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 In chemistry, the molar mass M is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by the amount of substance.[1] The base SI unit SI unit for molar mass is kg/mol. However, for historical reasons, molar masses are almost always expressed in g/mol. As an example, the molar mass of water: M(H2O) ≈ 6998180148800000000♠18.01488 g/mol.Contents1 Molar masses of elements 2 Molar masses of compounds 3 Average molar mass of mixtures 4 Related quantities4.1 Molecular mass 4.2 DNA DNA synthesis usage5 Precision and uncertainties 6 Measurement6.1 Vapour density 6.2 Freezing-point depression 6.3 Boiling-point elevation7 References 8 External linksMolar masses of elements Main articles: Relative atomic mass and Standard atomic weight The molar mass of atoms of an element is given by the Standard atomic weight of the element[2] multiplied by the molar mass constant, M u = 1 × 10−3 kg/mol = 1 g/mol:[3]M(H) = 1.007 97(7) × 1 g/mol = 1.007 97(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 2), sulfur (S 8), chlorine (Cl 2). The molar mass of molecules of these elements is the molar mass of the atoms multiplied by the number of atoms in each molecule:M(H 2) = 2 × 1.007 97(7) × 1 g/mol = 2.015 88(14) g/mol M(S 8) = 8 × 32.065(5) × 1 g/mol = 256.52(4) g/mol M(Cl 2) = 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 u:M(NaCl) = [22.989 769 28(2) + 35.453(2)] × 1 g/mol = 58.443(2) g/mol M(C 12H 22O 11) = ([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).[4][5] Average molar mass of mixtures The average molar mass of mixtures M ¯ displaystyle bar M can be calculated from the mole fractions x i displaystyle x_ i of the components and their molar masses M i displaystyle M_ i : M ¯ = ∑ i x i M i displaystyle bar M =sum _ i x_ i M_ i , It can also be calculated from the mass fractions w i displaystyle w_ i of the components: 1 / M ¯ = ∑ i w i M i , displaystyle 1/ bar M =sum _ i frac w_ i M_ i , As an example, the average molar mass of dry air is 28.97 g/mol.[6] Related quantities Molar mass is closely related to the relative molar mass (M r) 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 = 1.660 538 921(73)×10−27 kg).[7][3] 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 r).[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 Main article: Molecular mass The molecular mass (m) is the mass of a given molecule: it is measured in atomic mass units (u) or daltons (Da).[7] Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The molar mass 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 standard atomic weights[10] of each nuclide, while molar masses are calculated from the atomic mass of each element. The atomic mass 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 216O) and 22.027 7364(9) u (D 218O). 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.[11] DNA DNA synthesis usageThis section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. (December 2008) (Learn how and when to remove this template message)The term formula weight (F.W.) has a specific meaning when used in the context of DNA DNA synthesis: whereas an individual phosphoramidite nucleobase to be added to a DNA 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 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. Most atomic masses are known to a precision of at least one part in ten-thousand, often much better[2] (the atomic mass of lithium is a notable, and serious,[12] 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.[13] Measurement 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 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 Main article: 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: p V = n R T   displaystyle pV=nRT where n is the amount of substance. The vapour density (ρ) is given by ρ = n M V .   displaystyle rho = nM over V . Combining these two equations gives an expression for the molar mass in terms of the vapour density for conditions of known pressure and temperature. M = R T ρ p   displaystyle M= RTrho over p Freezing-point depression Main article: 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 f) 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 M = w K f Δ T .   displaystyle M= wK_ f over Delta T . Boiling-point elevation Main article: 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 b) 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 M = w K b Δ T .   displaystyle M= wK_ b over Delta T . References^ a b International Union of Pure and Applied Chemistry Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry, 2nd edition, Oxford: Blackwell Science. ISBN 0-632-03583-8. p. 41. Electronic version. ^ 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   ^ a b 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. ^ International Union of Pure and Applied Chemistry Chemistry (1984). "Note on the terminology for molar masses in polymer science". J. Polym. Sci., Polym. Lett. Ed. 22 (1): 57. Bibcode:1984JPoSL..22...57.. doi:10.1002/pol.1984.130220116.  ^ Metanomski, W. V. (1991). Compendium of Macromolecular Nomenclature. Oxford: Blackwell Science. pp.  47–73. ISBN 0-632-02847-5.  ^ The Engineering ToolBox Molecular Mass Mass of Air ^ a b International Bureau of Weights and Measures 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  ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "relative molar mass". ^ 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. ^ "Atomic Weights and Isotopic Compositions for All Elements". NIST. Retrieved 2007-10-14.  ^ "Author Guidelines – Article Layout". RSC Publishing. Retrieved 2007-10-14.  ^ Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. p. 21. ISBN 0-08-037941-9.  ^ See, e.g., Weast, R. C., ed. (1972). Handbook of Chemistry Chemistry and Physics (53rd ed.). Cleveland, OH: Chemical Rubber Co. External linksHTML5 Molar Mass Mass Calculator web and mobile application. Online Molar Mass Mass Calculator with the uncertainty of M and all the calculations shown Molar Mass Mass Calculator Online Molar Mass Mass and Elemental Composition Calculator Stoichiometry Add-In for Microsoft Excel for calculation of molecular weights, reaction coefficients and stoichiometry. It includes both average atomic weights and isotopic weights. Molar mass: chemistry second-l

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