Molar mass

In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance in that sample, measured in moles.[1] 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.

The molecular weight is very commonly used as a synonym of molar mass, particularly for molecular compounds; however, the most authoritative sources define it differently (see molecular mass).

The formula weight is a synonym of molar mass that is frequently used for non-molecular compounds, such as ionic salts.

The molar mass is an intensive property of the substance, that does not depend on the size of the sample. In the International System of Units (SI), the base unit of molar mass is kg/mol. However, for historical reasons, molar masses are almost always expressed in g/mol.

The mole was defined in such as way that the molar mass of a compound, in g/mol, is numerically equal (for all practical purposes) to the average mass of one molecule, in atomic mass units (daltons). Thus, for example, the average mass of a molecule of water is about 18.0153 daltons, and the molar mass of water is about 18.0153 g/mol.

For chemical elements without isolated molecules, such as carbon and metals, the molar mass is computed dividing by the number of moles of atoms instead. Thus, for example, the molar mass of iron is about 55.845 g/mol.

Between 1971 and 2019, SI defined the "amount of substance" as a separate dimension of measurement, and the mole was defined as the amount of substance that has as many constituent particles as there are atoms in 12 grams of carbon-12. In that period, the molar mass of carbon-12 was thus exactly 12 g/mol, by definition. Since 2019, a mole of any substance has been redefined in the SI as the amount of that substance containing an exactly defined number of particles, N = 6.02214076×1023. Therefore, the molar mass of a compound now is simply the mass of this number of molecules of the compound.

Molar mass
Common symbols
SI unitkg/mol
Other units

Molar masses of elements

Before reading this section, it must be understood that the 2019 redefinition of the SI base units concluded that the molar mass constant is not exactly 1×10−3 kg/mol, but Mu = 0.99999999965(30)×10−3 kg⋅mol−1.[2]

The molar mass of atoms of an element is given by the standard atomic weight of the element[3] multiplied by the molar mass constant, Mu ≈ 1 × 10−3 kg/mol = 1 g/mol:[4]

The molar mass Mm can be calculated from equation

   Mm = m/n

where m is the mass of substance and n is the number of moles of the substance.

M(H) = 1.00797(7) × 1 g/mol = 1.00797(7) g/mol
M(S) = 32.065(5) × 1 g/mol = 32.065(5) g/mol
M(Cl) = 35.453(2) × 1 g/mol = 35.453(2) g/mol
M(Fe) = 55.845(2) × 1 g/mol = 55.845(2) g/mol.

Multiplying by the molar mass constant ensures that the calculation is dimensionally correct: standard relative atomic masses are dimensionless quantities (i.e., pure numbers) whereas molar masses have units (in this case, grams/mole).

Some elements are usually encountered as molecules, e.g. hydrogen (H
), sulfur (S
), chlorine (Cl
). The molar mass of molecules of these elements is the molar mass of the atoms multiplied by the number of atoms in each molecule:

) = 2 × 1.007 97(7) × 1 g/mol = 2.01588(14) g/mol
) = 8 × 32.065(5) × 1 g/mol = 256.52(4) g/mol
) = 2 × 35.453(2) × 1 g/mol = 70.906(4) g/mol.

Molar masses of compounds

The molar mass of a compound is given by the sum of the standard atomic weight (namely, the standard relative atomic mass) of the atoms which form the compound multiplied by the molar mass constant, M

M(NaCl) = [22.989 769 28(2) + 35.453(2)] × 1 g/mol = 58.443(2) g/mol
) = ([12 × 12.0107(8)] + [22 × 1.007 94(7)] + [11 × 15.9994(3)]) × 1 g/mol = 342.297(14) g/mol.

