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Molar mass, symbol M,[1] is the mass of one mole of a substance (chemical element or chemical compound). Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this A chemical element is a type of Atom that is distinguished by its Atomic number; that is by the number of Protons in its nucleus. A chemical compound is a substance consisting of two or more different elements chemically bonded together in a fixed proportion by Mass. [2] It is a physical property which is characteristic of each pure substance. A physical property is any aspect of an object or substance that can be measured or perceived without changing its identity. The base SI unit for mass is the kilogram[1] but, for both practical and historical reasons, molar masses are almost always quoted in grams per mole (g/mol or g mol–1), especially in chemistry. Chemistry (from Egyptian kēme (chem meaning "earth") is the Science concerned with the composition structure and properties

Molar mass is closely related to the formula weight (F. W. ) or relative molar mass (Mr) of a compound, and to the relative atomic masses or the standard atomic weights of its constituent elements. The atomic mass (ma is the Mass of an atom most often expressed in unified atomic mass units The atomic mass may be considered to be the total mass The atomic mass (ma is the Mass of an atom most often expressed in unified atomic mass units The atomic mass may be considered to be the total mass 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 molecular mass (abbreviated m of a substance, more commonly referred to as molecular weight and abbreviated as MW, is the Mass of one The atomic mass (ma is the Mass of an atom most often expressed in unified atomic mass units The atomic mass may be considered to be the total mass 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 molecular mass (1 Da = 1. The unified atomic mass unit ( u) or Dalton ( Da) or sometimes universal mass unit, is an unit of Mass used to express Biochemistry is the study of the chemical processes in living Organisms It deals with the Structure and function of cellular components such as 660 538 782(83)×10–27 kg). [3][4]

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 sheets (MSDS). A material safety data sheet ( MSDS) is a form containing data regarding the properties of a particular substance 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. A polymer is a large Molecule ( Macromolecule) composed of repeating Structural units typically connected by Covalent Chemical bonds Proteins are large Organic compounds made of Amino acids arranged in a linear chain and joined together by Peptide bonds between the Carboxyl Deoxyribonucleic acid ( DNA) is a Nucleic acid that contains the genetic instructions used in the development and functioning of all known

Contents

Molar masses of elements

Main article: Atomic mass

The molar mass of atoms of an element is given by the standard atomic weight of the element[5] multiplied by the molar mass constant, Mu = 1×10–3 kg/mol = 1 g/mol:[6]

M(H) = 1. The atomic mass (ma is the Mass of an atom most often expressed in unified atomic mass units The atomic mass may be considered to be the total mass History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny A chemical element is a type of Atom that is distinguished by its Atomic number; that is by the number of Protons in its nucleus. The atomic mass (ma is the Mass of an atom most often expressed in unified atomic mass units The atomic mass may be considered to be the total mass The molar mass constant, symbol M u is a Physical constant which relates Atomic weight and Molar mass. 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. 854(2) g/mol

Multiplying by the molar mass constant ensures that the calculation is dimensionally correct: atomic weights are dimensionless quantities (ie, pure numbers) whereas molar masses have units (in this case, g/mol). In mathematics the dimension of a Space is roughly defined as the minimum number of Coordinates needed to specify every point within it

Some elements are usually encountered as molecules, eg hydrogen (H2), sulfur (S8), chlorine (Cl2). In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 Sulfur or sulphur (ˈsʌlfɚ see spelling below) is the Chemical element that has the Atomic number 16 Chlorine (ˈklɔriːn from the Greek word 'χλωρóς' ( khlôros, meaning 'pale green' is the Chemical element with Atomic number 17 and 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(H2) = 2 × 1. 007 97(7) × 1 g/mol = 2. 015 88(14) g/mol
M(S8) = 8 × 32. 065(5) × 1 g/mol = 256. 52(4) g/mol
M(Cl2) = 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 weights of the atoms which form the compound multiplied by the molar mass constant, Mu:

