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Chemistry Final Equations Cheat Sheet by

math equations from all chapters

Exam 1

Kelvin to Celsius
K=C +273
Fahrenheit to Celsius
F=9F/5C (C) + 32F
density
d=m/V
SI: kg/m3; g/mL or g/cm3 commonly used
moles to atoms and molecules
1 mole = 6.022 x 1023 atoms or molecules
moles to grams
1 mole = atomic mass (g)
1 mole = formula mass (g)
grams to atoms or molecules
atomic mass (g) = 6.022 x 1023 atoms
formula mass (g) = 6.022 x 1023 molecules
avagadro’s number
6.022 x 1023 moles
kinetic energy of a moving object
Ek = 1/2 mu2
u: velocity
electr­ostatic energy
Eel = Q1Q2/d
Q1 and Q2: product of charges; d: distance between charges
joule
1 J = 1kg x m2/s2
1 J = 1 N x m
speed, wavele­ngth, and frequency
c = (wavel­eng­th)(v)
c: speed of light - 3.00 x 108 m/s; wavele­ngth: in meters; frequency (v): in s-1 or Hz
energy of a photon
E = hv
h: 6.63 x 10-34 J x s; v: frequency in s-1 or Hz
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)
hv = Ek + W
Ek = hv - W
wavelength of emitte­d/a­bsorbed light when an electron transi­tions from one quantum state to another
1/wave­length = 1.097 x 107 m-1(1/n(f)2 - 1/n(i)2)
difference in energy between two quantum states
E = hv = -2.18 x 10-18 J (1/n(f)2 - 1/n(i)2)
energy of an electron with a given quantum state
En = -2.18 x 10-18 J (1/n2)
wavelength of emitte­d/a­bsorbed light
1/wave­length = 2.18 x 10-18 J/hc (1/n(f)2 - 1/n(i)2)
de broglie wavelength
wavelength = h/mu
m: mass of particle in kg; u: velocity of the particle in s-1 or Hz
heinse­nberg uncert­ainty principle
deltax x deltap > h/4pi
deltax x mdeltau > h/4pi
position of particle: x; momentum of particle: p (defined as mass times velocity)
energy and wavelength
E = hc/wav­elength
wavelength = hc/E
charge of a single electron
-1.6022 x 10-19 C
C: coulombs
atomic mass units (amu)
1 amu = 1.66 x 10-24 g
1 amu = 1.66 x 10-27 kg
angstrom
1 A = 1 x 10-10 m
mass of a single electron
9.10 x 10-28 g
mass of a proton
1.67262 x 10-24 g
charge­-to­-mass ratio of an electron
1.76 x 108 C/g
 

Exam 2

effective nuclear charge (Zeff)
Zeff = Z - o
Z: number of protons; o: shielding constant or number of core electrons
force (coulomb’s law)
F = Q1Q2/d2
ionic EN difference
> or equal to 2.0
polar EN difference
.5 - 2.0
nonpolar (or purely covalent) EN difference
< .5
% by mass of an element
= n x atomic mass of elemen­t/m­ole­cular or formula mass of compound (100%)
% ionic character
= u (obser­ved)/u (calcu­lated) (100%)
u: dipole moment
dipole moment
u = Q x r
u: dipole moment (in debeye units (D)); Q: charge magnitude; r: distance between charges (bond length)
1 D = 3.336 x 10-30 C x m
charge magnitude
Q = u/r
formal charge
= valence electrons - (all nonbonding electrons + 1/2 bonding electrons)
electr­one­gat­ivity
EN = IE1 + EA /2
coulomb
1 C = 6.242 x 1018 electron charge
 

Exam 3

bond order
= number of electrons in bonding MO - number of electrons in antibo­nding MO/2
atom economy
= sum of molar mass of desired produc­t/sum of molar mass of reactants
% yield
= actual yield/­the­ore­tical yield (100%)
 

Exam 4

molarity
M = moles solute/L solution
dilution
Mc x Lc = Md x Ld
Mc x mLc = Md x mLd (product in millim­oles)
c: concen­trated; d: diluted
kinetic energy
Ek = 1/2 mu2
average kinetic energy of a group of gas molecules
u2 = uN2/N
u2: average speed for all the molecules in the sample; mean square speed
N: number of molecules in sample
total kinetic energy of one mole of any gas
Ek = 3/2 RT
R: 8.314 J/K x mol
T: temper­ature in Kelvin
root-m­ean­-sq­uar­e-speed
Urms = square root of 3RT/molar mass
R: 8.314 J/K x mol
molar mass in kg/mol
comparing Urms values of molecules in different gas samples
Urms(1­)/U­rms(2) = square root of molar mass (2)/molar mass (1)
graham’s law
rate = 1/square root of molar mass
rate of diffusion or effusion is inversely propor­tional to the square root of the molar mass
pressure
P= force/area
SI unit of force: Newton (1 N = 1kg x m/s2)
SI unit of pressure: pascal (Pa; 1 Pa = 1 N/m2)
pressure exerted by a column of fluid
P = hdg
P: pressure in Pa
h: height of column in meters
d: density of fluid in kg/m3
g: gravit­ational constant - 9.80665 m/s2
boyles law
P1V1=P2V2
pressure of a fixed amount of gas at constant temper­ature is inversely propor­tional to the volume of the gas
charles law
V1/T1=­V2/T2
volume of a fixed amount of gas at constant pressure is directly propor­tional to the absolute temper­ature of the gas
avogadros law
V1/n1=­V2/n2
volume of a sample of gas at constant temper­ature and pressure is directly propor­tional to the number of moles in the sample
combined gas law
P1V1/n­1T1­=P2­V2/n2T2
P1V1/T­1=P­2V2/T2
ideal gas equation
PV=nRT
R: 0.08206 L x atm/K x mol
T and n: K and mol
P and V: atm and L
density of a gas
d = P(molar mass)/RT
molar mass in kg/mol
R: 0.08206 L x atm/K x mol
molar mass of a gas
molar mass = dRT/P
R: 0.08206 L x atm/K x mol
molar mass: in kg/mol
van der waals equation
(P + an2/V2)(V - nb) = nRT
a and b depend on the element
compre­ssi­bility factor
Z = PV/RT
partial pressure
P total = sum of partial pressures
mole fraction
Xi = ni/n total
Xi = Pi/P total
Xi x n total = ni
Xi x P total = Pi
amount of reactant consumed
n = P x (V/RT) at constant volume and temper­ature
n: number of moles consumed
P: change in pressure
pressure exerted over water
P total = P O2 + P H2O
 

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  • Published: 13th December, 2022

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