Molecular mass

Last updated November 03, 2024

The molecular mass ( $m$ ) is the mass of a given molecule. Units of daltons (Da) are often used.^[1] Different molecules of the same compound may have different molecular masses because they contain different isotopes 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).^[2]

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 the substance, and is expressed in grams per mol (g/mol). That makes the molar mass an average of many particles or molecules (potentially containing different 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; 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 similar to the molar mass but with different units. In molecular biology, the mass 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" 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 nearly equivalent, although the difference is negligible for all practical purposes.

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 and relative molecular masses (molecular weights) 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 in terms of the mass of the isotope ¹²C (carbon-12). However, the name 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 g/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 CH₄, are calculated respectively as follows:

Molar mass of CH₄
	Standard atomic weight	Number of atoms	Total molar mass (g/mol) or molecular weight (unitless)
C	12.011	1	12.011
H	1.008	4	4.032
CH₄			16.043
Molecular mass of ¹²C¹H₄
	Nuclide mass (Da or u)	Number of atoms	Total molecular mass (Da or u)
¹²C	12.0000	1	12.0000
¹H	1.007825	4	4.0313
CH₄			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 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. 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 weights 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.^[4] 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,^[5] to detect protein oligomerisation states, and to identify complex macromolecular assemblies (ribosomes, GroEL, AAV) and protein interactions such as protein-protein interactions.^[6] 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 relations ^[7] 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).^[8] The apparent hydrodynamic size can then be used to approximate molecular mass using a series of macromolecule-specific standards.^[9] 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.

Related Research Articles

The mole (symbol mol) is a unit of measurement, the base unit in the International System of Units (SI) for amount of substance, a quantity proportional to the number of elementary entities of a substance. One mole contains exactly 6.02214076×10²³ elementary entities (approximately 602 sextillion or 602 billion times a trillion), which can be atoms, molecules, ions, ion pairs, or other particles. The number of particles in a mole is the Avogadro number (symbol N₀) and the numerical value of the Avogadro constant (symbol N_A) expressed in mol^-1. The value was chosen on the basis of the historical definition of the mole as the amount of substance that corresponds to the number of atoms in 12 grams of ¹²C, which made the mass of a mole of a compound expressed in grams, numerically equal to the average molecular mass or formula mass of the compound expressed in daltons. With the 2019 revision of the SI, the numerical equivalence is now only approximate but may be assumed for all practical purposes.

The Avogadro constant, commonly denoted $N A$ or $L$ , is an SI defining constant with an exact value of 6.02214076×10²³ mol⁻¹ (reciprocal moles). It is defined as the number of constituent particles (usually molecules, atoms, ions, or ion pairs) per mole (SI unit) and used as a normalization factor in the amount of substance in a sample. In the SI dimensional analysis of measurement units, the dimension of the Avogadro constant is the reciprocal of amount of substance, denoted N⁻¹. The Avogadro number, sometimes denoted $N 0$ , is the numeric value of the Avogadro constant (i.e., without a unit), namely the dimensionless number 6.02214076×10²³; the value chosen based on the number of atoms in 12 grams of carbon-12 in alignment with the historical definition of a mole. The constant is named after the Italian physicist and chemist Amedeo Avogadro (1776–1856).

The dalton or unified atomic mass unit is a unit of mass defined as ⁠1/12⁠ of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest. It is a non-SI unit accepted for use with SI. The atomic mass constant, denoted m_u, is defined identically, giving m_u = ⁠1/12⁠m(¹²C) = 1 Da.

Size-exclusion chromatography, also known as molecular sieve chromatography, is a chromatographic method in which molecules in solution are separated by their shape, and in some cases size. It is usually applied to large molecules or macromolecular complexes such as proteins and industrial polymers. Typically, when an aqueous solution is used to transport the sample through the column, the technique is known as gel-filtration chromatography, versus the name gel permeation chromatography, which is used when an organic solvent is used as a mobile phase. The chromatography column is packed with fine, porous beads which are commonly composed of dextran, agarose, or polyacrylamide polymers. The pore sizes of these beads are used to estimate the dimensions of macromolecules. SEC is a widely used polymer characterization method because of its ability to provide good molar mass distribution (Mw) results for polymers.