M(NaCl) = [22. A chemical compound is a substance consisting of two or more different elements chemically bonded together in a fixed proportion by Mass. The atomic mass (ma is the Mass of an atom most often expressed in unified atomic mass units The atomic mass may be considered to be the total mass History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny The molar mass constant, symbol M u is a Physical constant which relates Atomic weight and Molar mass. 989 769 28(2) + 35. 453(2)] × 1 g/mol = 58. 443(2) g/mol
M(C12H22O11) = ([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). Polymer science or macromolecular science is the subfield of Materials science concerned with Polymers primarily synthetic polymers such as Plastics A monomer (from Greek mono "one" and meros "part" is a small Molecule that may become chemically bonded to other [7]

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 (Mr). [2] This is a dimensionless quantity (ie, a pure number, without units) equal to the molar mass divided by the molar mass constant. In mathematics the dimension of a Space is roughly defined as the minimum number of Coordinates needed to specify every point within it The molar mass constant, symbol M u is a Physical constant which relates Atomic weight and Molar mass. [8]

Molecular mass

Main article: Molecular mass

The molecular mass (m) is the mass of a given molecule: it is measured in daltons (Da) or atomic mass units (u), where 1 Da = 1 u = 1. The molecular mass (abbreviated m of a substance, more commonly referred to as molecular weight and abbreviated as MW, is the Mass of one The unified atomic mass unit ( u) or Dalton ( Da) or sometimes universal mass unit, is an unit of Mass used to express The unified atomic mass unit ( u) or Dalton ( Da) or sometimes universal mass unit, is an unit of Mass used to express 660 538 782(83)×10–27 kg). [3][4] Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. Isotopes (Greek isos = "equal" tópos = "site place" are any of the different types of atoms ( Nuclides 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 masses[9] of each nuclide, while molar masses are calculated from the atomic weights of each element. The atomic mass (ma is the Mass of an atom most often expressed in unified atomic mass units The atomic mass may be considered to be the total mass A nuclide (from lat nucleus is a species of Atom characterized by the constitution of its nucleus and hence by the number of Protons, the number of The atomic mass (ma is the Mass of an atom most often expressed in unified atomic mass units The atomic mass may be considered to be the total mass A chemical element is a type of Atom that is distinguished by its Atomic number; that is by the number of Protons in its nucleus. The atomic weight takes into account the isotopic distribution of the element in a given sample (usually assumed to be "normal"). Isotopes (Greek isos = "equal" tópos = "site place" are any of the different types of atoms ( Nuclides For example, water has a molar mass of 18. Water ( H2[[oxygen O]] H OH) is the most abundant Molecule on Earth 's surface composing of about 70% of the Earth's surface as 0153(3) g/mol, but individual water molecules have molecular masses which range between 18. 010 564 6863(15) u (1H216O) and 22. 027 7364(9) u (2H218O).

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. Mass spectrometry is an analytical technique that identifies the chemical composition of a compound or sample based on the Mass-to-charge ratio of charged particles "Parts-per" notation is used especially in Science and Engineering, to denote Ratios (relative proportions in measured quantities particularly This is accurate enough to directly determine the chemical formula of a molecule. A chemical formula is a way of expressing information about the Atoms that constitute a particular Chemical compound, and how the relationship between those atoms changes [10]

Precision and uncertainties

The precision to which a molar mass is known depends on the precision of the atomic weights from which it was calculated. The atomic mass (ma is the Mass of an atom most often expressed in unified atomic mass units The atomic mass may be considered to be the total mass Most atomic weights are known to a precision of at least one part in ten-thousand, often much better[5] (the atomic weight of lithium is a notable, and serious,[11] exception). Lithium (ˈlɪθiəm is a Chemical element with the symbol Li and Atomic number 3 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. Analytical chemistry is the study of the Chemical composition of natural and artificial Materials.

