CHEMIESTUDYSHEET - my little "cheat sheet" | Useful sites ...



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the basics

~ nuclear model

~ avogadro’s number: 6.02 x 1023 atoms = 1 mol

~ % composition by mass: what % of molar mass belongs to each element

~ significant figures

▪ multiply/divide: keep lowest # of sig figs

▪ add/subtract: keep lowest # of decimal places

▪ decimal places in log function = sig figs in answer

~ molecular vs. empirical

▪ molecular: actual amount of atoms

→ molar mass / empirical mass = ratio of molecular to empirical

▪ empirical: simplest ratio of atoms in formula or moles of each element

~ concentration

▪ % by mass (g / g)

▪ molarity (mol / L)

~ dilution

▪ (Lbefore)(Mbefore) = (Lafter)(Mafter)

~ limiting reagent

▪ convert to mols; whichever produces less product = limiting reagent

▪ % yield = actual / theoretical * 100%

atomic theory

~ dalton’s atomic theory

▪ elements consist of atoms

▪ all atoms of an element are alike in mass and other properties; atoms of one element differ from those of another

▪ different elements combine in a simple numerical ratio

~ thomson & cathode ray experiment

▪ “plum pudding model”

~ rutherford’s gold foil experiment

▪ alpha particles (He2+)

~ average atomic mass = (fraction isotope 1)(mass 1) + (frac 2)(mass 2) + …

light

~ 1 nm = 10-9 m

~ 1 Å = 10-10 m

~ C = 3.00 x 10-8 ms-1 = (λ)(υ)

~ frequency (υ) = number of peaks per second

▪ 1 Hertz (Hz) = 1 s-1

~ wavelength (λ)

▪ visible light: 400 nm – 700 nm

~ Ephoton = h υ(s-1) = hc / λ(m)

▪ h (Planck’s constant) = 6.63 x 10-34 J*s

~ bohr’s H atom

▪ for H & 1e- ions:

→ En = -z2RH / n2

o z: atomic number

o RH: 2.18 x 10-18 J

o n: 1, 2, 3, 4…

→ ΔE = z2RH(1/ni2 – 1/nf2)

electron configuration & orbital diagrams

~ e- configuration

~ anions: add to valence e-

~ cations: remove valence first (p before s); then d from inner level

~ orbital diagrams

▪ pair ↑↓ (Pauli exclusion principle)

▪ spread out e- if possible (e- repel)

▪ unpaired e- have parallel spins

→ paramagnetic: unpaired e- vs. diamagnetic: all e- paired

▪ exceptions: d5 (Cr, Mo) / d10 (Cu, Ag, Au)

quantum numbers

~ principle (n) = E levell

~ orbital (l): s = 0, p = 1, d = 2, f = 3

▪ l = 0, 1, 2, … (n-1)

~ magnetic (ml)

▪ ml = -l … 0 … +l

~ spin (ms)

▪ +1/2 or -1/2

periodic trends and molecular structures

~ atomic radius

▪ energy level

▪ greater zeff = smaller radius

▪ cations: less e- repulsion; smaller

▪ anions: more e- repulsion; larger

▪ isoelectronic: same # e-

~ ionization E (I) = E added to remove e-

▪ radius ↑ I1↓

▪ change in energy level = huge jump in E needed

▪ exceptions:

→ I1 (Al) < I1 (Mg); I1(B) < I1 (Be)

~ electron affinity (EA) = ΔE when e- added

▪ radius ↓, EA more (-) = easier to add

▪ s2, p6: EA >>> 0

▪ exceptions:

→ N, P, As, Sb: add e- repulsion to p3 = EA less (-)

→ F vs Cl: orbital of F too small = extra e- repulsion = EA less (-)

~ electronegativity (EN) = ability of atom to attract e- in chemical bond

~ bonding:

▪ ionic (metal & nonmetal; large ΔEN)

→ “formula unit”

▪ molecular (nonmetal & nonmetal; small ΔEN)

→ nonpolar covalent bond: ΔEN = 0

→ polar covalent bond: ΔEN > 0

→ bond length:

o radius ↑ bond length↑

o # bonds ↑; bond length ↓; bond energy ↑

→ bond order = total # bonds / # atoms bonded to center

o bigger = shorter

→ “free radical”: paramagnetic – one electron on center atom; bonds with similar electron on same kind of other atom through dimerization

→ “expanded octets”: only if center atom not in row 2

~ formal charge = (#valence e-) – (#nonbonding e-) – ½(#bonding e-)

