Chem final
photoelectric effect equation
(1/2)MeV² = hvphoton - Φ Φ = energy needed to release e-
uncertainty principle formula
(ΔX) * (ΔP) >/= h/(4pi) Δx= uncertainty in position Δp = uncertainty in momentum
λ, v, c equation c = v = λ =
(λ)*(v) = c c = speed of light = 3 x 10^8 m/s v = # of waves (frequency) 1/s λ = wavelength (nm)
periodic trends: ionization -concept -what happens -done using, how is e measured -higher ionization potential when..
- If we put in enough energy, we can remove an electron from an atom. -The electron is completely "removed" from the atom (potential energy = 0). Generally done using photons, with energy measured in eV (1 eV = 1.6 x 10-^19 J). The greater the propensity for an atom to "hold on" to its electrons, the higher the ionization potential will be.
Why not 3d before 4s?
-3d is closer to the nucleus -4s allows for closer approach; therefore, is energetically preferred
Periodic Trends: Electron Affinity
-Electron Affinity: the energy change associated with the addition of an electron to a gaseous atom. -energy released is a negative quantity
The Aufbau Principal -when do we use it -what does it state -how are orbitals filled
-For polyelectronic atoms, a direct solution of the Schrodinger Eq. is not possible. -When we construct polyelectronic atoms, we use the hydrogen-atom orbital nomenclature to discuss in which orbitals the electrons reside. -When placing electrons into orbitals in the construction of polyelectronic atoms, we use the Aufbau Principle. -This principle states that in addition to adding protons and neutrons to the nucleus, one simply adds electrons to the hydrogen-like atomic orbitals -Finally, orbitals are filled starting from the lowest energy.
spin -ms
-Further experiments demonstrated the need for one more quantum number. -Specifically, some particles (electrons in particular) demonstrated inherent angular momentum. -For the electron, ms has two values: +1/2 and -1/2
First Ionization Potentials...what happens when u move around the periodic table (2)
-It Increases as one goes from left to right. Reason: increased Z+ -it Decreases as one goes down a group. • Reason: increased distance from nucleus
Removal of valence versus core electrons -takes more energy or less
-Na ---> (Na+) + e- I = 495 kj/mol [Ne]3s1 [Ne] removing valence electrons -(Na+) ---> (Na2+) + e- I = 4560 kj/mol [Ne] 1s² 2s² 2p^5 removing core electrons -Takes significantly more energy to remove a core electron....tendency for core configurations to be energetically stable.
describe the photoeletric effect
-Shine light on a metal and observe electrons that are released. -Find that one needs a minimum amount of photon energy to see electrons ("v˚"). -Also find that for v ≥ v˚, number of electrons increases linearly with light intensity . -as frequency of incident light is increased, kinetic energy of emitted e- increases linearly.
The Bohr Model continued. -problem -solution -equation
-The problem is that because electrons are charged, they radiate away energy (and therefore speed) as they circle the nucleus -Atoms are predicted to survive < 10-12 s -Solution: electrons do not radiate energy, but jump from one discrete orbit to the other; only discrete orbits of (quantized) radius r are allowed so that: rmv=nh/2pi n= integer (1, 2, 3....)
periodic trends: properties correlate?
-The valence electron structure of atoms can be used to explain various properties of atoms. -In general, properties correlate down a group of elements.
Plancks equation + idea
-energy(in form of light) lost in integer values.. according to: ΔE = nhv h= 6.626 x 10^-34 J.s v = frequency (# of waves) (1/time; 1/sec)
metals, nonmetals, & metalliods gaining/losing e-
-metals: tend to give up e- -nonmetals: tend to gain e- -metalloids: can do either
What is the longest wavelength of light that will result in removal of the e- from H?
-replace N final with infinity --> equation becomes -2.178 x 10^-18 J * (0-1) ΔE = 2.178 x 10^-18
ΔT = 0, ---> ΔH = ?
0
3 laws of thermodynamics
1.) DE = q + w 2.) DS univ >/ 0 3.) The entropy of a perfect crystal is zero at absolute zero (0 K).
Entropy increasing
1.) Entropy increases during phase changes s → l l → g s → g 2.) Entropy increases when number of particles increases. BF3 (g) + NH3 (g) → BF3NH3 (s) [negative ΔS] N2O4 (g) → 2 NO2 (g) [positive ΔS] 3.) Entropy increases when temperature increases. - Number of modes of motion increases 4.) Entropy increases when a gas is produced in a chemical reaction. HNO3 (aq) + Rb2CO3 (s) → 2 RbNO3 (aq) + CO2 (g) + H2O (l) 2 HBr (aq) + Cd (s) → CdBr (aq) + H2 (g) 5.) Entropy increases when the volume of a gas increased.
quantum numbers: what is l; range. what is m; range.
