Molecular mass

The molecular mass (m) is the mass of a given molecule: it is measured in daltons (Da or u).[1][2] Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The related quantity relative molecular mass, as defined by IUPAC, is the ratio of the mass of a molecule to the unified atomic mass unit (also known as the dalton) and is unitless. 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 a substance and is expressed in g/mol. The molar mass is usually the more appropriate figure when dealing with macroscopic (weigh-able) quantities of a substance.

The definition of molecular weight is most authoritatively synonymous with molecular mass; however, in common practice, it is also highly variable as are the units used in conjunction with it. Many common preparatory sources use g/mol and effectively define it as a synonym of molar mass, while more authoritative sources use Da or u and align its definition more closely with the molecular mass. Even when the molecular weight is used with the units Da or u, it is frequently as a weighted average similar to the molar mass but with different units. In molecular biology, the weight of macromolecules is referred to as their molecular weight and is expressed in kDa, although the numerical value is often approximate and representative of an average.

The terms molecular mass, molecular weight, and molar mass are often used interchangeably in areas of science where distinguishing between them is unhelpful. In other areas of science, the distinction is crucial. 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 redefinition of SI base units quantities expressed in daltons (Da or u) were by definition numerically equivalent to otherwise identical quantities expressed in the units g/mol and were thus strictly numerically interchangeable. After the 20 May 2019 redefinition of units, this relationship is only nearly equivalent.

The molecular mass of small to medium size molecules, measured by mass spectrometry, can be used to determine the 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 masses of each nuclide present in the molecule, while molar masses are calculated from the standard atomic weights[3] of each element. The standard atomic weight takes into account the isotopic distribution of the element in a given sample (usually assumed to be "normal"). For example, water has a molar mass of 18.0153(3) g/mol, but individual water molecules have molecular masses which range between 18.010 564 6863(15) Da (¹H
₂¹⁶O) and 22.027 7364(9) Da (²H
₂¹⁸O).

Atomic and molecular masses are usually reported in daltons which is defined relative to the mass of the isotope ¹²C (carbon 12), which by definition[4] is equal to 12 Da. For example, the molar mass and molecular mass of methane, whose molecular formula is CH₄, are calculated respectively as follows:

Molar mass or molecular weight of CH₄
	Standard atomic weight	Number	Total molar mass (g/mol) or molecular weight (Da or g/mol)
C	12.011	1	12.011
H	1.008	4	4.032
CH₄			16.043
Molecular mass of ¹²C¹H₄
	Nuclide mass	Number	Total molecular mass (Da or u)
¹²C	12.00	1	12.00
¹H	1.007825	4	4.0313
CH₄			16.0313

The more formally defined term is "relative molecular mass". Relative atomic and molecular mass values as defined are dimensionless. However, the adjective 'relative' is omitted in practice as it is universally assumed that atomic and molecular masses are relative to the mass of ¹²C. Additionally, the "unit" Dalton is used in common practice. The mass of 1 mol of substance is designated as molar mass. By definition, the molar mass has the units of grams per mole.

In the example above the standard atomic weight of carbon is 12.011 g/mol, not 12.00 g/mol. This is because naturally occurring carbon is a mixture of the isotopes ¹²C, ¹³C and ¹⁴C which have masses of 12 Da, 13.003355 Da, and 14.003242 Da respectively. Moreover, the proportion of the isotopes varies between samples, so 12.011 g/mol is an average value across different places on earth. By contrast, there is less variation in naturally occurring hydrogen so the standard atomic weight has less variance. The precision of the molar mass is limited by the highest variance standard atomic weight, in this example that of carbon. This uncertainty is not the same as the uncertainty in the molecular mass, which reflects variance (error) in measurement not the natural variance in isotopic abundances across the globe. In high-resolution mass spectrometry the mass isotopomers ¹²C¹H₄ and ¹³C¹H₄ 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. ¹²C ²H ¹H₃ can also be observed with molecular mass of 17 Da.

