Exam 1 Set 1 - Orbitals

inorganic chemistry

specifically the study of everything that isn’t carbon and its reactions

why do atoms form molecules?

this increases their stability

driven by energy → atoms want to be at the lowest potential energy

still have to adhere to bonding rules and such - only some bonds are favorable

IMF strength relative to the intermolecular bonds can grant a lot of flexibility into where the e- are in the molecule (creating charged regions and such)

why do elements react different to one another?

different elemental properties arise from the balance of and interaction between the neg e- and the pos protons and how close they are to each other

differing proton counts and identities

differing potential E - PE = kq1q2/d where:

• q1 = charge on +

• q2 = charge on -

• d = separation

periodic table grouping

elements in the periodic table are grouped according to similar reaction patterns

groups (columns) - tend to react similarly

periods (rows) - same valence orbital type

as you go down, size increases a lot as e- move farther from the nucleus into new orbitals

atomic line spectra

classical physics expects an unbroken spectrum as energy increases, cus theoretically any energy is possible and able to produce light

E = hv = hc/lambda where:

• h = planck’s constant

• c = speed of light

however, for each element only certain wavelength are observed as the emission spectrum - the e- then have only certain allowed energies - only certain bond distances between the nucleus and the e- are allowed, depending on the atom

E = hc/lambda = kq1q2/d where lambda and d are comparable - this implies that e- are also only located at specific distances from the nucleus

e- are ordered within the atom, occupying only set allowed distances

Bohr’s orbitals

Bohr model only works as a predictor for H

though e- made circular orbits around the nucleus, with schrod thinking angular momentum kept them from sinking into the nucleus

E = R((1/nl²) - (1/nh²)) where R is 2.179e^-18 J

multi-electron atoms must be predicted using ellipses rather than round orbitals

• ellipses are defined with the two variables n and l, hence why they’re in the E equation

• larger maxn, bigger atom

emission spectra emitted from the wavelength of light corresponding to the E expended in a jump down to a lower energy level

einstein photoelectric effect

predicted that a steady increase in inbound light frequency exciting electrons in metal would produce a steadily increasing current

instead found that current remained 0 until a threshold frequency had been reached or surpassed, at which point the current would jump to a new constant

if light only acted as a wave, then every wavelength should cause some amount of current

if light consisted of particles, only particles with enough E would be able to knock e- out of the metal atoms to allow them to conduct charge

therefore, light can also behave as a particle and must be treated as either a wave or a particle

particles of light are photons

more evidence that e- must have a discrete (specific) E

discrete E needed to excite an e- also relates to the orbitals at distinct distances from the nucleus

DeBroglie and particles

already had how waves can act like particles from Einstien - this in the inverse

lambda = h/p where lambda is wavelength and p is momentum

h/p = h/mv as mv = p

h = 6.626 × 10^-34 J*s

doing the math for objects of different mass shows that only objects with very very little mass moving very very fast (like an e-) are significantly affected by wavelike motion - only then is the wavelength of motion observable

Heisenberg uncertainly principle

the true position of a moving particle doesn’t matter - you just need to know how accurately the position can be discerned (how accurate of an estimate can be made) to predict other things

deltax(deltap) >/= hbar/2

hbar = h/2pi

questions like “a proton is accelerated to a speed known within x, what is the minimum uncertainty in its position)

recall that delta means a change in the measurement it is applied to

uncertainty thing similar to taking a picture of a moving car - you’re most likely to have captured some of the car in the middle of the images as the edges blur - how the uncertainty of a particle is

can’t discern the speed and position of a particle as any attempt to observe it would disrupt this

as momentum uncertainty becomes smaller, position uncertainty increases

Schrodinger’s standing waves

a standing wave is fixed at both ends - the value of the function defining the wave at either end must thus = 0

the value of the function can also go to 0 within the region of the wave, forming nodes

know from previous stuff that only certain wavelengths are allowed for e- (emission spectrum) so only certain energies are allowed (einstein stuff) - treating e- as standing waves thus explains their discrete spectra