An average molar mass may be defined for mixtures of compounds.[1] This is particularly important in polymer science, where different polymer molecules may contain different numbers of monomer units (non-uniform polymers).[5][6]

Average molar mass of mixtures

The average molar mass of mixtures can be calculated from the mole fractions of the components and their molar masses :

It can also be calculated from the mass fractions of the components:

As an example, the average molar mass of dry air is 28.97 g/mol.[7]

Related quantities

Molar mass is closely related to the relative molar mass (M
) of a compound, to the older term formula weight (F.W.), and to the standard atomic masses of its constituent elements. However, it should be distinguished from the molecular mass (also known as molecular weight), which is the mass of one molecule (of any single isotopic composition) and is not directly related to the atomic mass, the mass of one atom (of any single isotope). The dalton, symbol Da, is also sometimes used as a unit of molar mass, especially in biochemistry, with the definition 1 Da = 1 g/mol, despite the fact that it is strictly a unit of mass (1 Da = 1 u = 1.660 539 066 60(50) ×10−27 kg, as of 2018 CODATA recommended values).

Gram atomic mass is another term for the mass, in grams, of one mole of atoms of that element. "Gram atom" is a former term for a mole.

Molecular weight (M.W.) is an older term for what is now more correctly called the relative molar mass (M
).[8] This is a dimensionless quantity (i.e., a pure number, without units) equal to the molar mass divided by the molar mass constant.[9]

Molecular mass

The molecular mass (m) is the mass of a given molecule: it is measured in unified atomic mass units (u or Da).[10] Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. This is distinct but related to the molar mass, which is a measure of the average molecular mass of all the molecules in a sample and is usually the more appropriate measure when dealing with macroscopic (weigh-able) quantities of a substance.

Molecular masses are calculated from the atomic masses of each nuclide, while molar masses are calculated from the standard atomic weights[11] 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) u (1H
16O) and 22.027 7364(9) u (2H

The distinction between molar mass and molecular mass is important because relative molecular masses can be measured directly by mass spectrometry, often to a precision of a few parts per million. This is accurate enough to directly determine the chemical formula of a molecule.[12]

DNA synthesis usage

The term formula weight (F.W.) has a specific meaning when used in the context of DNA synthesis: whereas an individual phosphoramidite nucleobase to be added to a DNA polymer has protecting groups and has its molecular weight quoted including these groups, the amount of molecular weight that is ultimately added by this nucleobase to a DNA polymer is referred to as the nucleobase's formula weight (i.e., the molecular weight of this nucleobase within the DNA polymer, minus protecting groups).

Precision and uncertainties

The precision to which a molar mass is known depends on the precision of the atomic masses from which it was calculated, and value of the molar mass constant. Most atomic masses are known to a precision of at least one part in ten-thousand, often much better[3] (the atomic mass of lithium is a notable, and serious,[13] exception). This is adequate for almost all normal uses in chemistry: it is more precise than most chemical analyses, and exceeds the purity of most laboratory reagents.

The precision of atomic masses, and hence of molar masses, is limited by the knowledge of the isotopic distribution of the element. If a more accurate value of the molar mass is required, it is necessary to determine the isotopic distribution of the sample in question, which may be different from the standard distribution used to calculate the standard atomic mass. The isotopic distributions of the different elements in a sample are not necessarily independent of one another: for example, a sample which has been distilled will be enriched in the lighter isotopes of all the elements present. This complicates the calculation of the standard uncertainty in the molar mass.

A useful convention for normal laboratory work is to quote molar masses to two decimal places for all calculations. This is more accurate than is usually required, but avoids rounding errors during calculations. When the molar mass is greater than 1000 g/mol, it is rarely appropriate to use more than one decimal place. These conventions are followed in most tabulated values of molar masses.[14][15]


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 sheets (SDS). Molar masses typically vary between:

1–238 g/mol for atoms of naturally occurring elements;
10–1000 g/mol for simple chemical compounds;
1000–5,000,000 g/mol for polymers, proteins, 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 spectrometric measurements of atomic weights and molecular masses, and are of mostly historical interest. All of the procedures rely on colligative properties, and any dissociation of the compound must be taken into account.

