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{{Not to be confused|Molar mass}}{{Short description|Mass of a given molecule in daltons}}

The '''molecular mass''' ({{mvar|m}}) is the mass of a given [[molecule]], often expressed in [[unit of measurement|units]] of [[dalton (unit)|dalton]]s (Da).<ref name="SI">{{SIbrochure9th|page=145}}</ref> Different molecules of the same compound may have different molecular masses because they contain different [[isotope]]s of an element. The derived quantity '''relative molecular mass''' is the [[unitless]] ratio of the mass of a molecule to the [[atomic mass constant]] (which is equal to one dalton).<ref>IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). Online version (2019-) created by S. J. Chalk. ISBN 0-9678550-9-8. https://doi.org/10.1351/goldbook.</ref>

The molecular mass and relative molecular mass are distinct from but related to the ''[[molar mass]]''. The '''molar mass''' is defined as the mass of a given substance divided by the [[amount of substance|amount of the substance]], and is expressed in [[grams]] per [[Mole (unit)|mole]] (g/mol). That makes the molar mass an ''average'' of many particles or molecules (weighted by abundance of the [[Isotope|isotopes]]), and the molecular mass the mass of one specific particle or molecule. The molar mass is usually the more appropriate quantity when dealing with macroscopic (weigh-able) quantities of a substance.

The definition of '''molecular weight''' is most authoritatively synonymous with ''relative molecular mass'', which is dimensionless; however, in common practice, use of this terminology is highly variable. When the molecular weight is given with the unit Da, it is frequently as a weighted average (by abundance) similar to the molar mass but with different units. In [[molecular biology]] and [[biochemistry]], the mass of macromolecules is referred to as their molecular weight and is expressed in [[Kilo-|kilo]]<nowiki/>daltons (kDa), although the numerical value is often approximate and representative of an average.

The terms "molecular mass", "molecular weight", and "molar mass" may be used interchangeably in less formal contexts where unit- and quantity-correctness is not needed. The molecular mass is more commonly used when referring to the mass of a single or specific well-defined molecule and less commonly than molecular weight when referring to a weighted average of a sample. Prior to the [[2019 revision of the SI]], quantities expressed in daltons (Da) were by definition numerically equivalent to molar mass expressed in the units g/mol and were thus strictly numerically interchangeable. After the 2019 revision, this relationship is only approximate, but the equivalence may still be assumed for all practical purposes.

The molecular mass of small to medium size molecules, measured by mass spectrometry, can be used to determine the [[Chemical composition|composition]] of elements in the molecule. The molecular masses of macromolecules, such as proteins, can also be determined by mass spectrometry; however, methods based on [[viscosity]] and light-scattering are also used to determine molecular mass when [[crystallographic]] or mass spectrometric data are not available.

== Calculation ==
Molecular masses are calculated from the [[atomic mass]]es of each [[nuclide]] present in the molecule, while [[Molar mass|molar masses]] and relative molecular masses (molecular weights) are calculated from the [[standard atomic weight]]s<ref>{{cite web | title = Atomic Weights and Isotopic Compositions for All Elements | url = http://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=&all=all&ascii=html&isotype=some | publisher = [[NIST]] | access-date = 2007-10-14}}</ref> of each [[Chemical element|element]]. The standard atomic weight takes into account the [[Isotope|isotopic distribution]] of the element in a given sample (usually assumed to be "normal"). For example, [[water (molecule)|water]] has a molar mass of 18.0153(3) g/mol, but individual water molecules have molecular masses which range between 18.010&nbsp;564&nbsp;6863(15)&nbsp;Da (<sup>1</sup>H{{su|b=2}}<sup>16</sup>O) and 22.027&nbsp;7364(9)&nbsp;Da (<sup>2</sup>H{{su|b=2}}<sup>18</sup>O).

