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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