Molecular mass

Molecular mass

Overview
The molecular mass of a substance
Chemical compound
A chemical compound is a pure chemical substance consisting of two or more different chemical elements that can be separated into simpler substances by chemical reactions. Chemical compounds have a unique and defined chemical structure; they consist of a fixed ratio of atoms that are held together...

 is the mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

 of one molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

 of that substance, in unified atomic mass unit(s) u (equal to 1/12 the mass of one atom of the isotope
Isotope
Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...

  carbon-12
Carbon-12
Carbon-12 is the more abundant of the two stable isotopes of the element carbon, accounting for 98.89% of carbon; it contains 6 protons, 6 neutrons, and 6 electrons....

). This is numerically equivalent to the relative molecular mass (Mr) of a molecule, frequently referred to by the term molecular weight, which is the ratio of the mass of that molecule to 1/12 of the mass of carbon-12 and is a dimensionless number.
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Encyclopedia
The molecular mass of a substance
Chemical compound
A chemical compound is a pure chemical substance consisting of two or more different chemical elements that can be separated into simpler substances by chemical reactions. Chemical compounds have a unique and defined chemical structure; they consist of a fixed ratio of atoms that are held together...

 is the mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

 of one molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

 of that substance, in unified atomic mass unit(s) u (equal to 1/12 the mass of one atom of the isotope
Isotope
Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...

  carbon-12
Carbon-12
Carbon-12 is the more abundant of the two stable isotopes of the element carbon, accounting for 98.89% of carbon; it contains 6 protons, 6 neutrons, and 6 electrons....

). This is numerically equivalent to the relative molecular mass (Mr) of a molecule, frequently referred to by the term molecular weight, which is the ratio of the mass of that molecule to 1/12 of the mass of carbon-12 and is a dimensionless number. Thus, it is incorrect to express relative molecular mass (molecular weight) in daltons (Da). The terms molecular weight and molecular mass have been confused on numerous websites, which often state that molecular weight was used in the past as another term for molecular mass.

Molecular mass differs from more common measurements of the mass of chemicals, such as molar mass
Molar mass
Molar mass, symbol M, is a physical property of a given substance , namely its mass per amount of substance. The base SI unit for mass is the kilogram and that for amount of substance is the mole. Thus, the derived unit for molar mass is kg/mol...

, by taking into account the isotopic composition of a molecule rather than the average isotopic distribution of many molecules. As a result, molecular mass is a more precise number than molar mass; however it is more accurate to use molar mass on bulk samples. This means that molar mass is appropriate most of the time except when dealing with single molecules.

The concept of molecular mass is important for all molecules, especially for complex molecules like polymers and biopolymers such as proteins and carbohydrates. The determination of their molecular mass is often difficult, and is usually inferred from gel permeation chromatography
Gel Permeation Chromatography
Gel permeation chromatography is a type of size exclusion chromatography , that separates analytes on the basis of size. The technique is often used for the analysis of polymers. As a technique, SEC was first developed in 1955 by Lathe and Ruthven. The term gel permeation chromatography can be...

 and mass spectrometry
Mass spectrometry
Mass spectrometry is an analytical technique that measures the mass-to-charge ratio of charged particles.It is used for determining masses of particles, for determining the elemental composition of a sample or molecule, and for elucidating the chemical structures of molecules, such as peptides and...

.

Definition


There are varying interpretations of this definition. Many chemists use molecular mass as a synonym of molar mass
Molar mass
Molar mass, symbol M, is a physical property of a given substance , namely its mass per amount of substance. The base SI unit for mass is the kilogram and that for amount of substance is the mole. Thus, the derived unit for molar mass is kg/mol...