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:

where n is the amount of substance. The vapour density (ρ) is given by

Combining these two equations gives an expression for the molar mass in terms of the vapour density for conditions of known pressure and temperature.

Freezing-point depression

The freezing point of a solution is lower than that of the pure solvent, and the freezing-point depression (ΔT) 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 (K
) and is characteristic for each solvent. If w represents the mass fraction of the solute in solution, and assuming no dissociation of the solute, the molar mass is given by

Boiling-point elevation

The boiling point of a solution of an involatile solute is higher than that of the pure solvent, and the boiling-point elevation (ΔT) 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 (K
) and is characteristic for each solvent. If w represents the mass fraction of the solute in solution, and assuming no dissociation of the solute, the molar mass is given by


  1. ^ a b International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry, 2nd edition, Oxford: Blackwell Science. ISBN 0-632-03583-8. p. 41. Electronic version.
  2. ^ "2018 CODATA Value: molar mass constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  3. ^ a b Wieser, M. E. (2006), "Atomic Weights of the Elements 2005" (PDF), Pure and Applied Chemistry, 78 (11): 2051–66, doi:10.1351/pac200678112051
  4. ^ Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2011). "CODATA Recommended Values of the Fundamental Physical Constants: 2010". Cite journal requires |journal= (help) Database developed by J. Baker, M. Douma, and S. Kotochigova. National Institute of Standards and Technology, Gaithersburg, MD 20899.
  5. ^ "International union of pure and applied chemistry, commission on macromolecular nomenclature, note on the terminology for molar masses in polymer science". Journal of Polymer Science: Polymer Letters Edition. 22 (1): 57. 1984. Bibcode:1984JPoSL..22...57.. doi:10.1002/pol.1984.130220116.
  6. ^ Metanomski, W. V. (1991). Compendium of Macromolecular Nomenclature. Oxford: Blackwell Science. pp. 47–73. ISBN 0-632-02847-5.
  7. ^ The Engineering ToolBox Molecular Mass of Air
  8. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "relative molar mass". doi:10.1351/goldbook.{{{file}}}Error in template * mandatory parameter missing (GoldBookRef): file
  9. ^ The technical definition is that the relative molar mass is the molar mass measured on a scale where the molar mass of unbound carbon 12 atoms, at rest and in their electronic ground state, is 12. The simpler definition given here is equivalent to the full definition because of the way the molar mass constant is itself defined.
  10. ^ 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
  11. ^ "Atomic Weights and Isotopic Compositions for All Elements". NIST. Retrieved 2007-10-14.
  12. ^ "Author Guidelines – Article Layout". RSC Publishing. Retrieved 2007-10-14.
  13. ^ Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. p. 21. ISBN 978-0-08-037941-8.
  14. ^ See, e.g., Weast, R. C., ed. (1972). Handbook of Chemistry and Physics (53rd ed.). Cleveland, OH: Chemical Rubber Co.
  15. ^ Possolo, Antonio; van der Veen, Adriaan M. H.; Meija, Juris; Hibbert, D. Brynn (2018-01-04). "Interpreting and propagating the uncertainty of the standard atomic weights (IUPAC Technical Report)". Pure and Applied Chemistry. 90 (2): 395–424. doi:10.1515/pac-2016-0402.

External links

Atomic mass unit

The dalton or unified atomic mass unit (SI symbols: Da or u) is a unit of mass widely used in physics and chemistry. It is defined precisely as 1/12 of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest. A mass of 1 Da is also referred to as the atomic mass constant and denoted by mu.

This unit is commonly used in physics and chemistry to express the mass of atomic-scale objects, such as atoms, molecules, and elementary particles, both for discrete instances and multiple types of ensemble averages. For example, an atom of helium-4 has a mass of 4.0026 Da. This is an intrinsic property of the isotope and all helium-4 have the same mass. Acetylsalicylic acid (aspirin), C9H8O4, has an average mass of approximately 180.157 Da. However, there are no acetylsalicylic acid molecules with this mass. The two most common masses of individual acetylsalicylic acid molecules are 180.04228 Da and 181.04565 Da.