1.) the energy levels are quantized 2.) 2 other quantum numbers become evident: 1. l, the orbital angular momentum quantum number. -Ranges in value from 0 to (n-1). 2. m, the "z component" of orbital angular momentum. -Ranges in value from -l to 0 to l. We can then characterize the wavefunctions based on the quantum numbers (n, l, m).
nm/m conversion
10^9 nm / 1 m
Quantum Number order
1s² 2s² 2p^6 3s² 3p^6 4s² 3d^10
given .25 ppm...
6.022 x 10^23 air particles * (.25 molecules / (1 x 10^6))
1 molecule photons /
6.022 x 10^23 photons
254 nm to m conversion
= 254 x 10^9 m
ionization energy greater for removing core or valence electrons
> when removing core (Na+-->Na2++2e-) -core configs more energectically stable
As reaction goes right
As reaction goes to right, Q increases; thus ΔG increases - As reaction goes to left, Q decreases; thus ΔG decreases
Atomic Radii -what happens when u move around periodic table
Atomic Radii are defined as the covalent radii, and are obtained by taking 1/2 the distance of a bond -Decrease to right due to increase in Z+ -Increase down column due to population of orbitals of greater n.
More on Bohr
Bohr model for the H atom was capable of reproducing the energy levels given by the empirical formulas of Balmer and Rydberg exactly: 1. E= -2.178 x 10^-18 J ((Z²)/(n²)) -Z = atomic number (1 for H) -n= integer (1,2,3...) 2. Ry x h = -2.178 x 10-18 J (!) En= (Z²)(e^4)m / 8(ɛ˚²)h² all multiplied by (1/(n²))
"The Ultraviolet Catastrophe
Classical prediction is for significantly higher intensity as smaller wavelengths than what is observed.
shift equilibrium to products what does DG do
DG dcr, E cell incr.
at equillibium
DGrxn=0, DG = -w, K=Q
State Functions ΔT=0
DH=0 ΔE = 0 ---> w = -q w=-PDV wrev = -nRTln(Vf / Vi) ΔS = nRln(Vf / Vi) or nRln(P1/P2)
De Broglies Wavelength Equation
De Broglie provided a relationship between the electron properties and their 'wavelength' which was later experimentally demonstrated by diffraction experiments λ = h / p = h/mv -leave m in kg because h= 6.626 x 10^-34 Kgm²/s
Shine light through a crystal and look at pattern of scattering -what is this -how can this be explained
Diffraction can only be explained by treating light as a wave instead of a particle.
if DGrxn <0,
Ecell >0, K > 1. favors products. shifts right
what do electrons do to construct polyelectronic atoms
Electrons go into hydrogen-like orbitals to construct polyelectronic atoms.
Energy levels for a quantum particle in a box
En = ((n²)(h²)) ÷ 8m(L²)
Energy levels for the hydrogen atom (Bohr) equation
En= [ (Z²)(e^4)m ÷ 8(ɛ˚²)h² ] x (1/(n²))
Energy levels for a quantum linear oscillator (Planck)
En= hv(n+(½))
relationship between frequency and "photon" energy equation
Ephoton = hv
Ephoton equation
Ephoton = hv = h (c / λ)
Schrodinger Equation
Erwin Schrodinger develops a mathematical formalism that incorporates the wave nature of matter: Ĥψ = Eψ the wavelength: Ĥ = (p²)/(2m) + PE d2/dx² compositive of potential energy and kinetic energy
Ecell
E˚cell = E˚cath - E˚anode E˚cell = -ΔG˚ / nF Ecell = -w / q(charge) E˚cell = (RT / nF)*(lnK) or (0.0257V/n)*(lnK) or (0.0591V/n)*(log(K)) Ecell = E˚cell - (0.0591/n)*(logQ) Ecell = E˚cell - 0.0591(log[H+]) + constant
TRUE/FALSE: electron is excited from ground state to the n=3 state in Hydrogen Atom.. -it takes more energy to ionize (remove) the electron from n=3 than from the ground state
False. it takes less energy to ionize an electrom from n=3 than from ground state
Elements that have high electron affinity
Group 7 (the halogens) and Group 6 (O and S specifically)...cl...F. this means there electron affinities are really big negative numbers. N. EA poor. EA>0. its unstable and e- has to go to occupied orbital. vs. O & S where electron -->[ne]
Rydberg Model -what does this suggest
Johann Rydberg extends the Balmer model by finding more emission lines outside the visible region of the spectrum: v = Ry ( (1/(n1²)) - (1/(n2²)) ) n1= 1,2,3... n2= n1 + 1, n1 + 2.... Ry= 3.29 x 10^15 1/s This suggests that the energy levels of the H atom are quantized and proportional to 1/n2
Balmer Model Equation -what does this predict
Joseph Balmer (1885) first noticed that the frequency of visible lines in the H atom spectrum could be reproduced by: v Ժ 1/(2²) - 1/(n²) n = 3, 4, 5..... The above equation predicts that as n increases, the frequencies become more closely spaced. ƛƛɸΦγψλĤ÷ƱɛΔπԑԺẢ
if DG rxn<DGknot rxn
K will shift a little towards reactants
Koopmans' Theorem:
Koopmans' Theorem: The ionization energy of an electron is equal to the energy of the orbital from where the electron came.
