Molar mass 144241 222844307 2008-07-01T11:38:38Z 66.146.140.199 '''Molar mass''', symbol ''M'',<ref name="GreenBook">{{GreenBookRef|page=41}}</ref> is the [[mass]] of one [[mole (unit)|mole]] of a substance ([[chemical element]] or [[chemical compound]]).<ref name="GoldBook">{{GoldBookRef|title=relative molar mass|url=http://goldbook.iupac.org/R05270.html}}</ref> It is a [[physical property]] which is characteristic of each pure substance. The base [[SI unit]] for mass is the [[kilogram]]<ref name="GreenBook"/> but, for both practical and historical reasons, molar masses are almost always quoted in grams per mole (g/mol or g&nbsp;mol<sup>–1</sup>), especially in [[chemistry]]. Molar mass is closely related to the '''[[molecular weight]]''' or '''relative molar mass''' (''M''{{su|b=r}}) of a compound, and to the [[relative atomic mass]]es or the [[standard atomic weight]]s of its constituent elements. However, it should be distinguished from the [[molecular mass]] , 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 (unit)|dalton]], symbol Da, is also sometimes used as a unit of molar mass, especially in [[biochemistry]], with the definition 1&nbsp;Da&nbsp;= 1&nbsp;g/mol, despite the fact that it is strictly a unit of molecular mass (1&nbsp;Da&nbsp;= 1.660&nbsp;538&nbsp;782(83)×10<sup>–27</sup>&nbsp;kg).<ref name="SI">{{SIbrochure|page=126}}</ref><ref name="CODATAu">{{cite web | title = CODATA value: atomic mass constant | url = http://physics.nist.gov/cgi-bin/cuu/Value?u | publisher = [[NIST]] | accessdate = 2007-10-14}}</ref> Molar masses are almost never measured directly. They may be calculated from standard atomic weights, and are often listed in chemical catalogues and on [[material safety data sheet]]s (MSDS). 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 [[polymer]]s, [[protein]]s, [[DNA]] fragments, etc. == Molar masses of elements == {{main|Atomic mass}} The molar mass of [[atom]]s of an [[Chemical element|element]] is given by the [[standard atomic weight]] of the element<ref name="AtWt">{{cite journal | author = [[International Union of Pure and Applied Chemistry]] Commission on Isotopic Abundances and Atomic Weights | title = Atomic Weights of the Elements 2005 | url = http://www.iupac.org/publications/pac/2006/pdf/7811x2051.pdf | journal = [[[Pure and Applied Chemistry|Pure Appl. Chem.]] | year = 2006 | volume = 78 | pages = 2051–66 | doi = 10.1351/pac200678112051}}</ref> multiplied by the [[molar mass constant]], ''M''{{su|b=u}}&nbsp;= 1×10<sup>–3</sup>&nbsp;kg/mol&nbsp;= 1&nbsp;g/mol:<ref name="CODATA">{{cite journal | last = Mohr | first = Peter J. | coauthors = Taylor, Barry N. | title = CODATA recommended values of the fundamental physical constants: 2002 | journal = [[Reviews of Modern Physics|Rev. Mod. Phys.]] | year = 2005 | volume = 77 | pages = 1–107 | doi = 0034-6861/2005/77(1)/1(107) | doi_brokendate = 2008-06-26}}</ref> :''M''(H)&nbsp;= 1.007&nbsp;97(7)&nbsp;× 1&nbsp;g/mol&nbsp;= 1.007&nbsp;97(7)&nbsp;g/mol :''M''(S)&nbsp;= 32.065(5)&nbsp;× 1&nbsp;g/mol&nbsp;= 32.065(5)&nbsp;g/mol :''M''(Cl)&nbsp;= 35.453(2)&nbsp;× 1&nbsp;g/mol&nbsp;= 35.453(2)&nbsp;g/mol :''M''(Fe)&nbsp;= 55.845(2)&nbsp;× 1&nbsp;g/mol&nbsp;= 55.854(2)&nbsp;g/mol Multiplying by the molar mass constant ensures that the calculation is [[Dimension|dimensionally]] correct: atomic weights are dimensionless quantities (ie, pure numbers) whereas molar masses have units (in this case, g/mol). Some elements are usually encountered as [[molecule]]s, eg [[hydrogen]] (H{{su|b=2}}), [[sulfur]] (S{{su|b=8}}), [[chlorine]] (Cl{{su|b=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{{su|b=2}})&nbsp;= 2&nbsp;× 1.007&nbsp;97(7)&nbsp;× 1&nbsp;g/mol&nbsp;= 2.015&nbsp;88(14)&nbsp;g/mol :''M''(S{{su|b=8}})&nbsp;= 8&nbsp;× 32.065(5)&nbsp;× 1&nbsp;g/mol&nbsp;= 256.52(4)&nbsp;g/mol :''M''(Cl{{su|b=2}})&nbsp;= 2&nbsp;× 35.453(2)&nbsp;× 1&nbsp;g/mol&nbsp;= 70.906(4)&nbsp;g/mol == Molar masses of compounds == The molar mass of a [[Chemical compound|compound]] is given by the sum of the [[standard atomic weight]]s of the [[atom]]s which form the compound multiplied by the [[molar mass constant]], ''M''{{su|b=u}}: :''M''(NaCl)&nbsp;= [22.989&nbsp;769&nbsp;28(2)&nbsp;+ 35.453(2)]&nbsp;× 1&nbsp;g/mol&nbsp;= 58.443(2)&nbsp;g/mol :''M''(C{{su|b=12}}H{{su|b=22}}O{{su|b=11}})&nbsp;= ([12&nbsp;× 12.0107(8)]&nbsp;+ [22&nbsp;×1.007&nbsp;94(7)]&nbsp;+ [11&nbsp;×15.9994(3)])&nbsp;× 1&nbsp;g/mol&nbsp;= 342.297(14)&nbsp;g/mol An average molar mass may be defined for mixtures of compounds.