Atomic and molecular masses are usually reported in [[dalton (unit)|dalton]]s, which is defined in terms of the mass of the [[isotope]] <sup>12</sup>C (carbon-12). However, the name ''[[Dalton (unit)|unified atomic mass unit]]'' (u) is still used in common practice. Relative atomic and molecular masses as defined are [[dimensionless]]. Molar masses when expressed in [[Gram|g]]/[[Mole (unit)|mol]] have almost identical numerical values as relative atomic and molecular masses. For example, the molar mass and molecular mass of [[methane]], whose molecular formula is CH<sub>4</sub>, are calculated respectively as follows:

{| class="wikitable plainrowheaders"
!colspan=4|Molar mass of CH<sub>4</sub>
|-
!  !! Standard atomic weight       !! Number<br>of atoms !! Total molar mass (g/mol) <br> or molecular weight (unitless)
|-
| C || {{Atomic mass|C}} || 1      || style="text-align:right;"|{{Atomic mass|C}}
|-
| H || {{Atomic mass|H}} || 4      || style="text-align:right;"|{{Molecular mass|H|4}}
|-
| CH<sub>4</sub> ||      ||        || style="text-align:right;"|{{Molecular mass|C|1|H|4}}
|-
!colspan=4|Molecular mass of <sup>12</sup>C<sup>1</sup>H<sub>4</sub>
|-
!  !! Nuclide mass (Da or u)      !! Number<br>of atoms !! Total molecular mass (Da or u)
|-
| <sup>12</sup>C || 12.0000 || 1      || style="text-align:right;"|12.0000
|-
| <sup>1</sup>H || 1.007825 || 4      ||style="text-align:right;"| 4.0313
|-
| CH<sub>4</sub> ||      ||        ||style="text-align:right;"| 16.0313
|}

The uncertainty in molecular mass reflects variance (error) in measurement not the natural variance in isotopic abundances across the globe. In high-resolution [[mass spectrometry]] the mass isotopomers <sup>12</sup>C<sup>1</sup>H<sub>4</sub> and <sup>13</sup>C<sup>1</sup>H<sub>4</sub> are observed as distinct molecules, with molecular masses of approximately 16.031 Da and 17.035 Da, respectively. The intensity of the mass-spectrometry peaks is proportional to the isotopic abundances in the molecular species. <sup>12</sup>C <sup>2</sup>H <sup>1</sup>H<sub>3</sub> can also be observed with molecular mass of 17 Da.

== Determination ==
=== Mass spectrometry ===
{{main|Mass spectrometry}}
In mass spectrometry, the molecular mass of a small molecule is usually reported as the [[monoisotopic mass]]: that is, the mass of the molecule containing only the most common isotope of each element. This also differs subtly from the molecular mass in that the choice of isotopes is defined and thus is a single specific molecular mass out of the (perhaps many) possibilities. The masses used to compute the monoisotopic molecular mass are found in a table of isotopic masses and are not found in a typical periodic table. The average molecular mass is often used for larger molecules, since molecules with many atoms are often unlikely to be composed exclusively of the most abundant isotope of each element. A theoretical average molecular mass can be calculated using the [[standard atomic weight]]s found in a typical periodic table. The average molecular mass of a very small sample, however, might differ substantially from this since a single sample average is not the same as the average of many geographically distributed samples.

=== Mass photometry ===
Mass photometry (MP) is a rapid, in-solution, label-free method of obtaining the molecular mass of proteins, lipids, sugars and nucleic acids at the single-molecule level. The technique is based on interferometric scattered light microscopy.<ref>Young et al. (2018). Quantitative imaging of single biological macromolecules. Science 360, 423-427. DOI: https://doi.org/10.1126/science.aar5839</ref> Contrast from scattered light by a single binding event at the interface between the protein solution and glass slide is detected and is linearly proportional to the mass of the molecule. This technique can also be used to measure sample homogeneity,<ref>Sonn-Segev, A., Belacic, K., Bodrug, T. et al. Quantifying the heterogeneity of macromolecular machines by mass photometry. Nat Commun 11, 1772 (2020). https://doi.org/10.1038/s41467-020-15642-w </ref> to detect protein [[oligomerisation]] states, and to identify complex macromolecular assemblies ([[ribosomes]], [[GroEL]], [[Adeno-associated virus|AAV]]) and protein interactions such as protein-protein interactions.<ref>Soltermman et al. Quantifying protein-protein interactions by molecular counting using mass photometry.  Angew. Chem Int Ed, 2020, 59(27), 10774-10779</ref> Mass photometry can accurately measure molecular mass over a wide range of molecular masses (40 kDa – 5 MDa).