Larger volume...DS
Larger volume means molecules can be in more places, the gas in the 20 L has more entropy.
Plancks Ideas
Light emitted from solid is heated, as it's heated, intensity increases & peak wavelengths decrease
What did Broglie suggest
Louis de Broglie suggests that for the e- orbits envisioned by Bohr, only certain orbits are allowed since they satisfy the standing wave condition.
The Bohr Model of Atom (1913) -idea
Niels Bohr uses the emission spectrum of hydrogen to develop a quantum model for H. -Central idea: electron circles the "nucleus" in only certain allowed elliptical orbits, like planets in a planetary system -The Coulombic attraction between negative charged electrons and the positively charged nucleus holds the system together (like gravitation for the solar system)
Can 2 electrons have the same quantum #s?
No 2 electrons can have the same quantum #'s
Pauli Exclusion Principle
No two electrons may have the same quantum numbers. Therefore, only two electrons can reside in an orbital (differentiated by ms).
Photon emission: define -equation -as energy increases,
Relaxation from one energy level to another by emitting a photon. -With ΔE = hc/ λ -If λ = 440 nm, ΔE = 4.5 x 10-19 J energy incr. , Emission dcr.
Second Law in terms of Gibbs Free Energy:
Second Law in terms of Gibbs Free Energy: ΔGsys < 0 ΔG < 0 rxn is spontaneous ΔG = 0 system is at equilibrium Recall ΔSuniv = 0 for reversible process. ΔG > 0 rxn is nonspontaneous; i.e., rxn does not happen
ΔS, ΔH, T (2)
T = ΔH˚ / ΔS˚, ΔS = nΔH / T
What does bohr's model not work for?
The Bohr model's successes are limited: -doesn't work for multi-electron atoms That said, the Bohr model was a pioneering, "quantized" picture of atomic energy levels.
The Coulombic potential can be generalized:
V(r) = -Ze²/ r
We can use the Bohr model to calculate...
We can use the Bohr model to calculate what ΔE is for any two energy levels ΔE = Ef - Ei ΔE= -2.178 x 10^-18 J [(1/(n^2final)) - (1/(n^2initial))]
uncertainty principle -who
Werner Heisenberg development of quantum mechanics leads him to the observation that there is a fundamental limit to how well one can know both the position and momentum of a particle.
When Heat exchange not involved..DS
When heat exchange is not involved, spontaneous processes always increase entropy.
an increase in temp leads to
an increase in K. K dictated by DH, but not DS.
what point does buffer have highest capacity?
at midpoint where ph = pka
if n increases, frequencies
become more closely spaced (energy levels get closer together)
Continuous spectrum vs quantized
continous = any ΔE allowed quantizied= only certain ΔE
atomic raddi correlations
dcrs L-->R -due to increased Z+ incr. down a column -more obitials with greater n HE smallest
Anode
e- lost, oxidation
if a thing has a greater wavelength than another thing,
energy levels closer together
TRUE/FALSE: electron is excited from ground state to the n=3 state in Hydrogen Atom.. -the first excited state corresponds to n = 3
false. the ground state in hydrogen is n = 1 and all other allowed energy states are called excited states, n = 2 is the first excited state and n = 3 is the second excited state
is Fe2+ capable of redcuing Cr3+ to Cr2+?
flip Ecell of fe2+ because its the anode(oxidizing agent), if Ecell i neg. ---> no not capable
frequency KE # of electrons relationship
frequency incr, KE of ei incrs, # of electrons incr
if E cell is really low and negative..
good reducing agent
electron affinity correlations
higher EA for groups 6 (O&S) and 7. EA>0 is bad because its unstable. As element gets cloer to noble gas, EA goes down. Cl is most able to hold onto electrons so has most negative EA
elements higher in the periodic table's ionization energies are...
higher. bigger atomic number, lower ionization ergy. incr. left to right. decreases as one goes down
how do 1st ionization potentials correlate
increases L-->R -due to increased Z+ decreases down a group -due to increased distance from nuclues HE largest
a˳
is referred to as the Bohr radius, and = 0.529 Å
atomic number and wavelength relationship
larger atomic number, smaller wavelength
wave-particle duality -how do we explain this behavior
light behaves both as a particle and a wave. -quantum mechanics
Plancks relationship: light thought of as waves?
light can be thought of as a series of energy "packets" or photons.