Determination

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. Note that this also differs subtly from the molecular mass in that the choice of isotopes is defined and thus is a single specific molecular mass of the many possibilities. The masses used to compute the monoisotopic molecular mass are found on a table of isotopic masses and are not found on a typical periodic table. The average molecular mass is often used for larger molecules since molecules with many atoms are 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 weights found on a typical periodic table, since there is likely to be a statistical distribution of atoms representing the isotopes throughout the molecule. The average molecular mass of a sample, however, usually differs substantially from this since a single sample average is not the same as the average of many geographically distributed samples.

Hydrodynamic methods

To a first approximation, the basis for determination of molecular mass according to Mark–Houwink relations[5] is the fact that the intrinsic viscosity of solutions (or 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 DLS, SEC (also known as GPC when the eluent is an organic solvent), viscometry, and diffusion ordered nuclear magnetic resonance spectroscopy (DOSY).[6] The apparent hydrodynamic size can then be used to approximate molecular mass using a series of macromolecule-specific standards.[7] 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 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 refractive index increment, which describes the change in refractive index with concentration.

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References

International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 126, ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14
Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2011). "CODATA Recommended Values of the Fundamental Physical Constants: 2010". Database developed by J. Baker, M. Douma, and S. Kotochigova. National Institute of Standards and Technology, Gaithersburg, MD 20899.
"Atomic Weights and Isotopic Compositions for All Elements". NIST. Retrieved 2007-10-14.
International Union of Pure and Applied Chemistry (1980). "Atomic Weights of the Elements 1979" (PDF). Pure Appl. Chem. 52 (10): 2349–84. doi:10.1351/pac198052102349.
Paul, Hiemenz C., and Lodge P. Timothy. Polymer Chemistry. Second ed. Boca Raton: CRC P, 2007. 336, 338–339.
Johnson Jr., C. S. (1999). "Diffusion ordered nuclear magnetic resonance spectroscopy: principles and applications". Progress in Nuclear Magnetic Resonance Spectroscopy. 34: 203–256. doi:10.1016/S0079-6565(99)00003-5.
Neufeld, R.; Stalke, D. (2015). "Accurate Molecular Weight Determination of Small Molecules via DOSY-NMR by Using External Calibration Curves with Normalized Diffusion Coefficients" (PDF). Chem. Sci. 6: 3354–3364. doi:10.1039/C5SC00670H. PMC 5656982. PMID 29142693.

External links

A Free Android application for molecular and reciprocal weight calculation of any chemical formula
Stoichiometry Add-In for Microsoft Excel for calculation of molecular weights, reaction coefficients and stoichiometry.

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[SI-1] International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 126, ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14

[CODATA2010-2] Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2011). "CODATA Recommended Values of the Fundamental Physical Constants: 2010". Database developed by J. Baker, M. Douma, and S. Kotochigova. National Institute of Standards and Technology, Gaithersburg, MD 20899.

[3] "Atomic Weights and Isotopic Compositions for All Elements". NIST. Retrieved 2007-10-14.

[IUPAC1979-4] International Union of Pure and Applied Chemistry (1980). "Atomic Weights of the Elements 1979" (PDF). Pure Appl. Chem. 52 (10): 2349–84. doi:10.1351/pac198052102349.

[5] Paul, Hiemenz C., and Lodge P. Timothy. Polymer Chemistry. Second ed. Boca Raton: CRC P, 2007. 336, 338–339.

[6] Johnson Jr., C. S. (1999). "Diffusion ordered nuclear magnetic resonance spectroscopy: principles and applications". Progress in Nuclear Magnetic Resonance Spectroscopy. 34: 203–256. doi:10.1016/S0079-6565(99)00003-5.

[7] Neufeld, R.; Stalke, D. (2015). "Accurate Molecular Weight Determination of Small Molecules via DOSY-NMR by Using External Calibration Curves with Normalized Diffusion Coefficients" (PDF). Chem. Sci. 6: 3354–3364. doi:10.1039/C5SC00670H. PMC 5656982. PMID 29142693.