#"Molarity"# and #"molality"# are defined by the following relationships:
#"Molarity"="Moles of solute"/"Volume of solution"#, and thus has the units of #mol*L^-1#.............
#"Molality"="Moles of solute"/"Kilograms of solvent"#, and thus has the units of #mol*kg^-1#.............
As was said, at the lower concentrations, #"molarity"# and #"molality"# may be used interchangeably. When we use colligative properties, such as boiling point elevation, and freezing point depression, to measure solution concentrations (and thus maybe an estimate of molecular mass in solution), #"molality"# is used because it is independent of solution volume.
The classic means to establish molarity is by titration, where a known volume of unknown concentration is titrated by a known volume of titrant of known concentration..........or vice versa.