, differing only in units (see average molecular mass below). A stricter interpretation does not equate the two,as the mass of a single molecule is not the same as the average of an ensemble. Because a mole of molecules may contain a variety of molecular masses due to natural isotope
Isotope
Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...

s, the average mass is usually not identical to the mass of any single molecule. The actual numerical difference can be very small when considering small molecules and the molecular mass of the most common isotopomer in which case the error only matters to physicists and a small subset of highly specialized chemists; however it is always more correct, accurate and consistent to use molar mass
Molar mass
Molar mass, symbol M, is a physical property of a given substance , namely its mass per amount of substance. The base SI unit for mass is the kilogram and that for amount of substance is the mole. Thus, the derived unit for molar mass is kg/mol...

 in any bulk stoichiometric calculations. The size of this error
Margin of error
The margin of error is a statistic expressing the amount of random sampling error in a survey's results. The larger the margin of error, the less faith one should have that the poll's reported results are close to the "true" figures; that is, the figures for the whole population...

 becomes much larger when considering larger molecules or less abundant
Natural abundance
In chemistry, natural abundance refers to the abundance of isotopes of a chemical element as naturally found on a planet. The relative atomic mass of these isotopes is the atomic weight listed for the element in the periodic table...

 isotopomers. The molecular mass of a molecule which happens to contain heavier isotopes than the average molecule in the sample can differ from the molar mass by several mass units. Also the molar mass comes into comparison with the number of particles contained within the structure by multiplying the number of moles by Avogadro's constant: NA=6.022 141 79(30)·1023 mol−1.

Average mass


The average molecular mass (sometimes abbreviated as average mass) is another variation on the use of the term molecular mass. The average molecular mass is the abundance weighted mean
Mean
In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....

 (average) of the molecular masses in a sample
Sample (material)
In general, a sample is a limited quantity of something which is intended to be similar to and represent a larger amount of that thing. The things could be countable objects such as individual items available as units for sale, or a material not countable as individual items. Samples of countable...

. This is often closer to what is meant when "molecular mass" and "molar mass" are used synonym
Synonym
Synonyms are different words with almost identical or similar meanings. Words that are synonyms are said to be synonymous, and the state of being a synonym is called synonymy. The word comes from Ancient Greek syn and onoma . The words car and automobile are synonyms...

lousy and may have derived
Derived
In phylogenetics, a derived trait is a trait that is present in an organism, but was absent in the last common ancestor of the group being considered. This may also refer to structures that are not present in an organism, but were present in its ancestors, i.e. traits that have undergone secondary...

 from shortening of this term. The average molecular mass and the molar mass of a particular substance in a particular sample are in fact numerically identical and may be inter-converted by Avogadro's constant. It should be noted, however, that the molar mass is almost always a computed figure derived from the standard atomic weights, whereas the average molecular mass, in fields that need the term, is often a measured figure specific to a sample. Therefore, they often vary since one is theoretical and the other is experimental
Experimental physics
Within the field of physics, experimental physics is the category of disciplines and sub-disciplines concerned with the observation of physical phenomena in order to gather data about the universe...

. Specific samples may vary significantly from the expected isotopic composition due to real deviations from earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

's average isotopic abundances.

Computation


The molecular mass can be calculated as the sum of the individual
Individual
An individual is a person or any specific object or thing in a collection. Individuality is the state or quality of being an individual; a person separate from other persons and possessing his or her own needs, goals, and desires. Being self expressive...

 isotopic masses (as found in a table of isotopes) of all the atoms in any molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

. This is possible because molecules are created by chemical reaction
Chemical reaction
A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, typically following the input of some type of energy, such as heat, light or electricity...

s which, unlike nuclear reaction
Nuclear reaction
In nuclear physics and nuclear chemistry, a nuclear reaction is semantically considered to be the process in which two nuclei, or else a nucleus of an atom and a subatomic particle from outside the atom, collide to produce products different from the initial particles...

s, have very small binding energies
Binding energy
Binding energy is the mechanical energy required to disassemble a whole into separate parts. A bound system typically has a lower potential energy than its constituent parts; this is what keeps the system together—often this means that energy is released upon the creation of a bound state...

 compared to the rest mass of the atoms ( 10−9) and therefore create a negligible mass defect. The use of average atomic masses
Atomic weight
Atomic weight is a dimensionless physical quantity, the ratio of the average mass of atoms of an element to 1/12 of the mass of an atom of carbon-12...

