ADVANCED PLACEMENT CHEMISTRY EQUATIONS AND CONSTANTS ATOMIC STRUCTURE ∆E = h ν c = λν E = energy υ = velocity h λ = p = mν ν = frequency n = principal quantum number mυ λ= wavelength m = mass 2.178 x 10 -18 p = momentum E = - joule n 2 Speed of light, c = 3.00 x 10 8 ms -1 EQUILIBRIUM -34 + - Planck’s constant, h = 6.63 x 10 Js H A K = -23 -1 a []HA Boltzmann’s constant, k = 1.38 x 10 JK 23 -1 Avagadro’s number = 6.022 x 10 molecules mol - + -19 OH HB Electron charge, e = -1.602 x 10 coulomb Kb = []B 1 electron volt/atom = 96.5 kJmol -1 - + -14 Kw =[OH ] [H ] = 10 @ 25 °C = K a x K b Equilibrium constants pH = -log[H +], pOH = -log[OH -] 14 = pH + pOH Ka (weak acid) K (weak base) - b A pH = pK + log Kw (water) a []HA K (gas pressure) + p HB pOH = pK + log Kc (molar concentration) b []B S0 = standard entropy 0 pK a = - logK a, pK b = -logK b H = standard enthalpy 0 ∆n G = standard free energy Kp = K c(RT) where ∆n = moles of product gas - moles reactant gas E0 = standard reduction potential T = temperature THERMOCHEMISTRY/KINETICS n = moles ∆S0 = ΣS0 products - ΣS0 reactants m = mass q = heat 0 0 0 ∆H = ΣH f products - ΣH f reactants c = specific heat capacity 0 0 0 ∆G = ΣG f products - ΣG f reactants Cp = molar heat capacity at constant pressure 0 0 0 ∆G = ∆H - T ∆S Ea = activation energy = - RT ln K = -2.303 RT log K k = rate constant = - n ℑ E 0 ∆G = ∆G0 + RT ln Q = ∆G0 + 2.303 RT log Q A = frequency factor ∆ q = mc T ∆ = H Cp Faraday’s constant, ℑ = 96,500 coulombs per mole ∆T ln[A]t – ln[A] 0 = -kt of electrons 1 1 − = kt A [ A ] -1 -1 t 0 Gas Constant, R = 8.31 Jmol K -1 -1 − E 1 = 0.0821 L atm mol K ln k = a + ln A = 8.31 volt coulomb mol -1K-1 R T GASES, LIQUIDS, AND SOLUTIONS P = pressure PV = nRT V = volume T = Temperature n2 a () n = number of moles P + V-nb= nRT V 2 D = density m = mass υ= velocity moles of A PA = P total x X A, where X A = total moles Ptotal = P A + P B + P c + … υrms = root mean square velocity KE = kinetic energy m r = rate of effusion n = M M = molar mass π= osmotic pressure K = °C + 273 i= van’t Hoff factor Kf = molal freezing point depression constant Kb = molal boiling point elevation constant PV11 PV 22 = A = Absorbance T T 1 2 a = molar absorptivity m D = b = path length V c = concentration Q = reaction quotient =3kT = 3 RT urms I = current (amperes) m M q = charge (coulombs) 2 t = time (seconds) υ 0 KE per molecule = ½ m E = standard reduction potential 3 KE per mole = RT K = equilibrium constant 2 r1 M2 = -1 -1 r2 M1 Gas Constant, R = 8.31 Jmol K = 0.0821 L atm mol -1K-1 -1 -1 molarity, M = moles solute per liter solution = 8.31 volt coulomb mol K molality = moles solute per kilogram solvent -23 -1 Boltzmann’s constant, k = 1.38 x 10 JK ∆ Tf = i K f x molality -1 ∆T = i K x molality Kf for H 2O = 1.86 K kg mol b b K for H O = 0.512 K kg mol -1 Π = MRT b 2 1 atm = 760 mm Hg A = abc = 760 torr STP = 0.000 °C and 1.000 atm Faraday’s constant, ℑ = 96500 coulombs per mol OXIDATION REDUCTION; ELECTROCHEMISTRY of electrons [][]CDc d Q = , where aA + bB cC + dD [][]ABa b q I = t RT 0.0592 E = E0 - lnQ = E 0 - logQ @ 25 °C cell cellnℑ cell n nE 0 log K = 0.0592 .