The molecular masses of proteins, nucleic acids, and other large polymers are often expressed with the units kilodaltons (kDa), megadaltons (MDa), etc. Titin, one of the largest known proteins, has a molecular mass of between 3 and 3.7 megadaltons. The DNA of chromosome 1 in the human genome has about 249 million base pairs, each with an average mass of about 650 Da, or 156 GDa total.The mole is a unit of amount of substance, widely used in chemistry and physics, which was originally defined so that the mass of one mole of a substance, measured in grams, would be numerically equal to the average mass of one of its constituent particles, measured in daltons. That is, the molar mass of a chemical compound was meant to be numerically equal to its average molecular mass. For example, the average mass of one molecule of water is about 18.0153 daltons, and one mole of water is about 18.0153 grams. A protein whose molecule has an average mass of 64 kDa would have a molar mass of 64 kg/mol. However, while this equality can be assumed for almost all practical purposes, it is now only approximate, because of the way mole was redefined on 20 May 2019.In general, the mass in daltons of an atom is numerically close, but not exactly equal to the number of nucleons A contained in its nucleus. It follows that the molar mass of a compound (grams per mole) is numerically close to the average number of nucleons contained in each molecule. By definition, the mass of an atom of carbon-12, is 12 daltons, which corresponds with the number of nucleons that it has (6 protons and 6 neutrons). However, the mass of an atomic-scale object is affected by the binding energy of the nucleons in its atomic nuclei, as well as the mass and binding energy of its electrons. Therefore, this equality holds only for the carbon-12 atom in the stated conditions, and will vary for other substances. For example, the mass of one unbound atom of the common hydrogen isotope (hydrogen-1, protium) is 1.007825032241(94) Da, the mass of one free neutron is 1.00866491595(49) Da, and the mass of one hydrogen-2 (deuterium) atom is 2.014101778114(122) Da. In general, the difference (mass defect) is less than 0.1%; exceptions include hydrogen-1 (about 0.8%), helium-3 (0.5%), lithium (0.25%) and beryllium (0.15%).

The atomic mass unit should not be confused with unit of mass in the atomic units systems, which is instead the electron rest mass (me).


Degrees of general hardness (dGH or °GH) is a unit of water hardness, specifically of general hardness. General hardness is a measure of the concentration of divalent metal ions such as calcium (Ca2+) and magnesium (Mg2+) per volume of water. Specifically, 1 dGH is defined as 10 milligrams (mg) of calcium oxide (CaO) per litre of water. Since CaO has a molar mass of 56.08 g/mol, 1 dGH is equivalent to 0.17832 mmol per litre of elemental calcium and/or magnesium ions.

In water testing, paper strips often measure hardness in parts per million (ppm), where one part per million is defined as one milligram of calcium carbonate (CaCO3) per litre of water. Consequently, 1 dGH corresponds to 10 ppm CaO but 17.848 ppm CaCO3 which has a molar mass of 100.09 g/mol.

Density of air

The density of air or atmospheric density, denoted ρ (Greek: rho), is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in atmospheric pressure, temperature and humidity. At 1013.25 hPa (abs) and 15°C, air has a density of approximately 1.225 kg/m³ (0.001225 g/cm³, 0.0023769 slug/(cu ft), 0.0765 lb/(cu ft)) according to ISA (International Standard Atmosphere).Air density is a property used in many branches of science, engineering, and industry, including aeronautics; gravimetric analysis; the air-conditioning industry; atmospheric research and meteorology; agricultural engineering (modeling and tracking of Soil-Vegetation-Atmosphere-Transfer (SVAT) models); and the engineering community that deals with compressed air.Depending on the measuring instruments used, different sets of equations for the calculation of the density of air can be applied. Air is a mixture of gases and the calculations always simplify, to a greater or lesser extent, the properties of the mixture.


