• same number of protons and electrons, different number of neutrons
• same or similar chemical properties (because they have the same valence electrons)
• different atomic masses (because they have different numbers of neutrons)

R_H = 2.18 x 10 ^-18 J/electron

E = -R_H/n²

Discrete energy bundle

E = hν

E = hc/λ

Emission gives rise to fluorescence

Unique for each element

E = -R_H ((1/n_i)² - (1/(n_f)²)

• half the distance between centers of two atoms of an element that are just touching
• decreases left to right
• increases going down

• energy required to remove a valence electron
• increases going left to right
• decreases going down

• attraction atom has for electrons in a bond
• increases going left to right
• decreases going down

energy change that occurs when an electron is added to a gaseous atom

(highest in halogens, zero in noble gases)

• hydrogen (2)
• lithium (2)
• beryllium (4)
• boron (6)
• phosphorous, sulfur (expanded)

decreases as number of bonds increases

distance between two bonded atoms

increases as number of bonds increases

energy required to break a bond

valence electrons - 1/2bonding - nonbonding

sum of charges is charge on ion

less charges on structure means it is more stable

AX₃ trigonal planar

AX₂E bent

AX₄ tetrahedral

AX₃E trigonal pyramidal

AX₂E₂ bent

AX₅ trigonal bipyramidal

AX₄E see-saw

AX₃E₂ T-shaped

AX₂E₃ linear

AX₆ octahedral

AX₅E square pyramidal

AX₄E₂ square planar

AX₃E₃ T-shaped

AX₂E₄ linear

single bond

head to head overlap

pi bond

in multiple bonds

parallel overlap

ion dipole

hydrogen bonding

dipole dipole

dispersion forces

aA + bB -> cC + dD

rate = k [A]^x[B]^y

stoichiometric coeffeicients don't equal orders of reaction

stoichiometric coeffecients do equal superscript in equilibrium 

1. look for 2 trials where all but one substance concentration is held constant

2. repeat for all reactants

3. plug concentrations in to determine rate constnat

rate is independent of concentration

k units: M/sec

rate only changes with temperature

most common example is radioactive decay

k units: 1/sec

rate is proportional to concentration of one reactant

• reactant concentrations (greater concentrations lead to more collisions)
• temperature (higher temperature leads to greater kinetic energy, which increases number of collisions)
• medium
• catalysts

aA + bB -> cC + dD

Kc = [C]^c[D]^d

       [A]^a[B]^b

K_eq >> 1      products > reactants

K_eq << 1      reactants > products

K_eq ~ 1        reactants ~ products

A + B ↔ C + D

A increases, shifts to products

D decreases, shifts to products

Increase in pressure shifts equilibrium to side with fewer moles

Reduction in volume shifts equilibrium towards products

reactants added

products taken away

pressure applied

volume reduced

temperature reduced (if heat is a product)

product added

reactants taken away

pressure reduced

volume increased

temperature increased (if heat is a product)

ΔH_rxn = H_products - H_reactants

Bond formation is always exothermic (releases heat)

Bond dissociation is always endothermic (requires energy)

ΔS = S_final - S_initial

ΔS = q_rev/T

ΔS_universe = ΔS_system + ΔS_surroundings

ΔS_universe > 0 in spontaneous reactions

ΔG = ΔH - TΔS

ΔG   negative   spontaneous

ΔG   positive   nonspontaneous

ΔG   zero   equilibrium

ΔGº = -RT ln K_eq

ΔG = ΔGº + RT ln Q

standard temperature pressure

T = 0ºC

T = 25ºC

 used in standard enthalpy/entropy problems

pressure and volume are inversely related

P₁V₁ = P₂V₂

volume and temperature are directly proportional

V₁/T₁ = V₂/T₂

PV = nRT

d = m/V = P(MW)/RT

P_tot = P_A + P_B + P_C

P_A = P_TX_A

X_A = n_A/n_T

at high pressure, low temperature, and temperatures close to the boiling point

V will be less than predicted

1. particle volume is negligible when compared to container volume
2. gases have no intermolecular forces
3. gases particles are in continuous, random motion
4. collisions are elastic, so there is no overall gain or loss of energy
5. average kinetic energy of gas is proportional to the absolute temperature

heavier gases diffuse more slowly than lighter ones

r₁/r₂ = √((MW₂)/(MM₁))

evaporation: liquid to gas

condensation: gas to liquid

vapor pressure of liquid is the same as the external pressure

melting (fusion): solid to liquid

solidification (crystallization): liquid to solid

sublimation: solid to gas

deposition: gas to solid

∏ = MRT

water will move towards greater molarity or higher temperature

K_sp > Q   solute will continue to dissolve

Q > K_sp   precipitation will occur

Q = K_sp   equilibrium

=[H⁺][OH^-]

= 10^-14

pH + pOH = 14

Ka = [H₃O⁺][A^-]/[HA]

measures degree to which acid dissociates

have more than one equivalence point

(each equivalence point corresponds to the loss/gain of one electron)

lose electrons = oxidized

gain electrons = reduced

1. separate two half reactions
2. balance all atoms except H and O
3. add water to balance O
4. add H⁺ to balance H
5. add electrons to balance charge
6. multiply each half reaction so that number of electrons gained/lost is equal
7. add half reactions to cancel electrons

Galvanic cells have spontaneous reactions so -ΔG

Electrolytic cells have nonspontaneous reactions so +ΔG

positive in electrolytic cells

negative in galvanic cells

tendency of a species to aquire electrons and be reduced

a more positive Eº means greater tendency for reduction to occur

difference in potential between two cells

positive in galvanic cells

negative in electrolytic cells