In chemistry, the molar mass of a chemical compound is defined as the ratio between the mass and the amount of substance of any sample of the compound. The molar mass is a bulk, not molecular, property of a substance. The molar mass is an average of many instances of the compound, which often vary in mass due to the presence of isotopes. Most commonly, the molar mass is computed from the standard atomic weights and is thus a terrestrial average and a function of the relative abundance of the isotopes of the constituent atoms on Earth. The molar mass is appropriate for converting between the mass of a substance and the amount of a substance for bulk quantities.

Relative atomic mass, also known by the deprecated synonym atomic weight, is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a given sample to the atomic mass constant. The atomic mass constant is defined as being ⁠1/12⁠ of the mass of a carbon-12 atom. Since both quantities in the ratio are masses, the resulting value is dimensionless. These definitions remain valid even after the 2019 revision of the SI.

In chemistry, the dispersity is a measure of the heterogeneity of sizes of molecules or particles in a mixture. A collection of objects is called uniform if the objects have the same size, shape, or mass. A sample of objects that have an inconsistent size, shape and mass distribution is called non-uniform. The objects can be in any form of chemical dispersion, such as particles in a colloid, droplets in a cloud, crystals in a rock, or polymer macromolecules in a solution or a solid polymer mass. Polymers can be described by molecular mass distribution; a population of particles can be described by size, surface area, and/or mass distribution; and thin films can be described by film thickness distribution.

In chemistry, the amount of substance (symbol $n$ ) in a given sample of matter is defined as a ratio ( $n = N / N A$ ) between the number of elementary entities ( $N$ ) and the Avogadro constant ( $N A$ ). The entities are usually molecules, atoms, ions, or ion pairs of a specified kind. The particular substance sampled may be specified using a subscript, e.g., the amount of sodium chloride (NaCl) would be denoted as $n NaCl$ . The unit of amount of substance in the International System of Units is the mole (symbol: mol), a base unit. Since 2019, the value of the Avogadro constant $N A$ is defined to be exactly 6.02214076×10²³ mol⁻¹. Sometimes, the amount of substance is referred to as the chemical amount or, informally, as the "number of moles" in a given sample of matter.

In chemistry, equivalent weight is the mass of one equivalent, that is the mass of a given substance which will combine with or displace a fixed quantity of another substance. The equivalent weight of an element is the mass which combines with or displaces 1.008 gram of hydrogen or 8.0 grams of oxygen or 35.5 grams of chlorine.

In polymer chemistry, the molar mass distribution describes the relationship between the number of moles of each polymer species and the molar mass of that species. In linear polymers, the individual polymer chains rarely have exactly the same degree of polymerization and molar mass, and there is always a distribution around an average value. The molar mass distribution of a polymer may be modified by polymer fractionation.

Enzyme assays are laboratory methods for measuring enzymatic activity. They are vital for the study of enzyme kinetics and enzyme inhibition.

Monoisotopic mass (M_mi) is one of several types of molecular masses used in mass spectrometry. The theoretical monoisotopic mass of a molecule is computed by taking the sum of the accurate masses of the most abundant naturally occurring stable isotope of each atom in the molecule. For small molecules made up of low atomic number elements the monoisotopic mass is observable as an isotopically pure peak in a mass spectrum. This differs from the nominal molecular mass, which is the sum of the mass number of the primary isotope of each atom in the molecule and is an integer. It also is different from the molar mass, which is a type of average mass. For some atoms like carbon, oxygen, hydrogen, nitrogen, and sulfur, the M_mi of these elements is exactly the same as the mass of its natural isotope, which is the lightest one. However, this does not hold true for all atoms. Iron's most common isotope has a mass number of 56, while the stable isotopes of iron vary in mass number from 54 to 58. Monoisotopic mass is typically expressed in daltons (Da), also called unified atomic mass units (u).

The history of mass spectrometry has its roots in physical and chemical studies regarding the nature of matter. The study of gas discharges in the mid 19th century led to the discovery of anode and cathode rays, which turned out to be positive ions and electrons. Improved capabilities in the separation of these positive ions enabled the discovery of stable isotopes of the elements. The first such discovery was with the element neon, which was shown by mass spectrometry to have at least two stable isotopes: ²⁰Ne and ²²Ne. Mass spectrometers were used in the Manhattan Project for the separation of isotopes of uranium necessary to create the atomic bomb.