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.IUPAC has deprecated the use of the term polydispersity index, having replaced it with the term dispersity, represented by the symbol Đ (pronounced D-stroke) which can refer to either molecular mass or degree of polymerization. It can be calculated using the equation ĐM = Mw/Mn, where Mw is the weight-average molar mass and Mn is the number-average molar mass. It can also be calculated according to degree of polymerization, where ĐX = Xw/Xn, where Xw is the weight-average degree of polymerization and Xn is the number-average degree of polymerization. In certain limiting cases where ĐM = ĐX, it is simply referred to as Đ. IUPAC has also deprecated the terms monodisperse, which is considered to be self-contradictory, and polydisperse, which is considered redundant, preferring the terms uniform and non-uniform instead.

Graham's law

Graham's law of effusion (also called Graham's law of diffusion) was formulated by Scottish physical chemist Thomas Graham in 1848. Graham found experimentally that the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles. This formula can be written as:



Rate1 is the rate of effusion for the first gas. (volume or number of moles per unit time).
Rate2 is the rate of effusion for the second gas.
M1 is the molar mass of gas 1
M2 is the molar mass of gas 2.

Graham's law states that the rate of diffusion or of effusion of a gas is inversely proportional to the square root of its molecular weight. Thus, if the molecular weight of one gas is four times that of another, it would diffuse through a porous plug or escape through a small pinhole in a vessel at half the rate of the other (heavier gases diffuse more slowly). A complete theoretical explanation of Graham's law was provided years later by the kinetic theory of gases. Graham's law provides a basis for separating isotopes by diffusion—a method that came to play a crucial role in the development of the atomic bomb.

Graham's law is most accurate for molecular effusion which involves the movement of one gas at a time through a hole. It is only approximate for diffusion of one gas in another or in air, as these processes involve the movement of more than one gas.

In the same conditions of temperature and pressure, the molar mass is proportional to the mass density. Therefore the rate of diffusion of different gases is inversely proportional to the square root of their mass densities.

Higher alkanes

Higher alkanes are alkanes having nine or more carbon atoms. Nonane is the lightest alkane to have a flash point above 25 °C, and is not classified as dangerously flammable.

The term higher alkanes is sometimes used literally as "alkanes with a higher number of carbon atoms". One definition distinguishes the higher alkanes as the n-alkanes that are solid under natural conditions.


Molality, also called molal concentration, is a measure of the concentration of a solute in a solution in terms of amount of substance in a specified amount of mass of the solvent. This contrasts with the definition of molarity which is based on a specified volume of solution.

A commonly used unit for molality in chemistry is mol/kg. A solution of concentration 1 mol/kg is also sometimes denoted as 1 molal.


Molar may refer to:

Molar (tooth), the fourth kind of tooth in mammals

Molar (grape), another name for the Spanish wine grape Listan Negro

Molar (unit), a unit of concentration equal to 1 mole per litre

Molar mass

Molar volume

El Molar, Tarragona, a village in the comarca (county) of Priorat, province of Tarragona in the autonomous region of Catalonia, Spain

El Molar, Madrid, a town in the north of the Community of Madrid in the road to Burgos, after San Agustín de Guadalix

Molar concentration

Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solution. In chemistry, the most commonly used unit for molarity is the number of moles per litre, having the unit symbol mol/L. A solution with a concentration of 1 mol/L is said to be 1 molar, commonly designated as 1 M.

Molar heat capacity

The molar heat capacity of a chemical substance is the amount of energy that must be added, in the form of heat, to one mole of the substance in order to cause an increase of one unit in its temperature. Alternatively, it is the heat capacity of a sample of the substance divided by the number of moles of the sample; or also the specific heat capacity of the substance times its molar mass. The SI unit of specific heat is joule per kelvin times mole, J/K * mol.