 derived from the standard atomic weights found on a standard periodic table
Periodic table
The periodic table of the chemical elements is a tabular display of the 118 known chemical elements organized by selected properties of their atomic structures. Elements are presented by increasing atomic number, the number of protons in an atom's atomic nucleus...

 will result in an average molecular mass, whereas the use of isotopic masses will result in a molecular mass consistent with the strict interpretation of the definition, i.e. that of a single molecule. However, any given molecule may contain any given combination of isotopes, so there may be multiple molecular masses for each chemical compound.

Measurement


The molecular mass can also be measured directly using mass spectrometry
Mass spectrometry
Mass spectrometry is an analytical technique that measures the mass-to-charge ratio of charged particles.It is used for determining masses of particles, for determining the elemental composition of a sample or molecule, and for elucidating the chemical structures of molecules, such as peptides and...

. In mass spectrometry, the molecular mass of a small molecule is usually reported as the monoisotopic mass
Monoisotopic mass
The monoisotopic mass is the sum of the masses of the atoms in a molecule using the unbound, ground-state, rest mass of the principal isotope for each element instead of the isotopic average mass. For typical organic compounds, where the monoisotopic mass is most commonly used, this also results...

, 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 possible. 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. This however may differ from the true average molecular mass of the sample due to natural (or artificial) variations in the isotopic distributions.

The basis for determination of molecular weight according to the Staudinger
Hermann Staudinger
- External links :* Staudinger's * Staudinger's Nobel Lecture *....

 method (since replaced by the more general Mark-Houwink equation) is the fact that relative viscosity of suspensions
Suspension (chemistry)
In chemistry, a suspension is a heterogeneous fluid containing solid particles that are sufficiently large for sedimentation. Usually they must be larger than 1 micrometer. The internal phase is dispersed throughout the external phase through mechanical agitation, with the use of certain...

 depends on volumetric proportion of solid particles.

There are several companies that manufacture accurate instruments for determining absolute molecular weight quickly and easily. These companies include Brookhaven Instruments
Brookhaven Instruments
Brookhaven Instruments Corporation is a Nova Instruments company. Established in the late 1960s, Brookhaven Instruments pioneered modern techniques in characterizing nanoparticles, proteins, and polymers using light scattering techniques such as dynamic, static, electrophoretic, and phase analysis...

, Malvern Instruments
Malvern Instruments
Malvern Instruments is a Spectris plc company.Founded in the late 1960s, the company is a manufacturer and supplier of laboratory analytical instruments,was influential in the development of the Malvern Correlator...

, and Horiba
Horiba
is a Japanese manufacturer of precision instruments for measurement and analysis. They claim to have 80% of the world market for instruments that measure and analyze automobile exhaust gas, and also make instruments for environmental, medical and scientific applications.Horiba was founded in 1945...


Unit type variation


The molar mass
Molar mass
Molar mass, symbol M, is a physical property of a given substance , namely its mass per amount of substance. The base SI unit for mass is the kilogram and that for amount of substance is the mole. Thus, the derived unit for molar mass is kg/mol...

 of a substance is the mass of 1 mol (the SI unit for the basis SI quantity amount of substance, having the symbol n) of the substance. This has a numerical value which is the average molecular mass of the molecules in the substance multiplied by Avogadro's constant approximately 6.022×1023. The most common units of molar mass are g/mol because in those units the numerical value equals the average molecular mass in units of u.