=== Hydrodynamic methods ===
To a first approximation, the basis for determination of molecular mass according to [[Mark–Houwink equation|Mark–Houwink relations]]<ref>Paul, Hiemenz C., and Lodge P. Timothy. Polymer Chemistry. Second ed. Boca Raton: CRC P, 2007. 336, 338–339.</ref> is the fact that the [[intrinsic viscosity]] of [[Solution (chemistry)|solution]]s (or [[suspension (chemistry)|suspensions]]) of macromolecules depends on volumetric proportion of the dispersed particles in a particular solvent. Specifically, the hydrodynamic size as related to molecular mass depends on a conversion factor, describing the shape of a particular molecule. This allows the apparent molecular mass to be described from a range of techniques sensitive to hydrodynamic effects, including [[dynamic light scattering|DLS]], [[size exclusion chromatography|SEC]] (also known as [[Gel permeation chromatography|GPC]] when the eluent is an organic solvent), [[viscometry]], and diffusion ordered [[nuclear magnetic resonance spectroscopy]] (DOSY).<ref>{{cite journal|author1=Johnson Jr., C. S. |journal=[[Progress in Nuclear Magnetic Resonance Spectroscopy]]|year=1999| volume=34|pages=203–256|title=Diffusion ordered nuclear magnetic resonance spectroscopy: principles and applications |issue=3–4|doi=10.1016/S0079-6565(99)00003-5|bibcode=1999PNMRS..34..203J }}</ref> The apparent [[Hydrodynamic radius|hydrodynamic size]] can then be used to approximate molecular mass using a series of macromolecule-specific standards.<ref>{{cite journal|author1=Neufeld, R. |author2=Stalke, D. |journal=[[Chem. Sci.]]|year=2015| volume=6|pages=3354–3364|title=Accurate Molecular Weight Determination of Small Molecules via DOSY-NMR by Using External Calibration Curves with Normalized Diffusion Coefficients |issue=6 |doi=10.1039/C5SC00670H|doi-access=free|url=http://goedoc.uni-goettingen.de/goescholar/bitstream/handle/1/11975/c5sc00670h.pdf?sequence=1 |pmid=29142693 |pmc=5656982}}</ref> As this requires calibration, it's frequently described as a "relative" molecular mass determination method.

=== Static light scattering ===
It is also possible to determine absolute molecular mass directly from light scattering, traditionally using the [[Zimm plot|Zimm method]]. This can be accomplished either via classical [[static light scattering]] or via [[multi-angle light scattering]] detectors. Molecular masses determined by this method do not require calibration, hence the term "absolute". The only external measurement required is [[Static light scattering#Theory|refractive index increment]], which describes the change in refractive index with concentration.

== See also ==
* [[Cryoscopy]] and [[cryoscopic constant]]
* [[Ebullioscopy]] and [[ebullioscopic constant]]
* [[Dumas method of molecular weight determination]]
* [[François-Marie Raoult]]<!--everything above are important historical molecular mass determination methods that should be covered in this article-->
* [[Standard atomic weight]]
* [[Mass number]]
* [[Absolute molar mass]]
* [[Molar mass distribution]]
* [[Dalton (unit)]]
* [[SDS-PAGE]]

== References ==
{{Reflist}}

== External links ==
* [https://play.google.com/store/apps/details?id=malta.molecularcalculator&feature=more_from_developer#?t=W10. A Free Android application for molecular and reciprocal weight calculation of any chemical formula]
* [http://chemistry-in-excel.jimdo.com/ Stoichiometry Add-In for Microsoft Excel] {{Webarchive|url=https://web.archive.org/web/20110511073820/http://chemistry-in-excel.jimdo.com/ |date=2011-05-11 }} for calculation of molecular weights, reaction coefficients and stoichiometry.

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