Radial Probability
likelihood of finding the electron in each spherical shell
K
lnK = (-ΔH˚ / RT) + (ΔS˚ / R) ln(K2 / K1) = (-ΔH˚ / R)*( (1 / T2) - (1 / T1) ) K= e^nFEcell/rt
ln k equation
lnk = nFE˚cell / RT
log k equation
log k = nE˚cell / 0.0591v
Naming orbitals: l's letter values
n is simply referred to by the quantum number l (0 to (n-1)) is given a letter value as follows: 0 = s 1 = p 2 = d 3 = f -m1 (-1...0...1) is usually "dropped"
quantum numbers and orbitals table
n l Orbital ml # of Orb. 0 1s 0 1 0 2s 0 1 1 2p -1, 0, 1 3 0 3s 0 1 1 3p -1, 0, 1 3 2 3d -2, -1, 0, 1, 2 5
can energy and position of an electron be detemined simultaneously?
no.
EA> 0.. good or bad
poor electron affinity b/c it's unstable -e- must go to occupied orbital
Endothermic (pos DH) favors...
products at high temps. K decreases
state functions
q, w, E, H, and G
Emission spectrum of H, quantized or continous?
quantized, not continuous
State Functions ΔV = 0
qv=DE
r, m, v, n, h equation
rmv = nh / 2pi
TRUE/FALSE: electron is excited from ground state to the n=3 state in Hydrogen Atom.. =the wavelength of light emiited if the electron drops from n=3 to n=2 is shorter tha the wavelength of light emitted if the electron falls from n=3 to n=1
the energy difference between n = 3 to n = 2 is smaller than the energy difference to n= 2 electronic transition than for the n = 3 to n =1 transition. E and λ are inversley proportional to each other
The idea behind wave mechanics
the existence of the electron in fixed energy levels could be though of as a "standing wave".
TRUE/FALSE: electron is excited from ground state to the n=3 state in Hydrogen Atom.. -the electron is farther from the nucleus on average in n=3 state than in the ground state
true
TRUE/FALSE: electron is excited from ground state to the n=3 state in Hydrogen Atom.. -the wavelength of the light emitted when the electron returns to the ground state from n = 3 is the same as the wavelength of the light absorbed to go from =1 to n=3
true
w
w= -nRTln(v1 / v2) or -qrev w rev = wmax w useful max = ΔG when ΔP & ΔT both = 0
atomic number and wavelenght correlation
wavelength dcr. with incr. Z+
atm / mmHg conversion
x mmHg * (1 atm/ 760 mmHg)
ΔE, n, Z² equation
ΔE = (-2.178 x 10^-18 J)*( (1 / n²f) - (1 / n²i) )*(Z²)
ΔE, λ, Z : Ժ equation
ΔE Ժ Z²; ΔE Ժ (1/λ); λ Ժ (1/Z²)
ΔE & λ equations
ΔE= nhv ΔE= hc / λ λ = h / p λ = h / mv h = 6.626 x 10^-34 J/S
DG=
ΔG = wmax - As ΔG gets more negative, more work can be done by the system.
ΔG
ΔG = ΔH - TΔS ΔG = w useful max @ constant T & P ΔG˚ = -nFE˚cell (or -RTln(k)) ΔG = ΔG˚rxn + RTln(Pf / Pi) or Rtln(q) ΔG˚ = -RTln(k)
ΔG˚, T, ΔS˚, ΔH˚ (2)
ΔG˚ = ΔH˚ - TΔS˚ ΔS˚ = (ΔH˚ - ΔG˚) / T
ΔH
ΔH = q p + w useful ΔHsys = q p sys
State Functions ΔP = 0
ΔH = qp w = -pΔV ΔS = nCpln(Tf / Ti)
ΔS
ΔS = q rev / T ΔS = -Rln(Pf / Pi) or Rln(Vf / Vi) ΔS surr = -ΔHsys / T or -ΔS˚sys ΔS = ΔS˚ - Rln(Pf / Pi)
λH or λHe+ greater?
λH > λHe+
What is a wave function -probabilty of finding a particle in space -what can we describe w/ wavefunction
ψ = a probability amplitude -ψ*ψ -spatial distributions
Elements in same column have the same or different # of valence electrons?
• Elements in same column have the same # of valence electrons!
Bohr realized that as n...
• Energy levels get closer together as n increases -at n= infinity, E= 0
orbital energies: -energy increases as.. -orbitals of same n, different l... -"ground" or lowest energy orbital
• energy increases as 1/n2 • orbitals of same n, but different l are considered to be of equal energy ("degenerate"). • the "ground" or lowest energy orbital is the 1s.