E = nhc/L where n is an integer

coordinates

polar coordinates - x and y

• cartesian system

polar coordinate system - r and rho

• a point is located at a distance r from the origin at an angle of rho from 0 degrees

if the x-axis is treated as 0 deg, we can convert between cartesian and polar coords

in 3D space, another angle is needed to define position - theta is used to define the angle from the Z axis

z = rcos(theta)

x = rsin(theta)cos(rho)

y = rsin(theta)sin(rho)

orbital quantum numbers

each electron’s E, and thus it’s most probable distance from the nucleus (as those are comparable as previously shown) can be calculated from the wave function phi

still don’t know exactly where the e- is, just where it is most likely to be - these are the orbitals

orbitals are areas defined by quantum numbers n, L, and m - possible values for these numbers are defined by the solutions to the wave function

n = 1,2,3…

L = 0,1…(n-1)

m = -L…L

L values:

• 0 = s

• 1 = p

• 2 = d

• 3 = f

n = orbital size

L = orbital shape

radial wavefunction graph

each line represents an orbital, and the area under the peaks represents the likelihood of an e- in that orbital being that relative distance away from the nucleus (effectively the origin)

e.g. 1s electron almost always close to the nucleus (so low E)

account for all of the peaks and their areas

radial notation

its Dz² because the function contains cos²(theta)

z = cos(theta)

orbital shapes and divisions

orbitals are aligned along the axis of their given subscript (e.g. px along the x axis)

for d orbitals, a squared subscript indicates the orbitals should be aligned on the axes - a normal subscript indicates they should be aligned between the axes

p orbitals are a single dumbell - 1 node (the perpendicular axis)

d orbitals are two dumbells - 1 node on each diagonal between the dumbell lobes

• the dz2 orbital is the only one that looks off, as it has one normal sized dumbell oriented up and a second shrunk dumbell perpendicular, meant to represent the dumbbell coming out of the screen and into it

angular nodes should be represented by straight dotted lines

for orbitals with radial nodes (have n>1), these are represented by dotted circles

• draw diff polarity recursions of each orbital lobe within each angular ring

• need quantum numbers n, L, and m to determine the number of angular and radial nodes

radial coordinate wavefunction portion

defines the distance from the nucleus

the d in PE = kq1q2/d is comparable to the n1L in R²n1Ldr

radial function solely depends on n and L values, not m

as n increases, E and distance also increase

L relates to orbital shape - as L increases, the shape becomes more complex and has more nodes - complicated shapes are higher in E

in general, n starts at 1 and L starts at 0

typically, energy wise, 1s<2s<2p<3s<3p…

however, when orbitals get big (e- are far from the nucleus), their distances and energies can overlap, leading to deviations from these rules:

3s<3p<4s<3d<4p…6s<4f<5s<6p - they’re all very close in E so things get a little messy

the angular part of the wavefunction defines the shape of the orbital (the area of probability at that particular energy)

the shape of these orbitals comes from actual functions plotted on polar coordinates

more on orbitals and their principles

an orbital is just a name for the location where an e- is most likely to be found

e- aren’t “put” into orbitals, but rather they take on a particular function and energy

atoms by default adopt a minimum energetic state (ground state) so e- take up the lower energy states (orbitals) first before filling higher ones - Aufbau principle

pauli exclusion principle - e- cannot have the same 4 quantum numbers

4th quantum # is spin, Ms (or just s), related to the sign of the wave function, ±1/2

number e- that can be found it a type of orbital = L*2

Hund’s rule - if orbitals are at the same e-, e- fill them one at a time with the same spin before pairing up in lobes

due to e- repulsion, prefer to spread out their negative charge

drawing orbitals

angular nodes (linear) = L

radial nodes (circular) = n - L - 1

value of m dictates whether it’s x, y, or z -

• p - x=+1, y =-1, z=0

• d = x²-y²=+2, xz=+1, z²=0, yz=-1, xy=-2

squared subscript indicates that the orbital is aligned on the axis if d (p always aligned)

shade pos part of dumbell

sign ALWAYS changes at a node

only know something about e- at a node (know that it isn’t there)

