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



Calculations.><

[fall]

basics

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

→ dilution: (Lbefore)(Mbefore) = (Lafter)(Mafter)

→ % yield = actual / theoretical * 100%

→ 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)

→ Ephoton = h υ(s-1) = hc / λ(m)

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

→ En = -z2RH / n2

- RH: 2.18 x 10-18 J

→ ΔE = z2RH(1/ni2 – 1/nf2)

lewis structures and the like

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

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

pressure

→ pV = nRT

→ d = mmP / RT

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

→ d1h1 = d2h2

→ PA = Ptotal(nA / ntotal)

→ Pbar = Pgas + Pwatervapor

thermodynamics

→ q(J) = m(g)s(J/gºC)Δt

→ coffee cup calorimetry:

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

→ bomb calorimetry:

- heat of combustion = -(htcap)(Δt) / #g or mol burned

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

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

→ work(w) = +/- P|ΔV|

→ Δu (internal E) = q + w

→ born-haber cycle

- all substances → (g)

- break all bonds

- remove e- → cations; add e- → anions

- ions (g) → ionic (s)

- = ΔHºf of ionic solid

[winter]

equilibrium

→ 2NH3 (g) ( N2 (g) + 3H2 (g)

- Kc = [N2][H2]3 / [NH3]2

- Kp (atm) = PN2PH23 / PNH32

- * leave out (s) & (l)

- flip rxn = 1/K

- multiply rxn by x = Kx

- add rxns: multiply K values

→ Kp = Kc(RT)b-a

- b-a = Δn gas = right – left

entropy, spontaneity, & more thermodynamics

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

→ ΔSsurr = -ΔHrxn / T

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

→ ΔGºf = ΣnΔGºf(products) - ΣnΔGºf(reactants)

→ ΔGº = -RETlnK

→ van’t hoff equation

- ln(K2/K1) = ΔHº / RE (1/T1 – 1/T2)

→ clausius-clapeyron equation

- ln(P2/P1) = ΔHºvap / RE (1/T1 – 1/T2)

redox rxns and all related

→ ΔGº = -nFEºcell

→ Eºcell (J/C) = (RET / nF)lnK

- if at 25ºC (298K); Eºcell = (0.0257 / n)lnK

→ nernst equation

- Ecell = Eºcell – (0.0257 / n)lnQ

→ time(s) x current(A) = charge(C)

valence bond theory

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

heating curves & colligative properties

→ q = nΔHfusion or nΔHvaporization

→ Δtb = Kbμi = Kb(nsolute / kgsolvent)i

→ Δtf = Kfμi = Kf(nsolute / kgsolvent)i

[spring]

acids & bases

→ pH = -log[H+]

- [H+] = 10-pH

→ pOH = -log[OH-]

→ 10-14 = [H+][OH-]

→ pH + pOH = 14

→ weak acids

- Ka = x2 / (S – x) = 10-pKa

- pKa = -log(Ka)

- % ionization = (x / S)*100%

→ weak bases, Kb = x2 / (S – x) = 10-pKb

→ buffers

- HA / A-; pH = pKa + log(nA- / nHA)

- B / BH+; pOH = pKb + log(nBH+ / nB)

- excess: pH = -log(nH+excess / L total) or pOH = -log(nOH-excess / L total)

molar solubility

→ Ksp = (xs)x(ys)y

kinetics

→ rate = Δ[A] / Δtime

→ rate law = k[A]x[B]y

→ 0th order

- rate = k

- [A]t = -kt + [A]0

- t½ = [A]0 / 2k

→ 1st order

- rate = k[A]1

- ln[At] = -kt + ln[A]0

- t½ = 0.693 / k

→ 2nd order

- rate = k[A]2

- 1/[A]t = kt + 1/[A]0

- t½ = 1 / k[A]0

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

→ rxn mechanism:

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

→ arrhenius equation

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

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

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