Like the specific heat, measured the molar heat capacity of a substance, especially a gas, may be significantly higher when the sample is allowed to expand as it is heated (at constant pressure, or isobaric) than when is heated in a closed vessel that prevents expansion (at constant volume, or isochoric). The ratio between the two, however, is the same heat capacity ratio obtained from the corresponding specific heat capacities.

This property is most relevant in chemistry, when amounts of substances are often specified in moles rather than by mass or volume. The molar heat capacity generally increases with the molar mass, often varies with temperature and pressure, and is different for each state of matter. For example, at atmospheric pressure, the (isobaric) molar heat capacity of water just above the melting point is about 76 J/K * mol, but that of ice just below that point is about 37.84 J/K/mol. While the substance is undergoing a phase transition, such as melting or boiling, its molar heat capacity is technically infinite, because the heat goes into changing its state rather than raising its temperature. The concept is not appropriate for substances whose precise composition is not known, or whose molar mass is not well defined, such as polymers and oligomers of indeterminate molecular size.

A closely related property of a substance is the heat capacity per mole of atoms, or atom-molar heat capacity, in which the heat capacity of the sample is divided by the number of moles of atoms instead of moles of molecules. So, for example, the atom-molar heat capacity of water is 1/3 of its molar heat capacity, namely 25.3 J/K*mol

In informal chemistry contexts, the molar heat capacity may be called just "heat capacity" or "specific heat". However, international standards now recommend that "specific heat capacity" always refer to capacity per unit of mass, to avoid possible confusion. Therefore, the word "molar", not "specific", should always be used for this quantity.

Molar mass constant

The molar mass constant, usually denoted by Mu, is a physical constant defined as the ratio of the molar mass of an element (or a compound) and its relative mass.

The mole and the relative atomic mass were originally defined in the International System of Units (SI) in such a way that the constant was exactly 1 g/mol. That is, the numerical value of the molar mass of an element, in grams per mole of atoms, was equal to its atomic mass relative to the SI unit of atomic mass (dalton). Thus, for example the average atomic mass of chlorine is approximately 35.446 daltons, and the mass of one mole of chlorine atoms was approximately 35.446 grams.

On 20 May 2019, the SI definition of mole changed in such a way that the molar mass constant is no longer exactly 1 g/mol. However, the difference is insignificant for all practical purposes. According to the SI, the value of Mu now depends on the mass of one atom of carbon-12, which must be determined experimentally. As of that date, the 2018 CODATA recommended value of Mu is 0.99999999965(30)×10−3 kg⋅mol−1.The molar mass constant is important in writing dimensionally correct equations. While one may informally say "the molar mass of an element M is the same as it atomic weight A", the atomic weight (relative atomic mass) A is a dimensionless quantity, whereas the molar mass M has the units of mass per mole. Formally, M is A times the molar mass constant Mu.

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 (or molecular weight distribution) describes the relationship between the number of moles of each polymer species (Ni) and the molar mass (Mi) of that species. The molar mass distribution of a polymer may be modified by polymer fractionation.

Molar volume

The molar volume, symbol Vm, is the volume occupied by one mole of a substance (chemical element or chemical compound) at a given temperature and pressure. It is equal to the molar mass (M) divided by the mass density (ρ). It has the SI unit cubic metres per mole (m3/mol), although it is more practical to use the units cubic decimetres per mole (dm3/mol) for gases and cubic centimetres per mole (cm3/mol) for liquids and solids.

Mole (unit)

The mole (symbol: mol) is the base unit of amount of substance ("number of substance") in the International System of Units or System International (SI), defined as exactly 6.02214076×1023 particles, e.g., atoms, molecules, ions or electrons.The current definition was adopted in November 2018, revising its old definition based on the number of atoms in 12 grams of carbon-12 (12C) (the isotope of carbon with relative atomic mass 12 Da by definition).