The standard atomic weight of a chemical element (symbol A_r°(E) for element "E") is the weighted arithmetic mean of the relative isotopic masses of all isotopes of that element weighted by each isotope's abundance on Earth. For example, isotope ⁶³Cu (A_r = 62.929) constitutes 69% of the copper on Earth, the rest being ⁶⁵Cu (A_r = 64.927), so

In analytical chemistry, a tandem mass tag (TMT) is a chemical label that facilitates sample multiplexing in mass spectrometry (MS)-based quantification and identification of biological macromolecules such as proteins, peptides and nucleic acids. TMT belongs to a family of reagents referred to as isobaric mass tags which are a set of molecules with the same mass, but yield reporter ions of differing mass after fragmentation. The relative ratio of the measured reporter ions represents the relative abundance of the tagged molecule, although ion suppression has a detrimental effect on accuracy. Despite these complications, TMT-based proteomics has been shown to afford higher precision than label-free quantification. In addition to aiding in protein quantification, TMT tags can also increase the detection sensitivity of certain highly hydrophilic analytes, such as phosphopeptides, in RPLC-MS analyses.

The mass recorded by a mass spectrometer can refer to different physical quantities depending on the characteristics of the instrument and the manner in which the mass spectrum is displayed.

The molar mass constant, usually denoted by M_u, is a physical constant defined as one twelfth of the molar mass of carbon-12: M_u = M(¹²C)/12. The molar mass of an element or compound is its relative atomic mass or relative molecular mass multiplied by the molar mass constant.

<span class="mw-page-title-main">Isotope</span> Different atoms of the same element

Isotopes are distinct nuclear species of the same chemical element. They have the same atomic number and position in the periodic table, but different nucleon numbers due to different numbers of neutrons in their nuclei. While all isotopes of a given element have similar chemical properties, they have different atomic masses and physical properties.

The atomic mass (m_a or m) is the mass of an atom. Although the SI unit of mass is the kilogram (symbol: kg), atomic mass is often expressed in the non-SI unit dalton (symbol: Da) – equivalently, unified atomic mass unit (u). 1 Da is defined as 1⁄12 of the mass of a free carbon-12 atom at rest in its ground state. The protons and neutrons of the nucleus account for nearly all of the total mass of atoms, with the electrons and nuclear binding energy making minor contributions. Thus, the numeric value of the atomic mass when expressed in daltons has nearly the same value as the mass number. Conversion between mass in kilograms and mass in daltons can be done using the atomic mass constant $.$

Multi-Angle light scattering describes a technique for measuring the light scattered by a sample into a plurality of angles. It is used for determining both the absolute molar mass and the average size of molecules in solution, by detecting how they scatter light. A collimated beam from a laser source is most often used, in which case the technique can be referred to as multiangle laser light scattering (MALLS). The insertion of the word laser was intended to reassure those used to making light scattering measurements with conventional light sources, such as Hg-arc lamps that low-angle measurements could now be made.

References

↑ The International System of Units (PDF) (9th ed.), International Bureau of Weights and Measures, Dec 2022, p. 145, ISBN 978-92-822-2272-0
↑ 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.
↑ "Atomic Weights and Isotopic Compositions for All Elements". NIST . Retrieved 2007-10-14.
↑ Young et al. (2018). Quantitative imaging of single biological macromolecules. Science 360, 423-427. DOI: https://doi.org/10.1126/science.aar5839
↑ 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
↑ Soltermman et al. Quantifying protein-protein interactions by molecular counting using mass photometry. Angew. Chem Int Ed, 2020, 59(27), 10774-10779
↑ 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 (3–4): 203–256. Bibcode:1999PNMRS..34..203J. 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 (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 Archived 2011-05-11 at the Wayback Machine for calculation of molecular weights, reaction coefficients and stoichiometry.

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[SI-1] The International System of Units (PDF) (9th ed.), International Bureau of Weights and Measures, Dec 2022, p. 145, ISBN 978-92-822-2272-0

[2] 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.

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

[4] Young et al. (2018). Quantitative imaging of single biological macromolecules. Science 360, 423-427. DOI: https://doi.org/10.1126/science.aar5839

[5] 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

[6] Soltermman et al. Quantifying protein-protein interactions by molecular counting using mass photometry. Angew. Chem Int Ed, 2020, 59(27), 10774-10779

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

[8] Johnson Jr., C. S. (1999). "Diffusion ordered nuclear magnetic resonance spectroscopy: principles and applications". Progress in Nuclear Magnetic Resonance Spectroscopy . 34 (3–4): 203–256. Bibcode:1999PNMRS..34..203J. doi:10.1016/S0079-6565(99)00003-5.

[9] 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 (6): 3354–3364. doi: 10.1039/C5SC00670H . PMC 5656982 . PMID 29142693.

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