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Kelvin to Celsius
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K=C +273
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Fahrenheit to Celsius
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F=9F/5C (C) + 32F
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density
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d=m/V
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SI: kg/m3; g/mL or g/cm3 commonly used
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moles to atoms and molecules
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1 mole = 6.022 x 1023 atoms or molecules
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moles to grams
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1 mole = atomic mass (g)
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1 mole = formula mass (g)
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grams to atoms or molecules
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atomic mass (g) = 6.022 x 1023 atoms
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formula mass (g) = 6.022 x 1023 molecules
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avagadro’s number
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6.022 x 1023 moles
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kinetic energy of a moving object
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Ek = 1/2 mu2
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u: velocity
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electrostatic energy
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Eel = Q1Q2/d
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Q1 and Q2: product of charges; d: distance between charges
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joule
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1 J = 1kg x m2/s2
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1 J = 1 N x m
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speed, wavelength, and frequency
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c = (wavelength)(v)
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c: speed of light - 3.00 x 108 m/s; wavelength: in meters; frequency (v): in s-1 or Hz
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energy of a photon
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E = hv
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h: 6.63 x 10-34 J x s; v: frequency in s-1 or Hz
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energy (hv) of a photon used to eject electrons from a metal surface via the photoelectric effect is equal to the sum of kinetic energy of the ejected electron (Ek) and the work function (W)
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hv = Ek + W
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Ek = hv - W
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wavelength of emitted/absorbed light when an electron transitions from one quantum state to another
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1/wavelength = 1.097 x 107 m-1(1/n(f)2 - 1/n(i)2)
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difference in energy between two quantum states
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E = hv = -2.18 x 10-18 J (1/n(f)2 - 1/n(i)2)
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energy of an electron with a given quantum state
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En = -2.18 x 10-18 J (1/n2)
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wavelength of emitted/absorbed light
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1/wavelength = 2.18 x 10-18 J/hc (1/n(f)2 - 1/n(i)2)
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de broglie wavelength
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wavelength = h/mu
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m: mass of particle in kg; u: velocity of the particle in s-1 or Hz
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heinsenberg uncertainty principle
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deltax x deltap > h/4pi
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deltax x mdeltau > h/4pi
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position of particle: x; momentum of particle: p (defined as mass times velocity)
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energy and wavelength
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E = hc/wavelength
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wavelength = hc/E
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charge of a single electron
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-1.6022 x 10-19 C
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C: coulombs
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atomic mass units (amu)
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1 amu = 1.66 x 10-24 g
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1 amu = 1.66 x 10-27 kg
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angstrom
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1 A = 1 x 10-10 m
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mass of a single electron
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9.10 x 10-28 g
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mass of a proton
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1.67262 x 10-24 g
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charge-to-mass ratio of an electron
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1.76 x 108 C/g
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effective nuclear charge (Zeff)
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Zeff = Z - o
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Z: number of protons; o: shielding constant or number of core electrons
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force (coulomb’s law)
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F = Q1Q2/d2
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ionic EN difference
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> or equal to 2.0
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polar EN difference
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.5 - 2.0
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nonpolar (or purely covalent) EN difference
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< .5
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% by mass of an element
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= n x atomic mass of element/molecular or formula mass of compound (100%)
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% ionic character
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= u (observed)/u (calculated) (100%)
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u: dipole moment
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dipole moment
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u = Q x r
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u: dipole moment (in debeye units (D)); Q: charge magnitude; r: distance between charges (bond length)
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1 D = 3.336 x 10-30 C x m
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charge magnitude
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Q = u/r
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formal charge
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= valence electrons - (all nonbonding electrons + 1/2 bonding electrons)
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electronegativity
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EN = IE1 + EA /2
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coulomb
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1 C = 6.242 x 1018 electron charge
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bond order
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= number of electrons in bonding MO - number of electrons in antibonding MO/2
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atom economy
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= sum of molar mass of desired product/sum of molar mass of reactants
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% yield
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= actual yield/theoretical yield (100%)
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molarity
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M = moles solute/L solution
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dilution
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Mc x Lc = Md x Ld
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Mc x mLc = Md x mLd (product in millimoles)
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c: concentrated; d: diluted
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kinetic energy
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Ek = 1/2 mu2
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average kinetic energy of a group of gas molecules
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u2 = uN2/N
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u2: average speed for all the molecules in the sample; mean square speed
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N: number of molecules in sample
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total kinetic energy of one mole of any gas
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Ek = 3/2 RT
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R: 8.314 J/K x mol
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T: temperature in Kelvin
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root-mean-square-speed
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Urms = square root of 3RT/molar mass
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R: 8.314 J/K x mol
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molar mass in kg/mol
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comparing Urms values of molecules in different gas samples
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Urms(1)/Urms(2) = square root of molar mass (2)/molar mass (1)
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graham’s law
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rate = 1/square root of molar mass
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rate of diffusion or effusion is inversely proportional to the square root of the molar mass
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pressure
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P= force/area
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SI unit of force: Newton (1 N = 1kg x m/s2)
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SI unit of pressure: pascal (Pa; 1 Pa = 1 N/m2)
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pressure exerted by a column of fluid
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P = hdg
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P: pressure in Pa
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h: height of column in meters
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d: density of fluid in kg/m3
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g: gravitational constant - 9.80665 m/s2
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boyles law
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P1V1=P2V2
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pressure of a fixed amount of gas at constant temperature is inversely proportional to the volume of the gas
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charles law
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V1/T1=V2/T2
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volume of a fixed amount of gas at constant pressure is directly proportional to the absolute temperature of the gas
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avogadros law
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V1/n1=V2/n2
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volume of a sample of gas at constant temperature and pressure is directly proportional to the number of moles in the sample
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combined gas law
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P1V1/n1T1=P2V2/n2T2
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P1V1/T1=P2V2/T2
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ideal gas equation
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PV=nRT
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R: 0.08206 L x atm/K x mol
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T and n: K and mol
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P and V: atm and L
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density of a gas
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d = P(molar mass)/RT
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molar mass in kg/mol
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R: 0.08206 L x atm/K x mol
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molar mass of a gas
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molar mass = dRT/P
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R: 0.08206 L x atm/K x mol
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molar mass: in kg/mol
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van der waals equation
|
(P + an2/V2)(V - nb) = nRT
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a and b depend on the element
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compressibility factor
|
Z = PV/RT
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partial pressure
|
P total = sum of partial pressures
|
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mole fraction
|
Xi = ni/n total
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Xi = Pi/P total
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Xi x n total = ni
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Xi x P total = Pi
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amount of reactant consumed
|
n = P x (V/RT) at constant volume and temperature
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n: number of moles consumed
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P: change in pressure
|
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pressure exerted over water
|
P total = P O2 + P H2O
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