periodic notation

nA#

n = period

#= group

d always 1 less period than n states

radial v angular

radial - shape but no sense of direction

cartesian - sense of distance but no shape

electron structure

where e- are in an atom

2 ways of expressing it

electron config - e.g. N = 1s22s22p3 (1st number is the E level, second is the # of e- present)

atomic energy diagram

valence e- and core e-

highest n e- plus any e- w/ a lower n in an unfilled shell

the outermost e-/the farthest e- from the nucleus

easiest to remove

any new incoming e- are added to the valence

core e- = everything with a lower e- that has been filled

core e- prevent valence e- from experiencing the full positive charge of the nucleus (hence why they are easiest to remove - they aren’t being attracted as tightly)

shielding isn’t 100% effective, so a little pos charge builds up in the valence orbitals across a period

slater’s rules

electron groupings are written in the #s/p/d/f# format (like 1s2)

as written out in electron config, e- in higher groups (to the right) don’t shield lower groups from the nucleus

for s and p valence e-:

• e- in the same (ns, np) group contribute 0.35 to the score, except the 1s group, which contributes 0.30

  • always count 1 less e- than there is in the valence because you are calculating for that 1 e- left out!!

• e- in the n-1 group contribute 0.85

• electrons in the n-2 or lower groups contribute 1.00

for d and f valence e-:

• electrons in the same (nd or nf) group contribute 0.35

• electrons n groups to the left contribute 1.00

z = # protons = amount of + charge in the nucleus that you are adding points against

s = shielding constant, the tally of your points, how much - charge the e- contribute to the atom

Z* - the difference and the actual amount of charge experienced by the valence e-, the effective nuclear charge

e.g. calculate Z* of a 2p e- in O - here n is 2 b/c 2p

O = (1s2)(2s2 2p4)

(2s2 2p4) = 5×0.35 = 1.75

(1s2) = 2×0.85 = 1.70

S = 3.45

Z* = 8.00 (total # e-) - 3.45 = 4.55

comparing Z*

higher Z* means that the valence e- are being held tighter

means its easier to make an anion of that element because it grabs new incoming electrons better (which would be going into the valence)

therefore also hard to make into cations

higher Z* also means that element makes more polar bonds and is more EN

differences in element reactivity, atomic properties, etc. can all be explained with Z*

shielding is imperfect and e- move around and may randomly bunch up, so some pos charge will get through to the outside of the atom

the larger the atom, the more Z* is spread out

ionization E

the energy required to remove an e- from an atom or ion in the GAS phase

represented as deltaH with subscript IE and superscript n depending on whether it is the neutral atom or an ion

represented as a pos

going from the last valence in an upper shell to starting to remove the e- in the shell below is a significant increase of energy because you are suddenly going for the core e- in a filled shell

e- that are paired in an orbital are also harder to remove than unpaired ones

electron affinity

E required to an an e- to an atom in the gas phase (so opposite of IE)

represented as deltaH subscript EG (dunno why) superscript n

enthalpy from e- gain

first loss to become an anion should be a negative value

second loss should be 0 or positive

exception - sum of EG for adding two e- to a neutral 0 is negative because there is enough Z* to stabilize the change

radii

atomic - as Z* increases across a period, atoms decrease in size - they hold onto the e- stronger and pull them closer, shrinking the radius

• cations are always smaller than the parent atom b/c z* increases

• anions are always larger than their parent because Z* decreases

isoelectronic = elements at the same e- config by virtue of some or all being ions so their e- count ends up matching

electronegativity

ability of an atom to draw its e- density inwards

related to Z* but also affected by atomic/ionic size, as this affects Z* per unit surface area

atoms that have relatively large Z* but are big end up not being very EN because the influence of the Z* is more spread out

• Z*/r² proportionality

look at relative orbital sizes in the letters

noble gases

high effective nuclear charge (Z*) on valence, so hard to take them out

also hard to add e- because they would have to go into the next orbital and would be significantly shielded, meaning the atom wouldn’t be able to hold onto the new e-

n levels and orbitals

1 - just s

2 - s and p

3 - s, p, d

4 - s, p, d, f