Chemistry
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Mole

The mole is defined as the amount of substance that
contains as many elementary entities (e.g., atoms,
molecules, ions, electrons) as there are atoms in 12 g
of the isotope carbon-12

Or, a mole of any pure substance has a mass in grams
exactly equal to that substance's molecular or atomic
mass.

1 mole of C12 is 12 grams
1 mole of Ca40 is 40g (39.962g more exactly)

Or, 1 mole = 6.022×10^23 molecules of the substance
Avogadro constant, Na = 6.022e23 /mol
  It is the number of atoms (or molecules) per mole

Molar mass

Molar mass M is a physical property defined as the mass of a
given substance divided by the amount of substance. The base
SI unit for molar mass is kg/mol. However, for historical
reasons, molar masses are almost always expressed in g/mol.

Example: the molar mass of water: M(H₂O) ≈ 18.01488 g/mol

Molar volume

The molar volume Vm, is the volume occupied by one mole of a
substance at a given temperature and pressure. It is equal
to the molar mass (M) divided by the mass density (ρ). It
has the SI unit m³/mol, although it is more practical to use
dm³/mol) for gases and cm³/mol for liquids and solids.

Molar Concentration (molarity)

a measure of the concentration of a chemical species, in particular of
a solute in a solution, in terms of amount of substance per unit
volume of solution. In chemistry, the most commonly used unit for
molarity is the number of moles per litre, having the unit symbol
mol/L. A solution with a concentration of 1 mol/L is said to be 1
molar, commonly designated as 1 M.

1 M = 1 mol/L
1 mM = 0.001 mol/L
1 µM = 0.000001 mol/L

Molality, also called molal concentration, is a measure of the
concentration of a solute in a solution in terms of amount of substance
in a specified amount of mass of the solvent. This contrasts with the
definition of molarity which is based on a specified volume of solution.

A commonly used unit for molality in chemistry is mol/kg. A solution of
concentration 1 mol/kg is also sometimes denoted as 1 molal.


pH

pH is defined as the logarithm (base 10) of the reciprocal of the hydrogen
ion activity, aH+, in a solution.

Strong acides are pH of 1 to 5.5
weak acids 5.6 to 6.5
nwutral 6.6 to 7.3
weak bases 7.4 to 8.4
strong bases 8.5 to 14

pH = –log(aH+) = log(1/aH+)

pOH is a measure of the concentration of hydroxide ions.
pOH ≈ 14 − pH

strong acids/bases
pH is equal to minus the logarithm of the concentration value.
eg: The pH of a 0.01M solution of HCl is equal to −log(0.01), that is, pH=2
eg: he p[OH] value of a 0.01M solution of NaOH is equal
    to −log(0.01), that is, p[OH] = 2.

Speed of molecules

Vrms = √(3kʙT/m)
kʙ = Boltzmann constant, 1.381×10^−23 J/K
m is mass of molecule in kg
T is temp in kelvins

for N₂ molecule at room temp
V = √(3•298•1.381e-23/4.65e-23) = 16.2 m/s
N₂ molecular weight is 28
1 mole weighs 28g and is 6.022×10^23 molecules
therefore 1 molecule weighs 28/6.022e23 or 4.65e-23 kg