The number 6.02214076×1023 (the Avogadro number) was chosen so that the mass of one mole of a chemical compound, in grams, is numerically equal (for all practical purposes) to the average mass of one molecule of the compound, in daltons. Thus, for example, one mole of water contains 6.02214076×1023 molecules, whose total mass is about 18.015 grams – and the mean mass of one molecule of water is about 18.015 daltons.

The mole is widely used in chemistry as a convenient way to express amounts of reactants and products of chemical reactions. For example, the chemical equation 2H2 + O2 → 2H2O can be interpreted to mean that 2 mol dihydrogen (H2) and 1 mol dioxygen (O2) react to form 2 mol water (H2O). The mole may also be used to represent the number of atoms, ions, or other entities in a given sample of a substance. The concentration of a solution is commonly expressed by its molarity, defined as the amount of dissolved substance per unit volume of solution, for which the unit typically used is moles per litre (mol/l), commonly abbreviated M.

The term gram-molecule was formerly used for "mole of molecules", and gram-atom for "mole of atoms". Thus, for example, 1 mole of MgBr2 is 1 gram-molecule of MgBr2 but 3 gram-atoms of MgBr2.

Mole fraction

In chemistry, the mole fraction or molar fraction (xi) is defined as the amount of a constituent (expressed in moles), ni divided by the total amount of all constituents in a mixture (also expressed in moles), ntot:

The sum of all the mole fractions is equal to 1:

The same concept expressed with a denominator of 100 is the mole percent or molar percentage or molar proportion (mol%).

The mole fraction is also called the amount fraction. It is identical to the number fraction, which is defined as the number of molecules of a constituent Ni divided by the total number of all molecules Ntot. The mole fraction is sometimes denoted by the lowercase Greek letter χ (chi) instead of a Roman x. For mixtures of gases, IUPAC recommends the letter y.

The National Institute of Standards and Technology of the United States prefers the term amount-of-substance fraction over mole fraction because it does not contain the name of the unit mole.

Whereas mole fraction is a ratio of moles to moles, molar concentration is a quotient of moles to volume.

The mole fraction is one way of expressing the composition of a mixture with a dimensionless quantity; mass fraction (percentage by weight, wt%) and volume fraction (percentage by volume, vol%) are others.

Molecular mass

The molecular mass (m) is the mass of a given molecule: it is measured in unified atomic mass units (u or Da). 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 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 unified atomic mass units (u or Da) were by definition numerically equivalent to otherwise identical quantities expressed in the units g/mol and were thus strictly numerically interchangeable. After the May 20th, 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.

Potassium phosphate

Potassium phosphate is a generic term for the salts of potassium and phosphate ions including:

Monopotassium phosphate (KH2PO4) (Molar mass approx: 136 g/mol)

Dipotassium phosphate (K2HPO4) (Molar mass approx: 174 g/mol)

Tripotassium phosphate (K3PO4) (Molar mass approx: 212.27 g/mol)As food additives, potassium phosphates have the E number E340.

Reference ranges for blood tests

Reference ranges for blood tests are sets of values used by a health professional to interpret a set of medical test results from blood samples.

Reference ranges for blood tests are studied within the field of clinical chemistry (also known as "clinical biochemistry", "chemical pathology" or "pure blood chemistry"), the area of pathology that is generally concerned with analysis of bodily fluids.

Blood test results should always be interpreted using the reference range provided by the laboratory that performed the test.

Vapour density

Vapour density is the density of a vapour in relation to that of hydrogen. It may be defined as mass of a certain volume of a substance divided by mass of same volume of hydrogen.

vapour density = mass of n molecules of gas / mass of n molecules of hydrogen.


vapour density = molar mass of gas / molar mass of H2vapour density = molar mass of gas / 2.016

vapour density = ~½ × molar mass

(and thus: molar mass = ~2 × vapour density)

For example, vapour density of mixture of NO2 and N2O4 is 38. 3.Vapour density is a unitless quantity.

Mole concepts
Physical quantities


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