Editing Molar mass (section)

== Measurement ==
Molar masses are almost never measured directly. They may be calculated from standard atomic masses, and are often listed in chemical catalogues and on [[safety data sheet]]s (SDS). Molar masses typically vary between:
: 1–238&nbsp;g/mol for atoms of naturally occurring elements;
: {{val|10|–|1000|u=g/mol}} for [[Small molecule|simple chemical compounds]];
: {{val|1000|–|5000000|u=g/mol}} for [[polymer]]s, [[protein]]s, [[DNA]] fragments, etc.

While molar masses are almost always, in practice, calculated from atomic weights, they can also be measured in certain cases. Such measurements are much less precise than modern [[Mass spectrometry|mass spectrometric]] measurements of atomic weights and molecular masses, and are of mostly historical interest. All of the procedures rely on [[Colligative property|colligative properties]], and any [[dissociation (chemistry)|dissociation]] of the compound must be taken into account.

=== Vapour density ===
{{main|Vapour density}}
The measurement of molar mass by vapour density relies on the principle, first enunciated by [[Amedeo Avogadro]], that equal volumes of gases under identical conditions contain equal numbers of particles. This principle is included in the [[ideal gas equation]]:
: <math>pV = nRT ,</math>
where {{mvar|n}} is the [[amount of substance]]. The vapour density ({{mvar|ρ}}) is given by
: <math>\rho = {{nM}\over{V}} .</math>
Combining these two equations gives an expression for the molar mass in terms of the vapour density for conditions of known [[pressure]] and [[temperature]]:
: <math>M = {{RT\rho}\over{p}} .</math>

=== Freezing-point depression ===
{{main|Freezing-point depression}}
The [[freezing point]] of a [[Solution (chemistry)|solution]] is lower than that of the pure [[solvent]], and the freezing-point depression ({{math|Δ''T''}}) is directly proportional to the [[amount concentration]] for dilute solutions. When the composition is expressed as a [[molality]], the proportionality constant is known as the [[cryoscopic constant]] ({{math|''K''{{sub|f}}}}) and is characteristic for each solvent. If {{mvar|w}} represents the [[mass fraction (chemistry)|mass fraction]] of the [[solute]] in solution, and assuming no dissociation of the solute, the molar mass is given by
: <math>M = {{wK_\text{f}}\over{\Delta T}}.\ </math>

=== Boiling-point elevation ===
{{main|Boiling-point elevation}}
The [[boiling point]] of a [[Solution (chemistry)|solution]] of an involatile [[solute]] is higher than that of the pure [[solvent]], and the boiling-point elevation ({{math|Δ''T''}}) is directly proportional to the [[amount concentration]] for dilute solutions. When the composition is expressed as a [[molality]], the proportionality constant is known as the [[ebullioscopic constant]] ({{math|''K''{{sub|b}}}}) and is characteristic for each solvent. If {{mvar|w}} represents the [[mass fraction (chemistry)|mass fraction]] of the solute in solution, and assuming no dissociation of the solute, the molar mass is given by
: <math>M = {{wK_\text{b}}\over{\Delta T}}.\ </math>