<ref name="GreenBook"/> This is particularly important in [[polymer science]], where different polymer molecules may contain different numbers of [[monomer]] units (non-uniform polymers).<ref>{{cite journal | author = [[International Union of Pure and Applied Chemistry]] | title = Note on the terminology for molar masses in polymer science | year = 1984 | journal = [[Journal of Polymer Science|J. Polym. Sci., Polym. Lett. Ed. | volume = 22 | pages = 57 | doi = 10.1351/pac200678112051}} {{cite book | last = Metanomski | first = W. V. | title = Compendium of Macromolecular Nomenclature | year = 1991 | Publisher = Blackwell Science | location = Oxford | pages = pp.&nbsp;47–73 | isbn = 0-63202-847-5}}</ref> == Related properties == '''Molecular weight''' (M.W.) and '''formula weight''' (F.W.) are older terms for what is now more correctly called the '''relative molar mass''' (''M''{{su|b=r}}).<ref name="GoldBook"/> This is a [[Dimension|dimensionless]] quantity (ie, a pure number, without units) equal to the molar mass divided by the [[molar mass constant]].<ref>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.</ref> === Molecular mass === {{main|Molecular mass}} The molecular mass (''m'') is the mass of a given molecule: it is measured in [[Dalton (unit)|daltons]] (Da) or [[atomic mass unit]]s (u), where 1&nbsp;Da&nbsp;= 1&nbsp;u&nbsp;= 1.660&nbsp;538&nbsp;782(83)×10<sup>–27</sup>&nbsp;kg).<ref name="SI"/><ref name="CODATAu"/> Different molecules of the same compound may have different molecular masses because they contain different [[isotope]]s 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 (weighable) quantities of a substance. Molecular masses are calculated from the [[relative atomic mass]]es<ref>{{cite web | title = Atomic Weights and Isotopic Compositions for All Elements | url = http://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=&all=all&ascii=html&isotype=some | publisher = [[NIST]] | accessdate = 2007-10-14}}</ref> of each [[nuclide]], while molar masses are calculated from the [[atomic weight]]s of each [[Chemical element|element]]. The atomic weight takes into account the [[Isotope|isotopic distribution]] of the element in a given sample (usually assumed to be "normal"). For example, [[water (molecule)|water]] has a molar mass of 18.0153(3)&nbsp;g/mol, but individual water molecules have molecular masses which range between 18.010&nbsp;564&nbsp;6863(15)&nbsp;u (<sup>1</sup>H{{su|b=2}}<sup>16</sup>O) and 22.027&nbsp;7364(9)&nbsp;u (<sup>2</sup>H{{su|b=2}}<sup>18</sup>O). 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 [[Part per million|parts per million]]. This is accurate enough to directly determine the [[chemical formula]] of a molecule.<ref>{{cite web | title = Author Guidelines – Article Layout | url = http://www.rsc.org/Publishing/ReSourCe/AuthorGuidelines/ArticleLayout/sect3.asp | publisher = [[Royal Society of Chemistry|RSC Publishing]] | accessdate = 2007-10-14}}</ref> == Precision and uncertainties == The precision to which a molar mass is known depends on the precision of the [[atomic weight]]s from which it was calculated. Most atomic weights are known to a precision of at least one part in ten-thousand, often much better<ref name="AtWt"/> (the atomic weight of [[lithium]] is a notable, and serious,<ref>{{Greenwood&Earnshaw|page=21}}</ref> exception). This is adequate for