Conversion factor of average molecular mass to molar mass:
molar mass = average molecular mass × ((1/6.022)×10-23g/u)×(6.022×1023/mol)
or
molar mass in g/mol= average molecular mass in u

(Note that these relations are true for theoretical and experimental values, but not between experimental and theoretical values. Molar mass is most often theoretical and average molecular mass is most often experimental)

The average atomic mass of natural hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

 is 1.00794 u and that of natural oxygen
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...

 is 15.9994 u;
therefore, the molecular mass of natural water
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

 with formula H2O is (2 × 1.00794 u) + 15.9994 u = 18.01528 u.
Therefore, one mole
Mole (unit)
The mole is a unit of measurement used in chemistry to express amounts of a chemical substance, defined as an amount of a substance that contains as many elementary entities as there are atoms in 12 grams of pure carbon-12 , the isotope of carbon with atomic weight 12. This corresponds to a value...

 of water has a mass of 18.01528 grams. However, the exact mass of hydrogen-1 (the most common hydrogen isotope
Isotope
Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...

) is 1.00783, and the exact mass of oxygen-16 (the most common oxygen isotope) is 15.9949, so the mass of the most common molecule of water is 18.01056 u. The difference of 0.00472 u or 0.03% comes from the fact that natural water contain traces of water molecules containing, oxygen-17, oxygen-18 or hydrogen-2 (Deuterium
Deuterium
Deuterium, also called heavy hydrogen, is one of two stable isotopes of hydrogen. It has a natural abundance in Earth's oceans of about one atom in of hydrogen . Deuterium accounts for approximately 0.0156% of all naturally occurring hydrogen in Earth's oceans, while the most common isotope ...

) atoms. Although this difference is trivial in bulk chemistry calculations, it can result in complete failure in situations where the behavior of individual molecules matters, such as in mass spectrometry
Mass spectrometry
Mass spectrometry is an analytical technique that measures the mass-to-charge ratio of charged particles.It is used for determining masses of particles, for determining the elemental composition of a sample or molecule, and for elucidating the chemical structures of molecules, such as peptides and...

 and particle physics (where the mixture of isotopes does not act as an average).

There are also situations where the isotopic distributions are not typical such as with heavy water
Heavy water
Heavy water is water highly enriched in the hydrogen isotope deuterium; e.g., heavy water used in CANDU reactors is 99.75% enriched by hydrogen atom-fraction...

 used in some nuclear reactors which is artificially enriched with Deuterium. In these cases the computed values of molar mass and average molecular mass, which are ultimately derived from the standard atomic weights, will not be the same as the actual molar mass or average molecular mass of the sample. In this case the mass of deuterium is 2.0136 u and the average molecular mass of this water (assuming 100% deuterium enrichment) is (2 × 2.0136 u) + 15.9994 u = 20.0266 u. This is a very large difference of ~11% error from the expected average molecular mass based on the standard atomic weights. Furthermore the most abundant molecular mass is actually slightly less than the average molecular mass since oxygen-16 is still the most common. (2 × 2.0136 u) + 15.9949 u = 20.0221 u. Although this is an extreme artificial example, natural variation in isotopic distributions do occur and are measurable. For example, the atomic weight of lithium as found by isotopic analysis of 39 lithium reagents from several manufacturers varied from 6.939 to 6.996.

See also

  • Avogadro's number
    Avogadro's number
    In chemistry and physics, the Avogadro constant is defined as the ratio of the number of constituent particles N in a sample to the amount of substance n through the relationship NA = N/n. Thus, it is the proportionality factor that relates the molar mass of an entity, i.e...

  • Atomic mass unit
    Atomic mass unit
    The unified atomic mass unit or dalton is a unit that is used for indicating mass on an atomic or molecular scale. It is defined as one twelfth of the rest mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state, and has a value of...

  • Absolute molar mass
    Absolute molar mass
    Absolute Molar Mass is a process to determine the characteristics of molecules.- History :The first absolute measurements of molecular weights were based on fundamental physical characteristics and their relation to the molar mass...

  • Monoisotopic mass
    Monoisotopic mass
    The monoisotopic mass is the sum of the masses of the atoms in a molecule using the unbound, ground-state, rest mass of the principal isotope for each element instead of the isotopic average mass. For typical organic compounds, where the monoisotopic mass is most commonly used, this also results...

  • gram-molecular weight
  • Molar mass distribution
    Molar mass distribution
    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 in a polymer describes the relationship between the number of moles of each polymer species...


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