formed of the lowest energy - hence most favourable
38
What does thermodynamics state must be conserved?
Energy Momentum Angular momentum (This is in an isolated system)
39
What is V(r) a function of?
It is a function of the atoms position This is only ever completely repulsive or attractive.
40
What equation gives the potential energy of a spring?
V(r) = 1/2 k ( r - re )^2 Where re = equilibrium bond length r = bond length (The spring doesn’t exist but is a good model for the potential energy of the molecule)
41
What’s the better model for potential energy PiB or HO?
Harmonic oscillator - HO potential has softened ends
42
What is the importance of the Beer-Lambert law?
Intensity of spectral lines depends on it - and Boltzmann distributions
43
What is the Beer-Lambert equation?
I = I0 10^-eCL I is transmitted intensity I0 is the incident intensity L is the length of sample - longer = greater absorption C is molar conc (moldm-3) e is the molar absorption coefficient (mol-1dm3 cm-1)
44
What does absorbance = ?
Abs = log I0 / I
45
What does transmittance = ?
Trans = I0 / I
46
What does E(bonding) = Alpha + Beta represent?
Alpha is the coulomb integral - the energy of one of the orbitals in the presence of both nuclei Beta is the resonance integral - extra energy contribution when orbitals overlap, when electrons are shared between 2 atoms. This is the energy contribution from the mixing term.
47
When atoms are far apart what does beta = ?
0 as the energy of the orbital only sees one atom.
48
When atom A and B are close together, what happens to alpha?
Alpha becomes more negative as the energy increases due to the attraction of the wavefunction to both nuclei.
49
What happens to beta when atoms A and B are close?
Beta is negative and decreases with r (bond length)
50
Alpha and beta are both negative when close, what does this mean for anti-bonding?
a + B < a - B a - B means energy is lost between the bond, so occupying this orbital makes bond weaker
51
What is the energy difference between the bonding and anti-bonding levels?
2 Beta (Beta is the resonance - mixing term - that gives us a covalent bond)
52
Why is l = 0 for an s-orbital?
Because any rotation leaves the orbital unchanged
53
How do you calculate bond order?
Bond order = 1/2 ( e- in bonding - e- in anti bonding )
54
What is the general term for the number of nodes a wavefunction produces?
Nodes = n-1
55
What does greater overlap result in?
Bigger molecular orbital
56
Why can’t you combine a 1s orbital of an atom and a 2s orbital of another?
Atomic orbitals with very different energies do not combine well and form weak molecular orbitals - bonds.
57
What do p-orbitals that are at right angles to the bond form?
Pi-orbitals
58
Draw out sigma and pi bonding and anti-bonding orbitals using simple coin models
59
What does paramagnetic mean?
Attracted to a magnetic field
60
What is the order of molecular orbitals up to Nitrogen?
1∂ 2∂* 3∂ 4∂* 1pi 5∂ 2pi* 6∂*
61
Why does the 1pi and 5∂ molecular orbitals swap between O2 and F2?
Because the effect of the 5∂ MO is much greater in smaller molecules, hence its energy drops as molecules increase in size.
62
Draw a bonding and anti bonding s orbital in terms of PiB and a wavefunction
63
What is the difference between bonding and anti-bonding ∂ orbitals in terms of nodes?
Bonding ∂ orbital has no nodes - wavefunction doesn’t change sign Anti-bonding ∂ orbital has a node in centre of the bond - where wavefunction changes sign.
64
What 3 options are there for triatomic molecules in terms of bonding and nodes?
Totally anti-bonding orbital - n = 3 with node separating all orbitals No contribution from central atom - n = 2 with a node on top of central atom - non-bonding orbital Totally bonding orbital - n = 1 - with no sign changes or nodes, every atom has a positive contribution to bonding. The same applies for p orbitals
65
What 3 vibrations can a molecule do?
Symmetric Asymmetric Bend
66
What does 3 degrees of freedom mean for a molecule of N atoms?
It will have 3N degrees of freedom Of this, 3 are translations, and 3 are rotations for non - linear For linear molecules, there are 2 rotations
67
What is the equation describing the oscillating behaviour of the bond length?
V = 1/2 k x^2 Where x = r - re (bond length - equilibrium bond length)
68
The energy of the quantised vibrational levels are described by what equation?
69
What equation gives the fundamental frequency v?
The greater the force constant k - the stronger the bond
70
What frequency of photons do you need to cause a jump in energy levels in SHO model?
V (nu) - as levels are spaced evenly at hv throughout vibrational spec in SHO
71
Why would you only see one ‘line’ in vibrational spectrum?
Because all ∆E = hv for ALL transitions - therefore only one ‘line’ present at frequency v (nu)
72
What are the units of k - force constant?
Nm^-1
73
What does/doesn’t change when the isotope of an atom is changed on vibrations?
Changing the isotope doesn’t change the strength of the bonds - k stays the same Fundamental frequency changes because of reduced mass
74
What is the benefit of using an Anharmonic Oscillator AHO?
It allows a molecule to dissociate
75
How do you find the energy of bond dissociation?
The difference between V=0 (zero point energy) and the energy where the curve plateau’s - D0
76
What happens to the bond length in an AHO when energy of system increases?
The equilibrium bond length increases until dissociation occurs
77
What are the selection rules on of an AHO on vibrational spectra?
AHO allows ∆v to be + or - 1,2,3 More relaxed than SHO
78
What are overtones in spectra?
Overtones are where you see additional bands at roughly 2v, 3v etc, with decreasing intensity. Don’t occur exactly at 2v, 3v because vibrational energy levels converge as v increases due to anharmonicity
79
How do you work out if a molecular vibration gives rise to a change?
Draw vibration at extremes of motion Draw out individual bond dipoles Draw out overall dipole Compare overall dipole at 2 extremes, see if it changes
80
What are skeletal vibrations?
Where most of the atoms in the molecule are induced (generally below 1500cm^1 and lie in ‘fingerprint’ region of spectrum
81
How do characteristic group vibrations differ to skeletal vibrations?
Only small parts of the molecule are moving - very defined functional groups only Vibrational frequency observed is characteristic of that functional group, so gives direct clues of molecular structure
82
What’s the equation for finding the energy of an electron in PiB?

CHEM170 (2 decks)

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