▪ sum of formal charges = overall charge

▪ formal charges closest to 0 = most important

~ VSEPR theory: refer to attachment

▪ bond angles

→ dipole moment (μ): >0, polar; =0, nonpolar

→ no lone pairs on center = nonpolar (unless different outer elements)

→ lone pairs on center = polar (except AX2E3/linear; AX4E2/square planar)

pressure

~ barometric P

~ ideal gas law

▪ pV = nRT

▪ d = mmP / RT

~ effusion

▪ μA/ μB (speed) = √mmB/mmA = nA/nB = dA/dB = tB/tA

~ manometer

▪ d1h1 = d2h2

~ dalton’s law

▪ PA = Ptotal(nA / ntotal)

~ collecting gas “over water”

▪ Pbar = Pgas + Pwatervapor

thermodynamics

~ kinetic molecular theory (KMT): ideal gases

▪ V = L of empty space; assume no molecular V

▪ P = F/A; assume no IMFs

~ gas laws

▪ boyle’s law: P↑V↓

▪ charles’ law: T↑V↑

▪ avogadro’s law: n↑V↑

~ 1st law of thermodynamics: conservation of E

~ calorimetry

▪ q(J) = m(g)s(J/gºC)Δt

~ constant P “coffee cup” calorimetry

▪ ionic (s) → ionic (aq) or X(aq) + Y(aq) → products

▪ ΔHrxn = +/- (total gsoln)(Ssoln)(Δt) / #mols dissolved or # mols product

→ + endo; - exo

~ qcalorimeter = (htcap(kJ/ºC or J/ºC))(Δt)

~ constant V “bomb” calorimetry

▪ not in water: heat of combustion = -(htcap)(Δt) / #g or mol burned

▪ in water: heat of combustion = -[(gH2O)(SH2O)(Δt)+(htcap)(Δt)] / #g or mol burned

~ thermochemical equation

▪ based on molar ratio

▪ multiply rxn by x = multiply ΔH by x

▪ flip rxn = -ΔH

▪ hess’s law: add rxns = add ΔH

~ ΔHºrxn = ΣnΔHºf(products) - ΣnΔHºf(reactants)

▪ ΔHºf = 0 for standard state elements

~ breaking bonds: (+); forming bonds: (-)

▪ coefficient(type of bond) LEFT – coefficient(type of bond) RIGHT

~ work(w) = +/- P|ΔV|

▪ +: compressed; -: expands

~ Δu (internal E) = q + w

~ born-haber cycle

▪ standard state elements → 1 mol compound; ΔHºf

▪ X(g) → X+ (g) + 1e-; I1

▪ X(g) → X- (g); EA1

▪ X2 (g) → 2X (g); ΔHdissociation (bond energy)

▪ ions (g) → 1 mol ionic (s); lattice E (LE) [always K = goes left

▪ Q < K = goes right

entropy, spontaneity, & more thermodynamics

~ entropy (S) = disorder

▪ substance

→ T↑ = ΔS > 0

→ phase change

▪ rxn

→ ΔS > 0 if # mols (g) ↑

→ ΔSºrxn = ΣnΔSº(products) - ΣnΔSº(reactants)

→ Sº of standard elements IS NOT 0!

→ more bonds, S ↑

~ 2nd law of thermodynamics

▪ ΔSuniverse = ΔSrxn + ΔSsurr; if >0 = spontaneous

▪ ΔSsurr = -ΔHrxn / T

▪ ΔG(kJ/mol) = ΔHrxn (kJ/mol) – T(K)ΔSrxn(kJ/mol*K)

→ > 0, nonspontaneous; =0, equilibrium; 0 = spontaneous

▪ don’t multiply voltages!

▪ ox. || red

▪ Al (s) | Al3+ (aq) || Cl- (aq) | Cl2 (g) | Pt(s)

→ Pt(s): unreactive, so used as a cathode

~ ΔGº = -nFEºcell

▪ F = 96500 C/mol

~ Eºcell (J/C) = (RET / nF)lnK

▪ RE = 8.31 J

▪ if at 25ºC (298K);

→ Eºcell = (0.0257 / n)lnK

▪ if K is very high, reacts well

~ metal + strong acid (HCl, HBr, HI)

▪ red: 2H+ + 2e- → H2; 0V

~ metal + HNO3

▪ red: NO3- + 4H+ + 3e- → NO + 2H2O; 0.96V

~ nernst equation

▪ Ecell = Eºcell – (0.0257 / n)lnQ

~ electrolysis

▪ choose best ox & red (aq)