almost all normal uses in chemistry: it is more precise than most [[chemical analysis|chemical analyses]], and exceeds the purity of most laboratory reagents. The precision of atomics weights, and hence of molar masses, is limited by the knowledge of the [[Isotope|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 weight. The isotopic distributions of the different elements in a sample are not necessarily independent of one another: for example, a sample which has been [[Distillation|distilled]] will be [[Isotopic enrichment|enriched]] in the lighter [[isotope]]s 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 place]]s for all calculations. This is more accurate than is usually required, but avoids [[rounding error]]s during calculations. When the molar mass is greater than 1000&nbsp;g/mol, it is rarely appropriate to use more than one decimal place. These conventions are followed in most tabulated values of molar masses.<ref>See, eg, {{RubberBible53rd}}</ref> == Measurement == 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 spectrometry|mass spectrometric]] measurements of atomic weights and molecular masses, and are of mostly historical interest. All of the procedures rely on [[Colligative property|colligative properties]], and any [[dissociation]] of the compound must be taken into account. === Vapour density === {{main|Vapour density}} The measurement of molar mass by vapour density relies on the principle, first enounced by [[Amadeo Avogadro]], that equal volumes of gases under identical conditions contain equal numbers of particles. This principle is included in the [[ideal gas equation]]: ::<math>pV = nRT</math> where ''n'' is the [[amount of substance]]. The vapour density (&rho;) is given by ::<math>\rho = {{nM}\over{V}}</math>. Combining these two equations gives an expression for the molar mass in terms of the vapour density for conditions of known [[pressure]] and [[temperature]]. ::<math>M = {{RT\rho}\over{p}}</math> === Freezing-point depression === {{main|Freezing-point depression}} The [[freezing point]] of a [[solution]] is lower than that of the pure [[solvent]], and the freezing-point depression (&Delta;''T'') is directly proportional to the [[amount concentration]] for dilute solutions. When the amount concentration is expressed as a [[molality]], the proportionality constant is known as the [[cryoscopic constant]] (''K''{{su|b=f}}) and is characteristic for each solvent. If ''w'' represents the [[mass fraction (chemistry)|mass fraction]] of the [[solute]] in solution, and assuming no dissociation of the solute, the molar mass is given by ::<math>M = {{wK_f}\over{\Delta T}}</math>. === Boiling-point elevation === {{main|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 (&Delta;''T'') is directly proportional to the [[amount concentration]] for dilute solutions. When the amount concentration is expressed as a [[molality]], the proportionality constant is known as the [[ebullioscopic constant]] (''K''{{su|b=b}}) and is characteristic for each solvent. If ''w'' represents the [[mass fraction (chemistry)|mass fraction]] of the solute in solution, and assuming no dissociation of the solute, the molar mass is given by ::<math>M = {{wK_b}\over{\Delta T}}</math>. == References == <references /> ==External links== * [http://www.nightlab.ch/tools/molcalc.php Molecular Weight Calculator] Online Molecular Weight Calculator * [http://www.programowaniepc.pl/en/program_masy_molowe.php Molar Mass Calculator] Freeware Windows Application [[Category:Chemical properties]] [[Category:Mass]] [[ar:كتلة مولية]] [[ca:Massa molar]] [[cs:Molární hmotnost]] [[da:Molvægt]] [[de:Molare Masse]] [[es:Masa molar]] [[et:Molaarmass]] [[fa:جرم مولی]] [[fi:Moolimassa]] [[fr:Masse molaire]] [[id:Massa molar]] [[lt:Molinė masė]] [[no:Molar masse]] [[pl:Masa molowa]] [[pt:Massa molar]] [[ru:Молярная масса]] [[sl:Molska masa]] [[ur:مولرکمیت]] [[ur:مولرکمیت]] [[uz:Molyar massa]] [[zh:摩尔质量]]