Atomic Structure

rE = hv

c = (wavelength)(frequency)

wavelength = h / mv

p = mv

En = (-2.178 * 10^-18 / n² )joule

E = enrgy

v = frequency

p = momentum

v = velocity

n = principle quantum number

m = mass

Speed of light, c = 3.0 * 10⁸ ms^-1

Planck's constant, h = 6.63 * 10^-34 Js

Boltzmann's constant, k = 1.38 * 10^-23JK^-1

Avogadro's Number = 6.022 * 10²³ molecules / mol

Electron charge, e = -1.602 * 10^-19 coulomb

1 electron volt per atom = 96.5 kJ / mol

 

Equilibrium

Ka = [H+][A-] / [HA]

Kb = [OH-][HB+] / [B]

Kw = [OH-][H+] = 1.0 * 10^-14 at 25^oC

       = Ka * Kb

pH = -log[H+],    pOH = -log[OH-]

14 = pH + pOH

pH = pKa + log([A-]/[HA])

pOH = pKb + log([HB+]/[B])

pKa = -log Ka,    pKb = -log Kb

Kp = Kc(RT)rn

Ka (weak acid)

Kb (weak base)

Kw (water)

Kp (gas pressure)

Kc (molar concentrations)

 

Thermochemistry

rS = ES^oproducts - ES^oreactants

rH = ErHfproducts - ErHf reactants

rG = ErGfproducts - ErGf reactants

rG^o = ^H^o - T^S^o

          = -RT ln K = -2.303 RT log K

          = -nFE^o

rG = rG^o + 2.303 RT log Q

q = mcrT

Cp = rH / rT

S^o = standard entropy

H^o = standard enthalpy

G^o = standard free energy

E^o = standard reduction potential

T = temperature

n = moles

m = mass

q = heat

c = specific heat capacity

Cp = molar heat capacity at constant pressure

1 faraday, F = 96500 coulombs/mole of electrons

Gases, Liquids, and Solutions

PV = nRT

PA = Ptotal * XA, where XA = moles A / total moles

Ptotal = PA + PB + PC +...

n = m / M

K = ^oC + 273

P₁V₁ / T₁ = P₂V₂ / T₂

D = m / V

KE  per molecule = 1/2 ( mv²)

KE per mole = 3/2 (RTn)

molarity, M = moles solute per liter solution

molality, m = moles solute per kilogram solvent

rTf = iKf * molality

rTb = iKb * molality

osmosis pressure = (nRT / V) * i

P = pressure

V = volume

T = temperature

n = number of moles

D = density

m = mass

v = velocity

KE = kinetic energy

i = van't Hoff factor

Kf = molal freezing-point depression const.

Kb = molal boiling-point elevation const.

Q = reaction quotient

I = current (amperes)

q = charge (coulombs)

t = time (seconds)

E^o = standard reduction potential

K = equilibrium constant

 

Oxidation-Reduction; Electrochemistry

Q = [C]c[D]d / [A]a[B]b, where aA + bB --> cC +dD

I = q / t

Ecell = E^ocell - (RT/nF)ln Q

         = E^ocell - (0.0592 /n)logQ @ 25^oC

log K = nE^o / 0.0592

gas constant, R = 8.31 J / mol K

                             = 0.0821 L atm / mol K

                             = 8.31 volt coulomb / mol K

Boltzmann's constant, k = 1.38 * 10^-23 J / K

Kf for H₂O = 1.86 K kg / mol

Kb for H₂O = 0.512 K kg / mol

STP = 0.000^oC and 1.000 atm

1 faraday, F = 96500 coulombs/mole of electrons