▪ spectator ions: Na+, K+, SO42-, NO3-

▪ ox: 2H2O → O2 + 4H+ + 4e-; -1.229V

→ exception: 2Cl- → Cl2 + 2e-; -1.358V

▪ red: 2H2O + 2e- → H2 + 2OH-; -0.828V

▪ time(s) x current(A) = charge(C)

valence bond theory

~ hybridization

▪ atoms bonded to center / hybridization

→ 2 / sp

→ 3 / sp2

→ 4 / sp3

→ 5 / sp3d

→ 6 / sp3d2

~ single bond: σ bond

~ double, triple bond: π bond

▪ planar

~ resonance structures: delocalized molecular orbitals

~ molecular orbital theory

▪ σ1s σ1s* σ2s σ2s* σ2p π2p π2p* σ2p*

▪ switch σ2p π2p if no O, F, or N present

▪ bond order = #b – a(*) / 2 = bonding – antibonding / 2

crystal types

~ network covalent

▪ C(diamond), Si, SiC, SiO2 (quartz)

→ very high melting point (need to break many covalent bonds)

→ very hard (rigid structure of bonds)

→ poor conductor of electricity (localized e-)

▪ C(graphite)

→ trigonal planar structure

→ delocalized e- between layers of graphite = good conductor

→ weak attraction = flakes off easily

~ ionic (contains metal ion or ammonium ion)

▪ (s)

→ high melting point

→ brittle

→ poor conductor of electricity (ions are held in place)

▪ (l), (aq): good conductor; ions move freely

▪ coulomb’s law

→ charge difference ↑, size of ions ↓ = LE more (-), melting point ↑, solubility ↓

~ metallic (metal cation in a sea of e-)

▪ delocalized e- = good conductors

▪ size of metal cation ↓ = melting point ↑

~ molecular

▪ low melting/boiling points

▪ usually soft or brittle

▪ poor conductors

▪ van der waal’s forces

▪ hydrogen bonding (strongest)

→ occurs between two molecules containing hydrogen bonded directly to N, O, or F

→ density of ice less than density of water because H-bonds form in a way that leaves empty space

▪ london (dispersion) forces

→ instantaneous vs induced dipole

→ molar mass ↑, stronger london, mp/bp ↑

▪ dipole-dipole (weakest): for polar molecules only

→ hydrocarbons: nonpolar

→ has central oxygen: polar

▪ IMFs ↑, vapor P ↓

random topics

~ electrolytes

▪ nonelectrolytes: cannot conduct electricity at all

→ molecular compounds, pure acids (not ionic)

→ no ions to conduct electricity

▪ strong electrolytes: conduct very well

→ soluble ionics, strong acids

→ lots of ions to conduct

▪ weak electrolytes: weakly conduct

→ weak acids

~ real gases: low T, high P

▪ Vreal > Videal (empty space)

▪ Preal < Pideal (assume no IMFs)

▪ van der waal’s equation

→ (P + n2a/V2)(V – nb) = nRT

→ IMFs ↑ = a ↑

→ molecular V ↑ = b ↑

→ the higher a & b, the less ideal the gas is

~ “like dissolves like”

▪ polar / polar

▪ nonpolar / nonpolar

→ (polar / nonpolar = immiscible)

▪ H-bond / H-bond

▪ ionic / polar

→ * remember solubility rules first!

→ ion dipole attraction

→ ionic / nonpolar doesn’t work because system won’t receive lost energy, so nonspontaneous

→ benzene (C6H6): nonpolar; resonance: every other is double-bond

→ cyclohexane (C6H12): nonpolar

→ T ↑, solubility of most salts ↑

→ T ↑, solubility of most gases ↓

→ henry’s law: P↓solubility of gases↓

heating curves & phase diagrams

~ heating curve (refer to attachment)

~ phase changes: q = nΔHfusion or nΔHvaporization

▪ ΔHfusion Ea

~ boltzmann distribution & temperature changes (refer to attachment)

~ root-mean-square speed = μrms = √3RET(K) / mm(kg/mol)

▪ RE = 8.31 kg*m2 / s2*mol*K

~ rxn mechanism

▪ overall rate = (k of slow step)[reactants]x

▪ forward rate = reverse rate

~ effects of catalysts

▪ graphically (refer to attachment)

▪ graph (1/T K-1, lnk): (1/T)

→ slope = -Ea / RE

▪ arrhenius equation

→ ln(k2 / k1) = (Ea / RE)(1/T1 – 1/T2)

→ ln(t1 / t2) = (Ea / RE)(1/T1 – 1/T2)

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