The precision of atomics weights, and hence of molar masses, is limited by the knowledge of the isotopic distribution of the element. Isotopes (Greek isos = "equal" tópos = "site place" are any of the different types of atoms ( Nuclides 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 distilled will be enriched in the lighter isotopes of all the elements present. Distillation is a method of separating Mixtures based on differences in their volatilities in a boiling liquid mixture Isotope separation is the process of concentrating specific Isotopes of a Chemical element by removing other isotopes for example separating Natural uranium Isotopes (Greek isos = "equal" tópos = "site place" are any of the different types of atoms ( Nuclides 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. The precision of a value describes the number of digits that are used to express that value This is more accurate than is usually required, but avoids rounding errors during calculations. For the acrobatic movement roundoff see Roundoff. A round-off error, also called rounding error, is the difference between the 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. [12]

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 spectrometric measurements of atomic weights and molecular masses, and are of mostly historical interest. Mass spectrometry is an analytical technique that identifies the chemical composition of a compound or sample based on the Mass-to-charge ratio of charged particles All of the procedures rely on colligative properties, and any dissociation of the compound must be taken into account. Colligative properties are properties of solutions that depend on the number of particles in a given volume of solvent and not on the mass of the particles Dissociation is a state of acute mental Decompensation in which certain Thoughts Emotions Sensations and/or memories are

Vapour density

Main article: 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. Vapour density is the Density of a Vapour in relation to that of Hydrogen. Lorenzo Romano Amedeo Carlo Avogadro di Quaregna e di Cerreto, Count of Quaregna and Cerreto was an Italian Savant. This principle is included in the ideal gas equation:

pV = nRT

where n is the amount of substance. The ideal gas law is the Equation of state of a hypothetical Ideal gas, first stated by Benoît Paul Émile Clapeyron in 1834 The amount of substance, n, of a sample or system is a Physical quantity which is proportional to the number of elementary entities present The vapour density (ρ) is given by

\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. Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature

M = {{RT\rho}\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. Freezing-point depression describes the phenomenon that the freezing point of a Liquid (a Solvent) is depressed when another compound is added meaning Freezing Point (Chinese 冰點 Bīngdiǎn is a news journal in the People's Republic of China which has been the subject of controversy over its criticism In Chemistry, a solution is a Homogeneous Mixture composed of two or more substances A solvent is a liquid or gas that dissolves a solid liquid or gaseous Solute, resulting in a Solution. When the amount concentration is expressed as a molality, the proportionality constant is known as the cryoscopic constant (Kf) and is characteristic for each solvent. In Chemistry, concentration is the measure of how much of a given substance there is mixed with another substance In thermodynamics the cryoscopic constant, Kf allows one to relate Molality to Freezing point depression. 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 = {{wK_f}\over{\Delta T}}. In Chemistry the mass fraction is the fraction of one substance (x_A with mass m_A to the total mixture mass m_{tot} would be defined In Chemistry, a solution is a Homogeneous Mixture composed of two or more substances

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. Boiling-point elevation describes the phenomenon that the Boiling point of a Liquid (a Solvent) will be higher when another compound is added meaning that The boiling point of a liquid is the temperature at which the Vapor pressure of the liquid equals the environmental pressure surrounding the liquid In Chemistry, a solution is a Homogeneous Mixture composed of two or more substances In Chemistry, a solution is a Homogeneous Mixture composed of two or more substances A solvent is a liquid or gas that dissolves a solid liquid or gaseous Solute, resulting in a Solution. When the amount concentration is expressed as a molality, the proportionality constant is known as the ebullioscopic constant (Kb) and is characteristic for each solvent. In Chemistry, concentration is the measure of how much of a given substance there is mixed with another substance In thermodynamics the ebullioscopic constant, Kb allows one to relate Molality to Boiling point elevation. 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 = {{wK_b}\over{\Delta T}}. In Chemistry the mass fraction is the fraction of one substance (x_A with mass m_A to the total mixture mass m_{tot} would be defined

References

  1. ^ a b c International Union of Pure and Applied Chemistry (1993). The International Union of Pure and Applied Chemistry ( IUPAC) (aɪjuːpæk or ay-yoo-pec) is an international Non-governmental organization Quantities, Units and Symbols in Physical Chemistry (2nd Edn). Quantities Units and Symbols in Physical Chemistry Third Edition (ISBN 978-0-85404-433-7 also known as the Green Book, Prepared for publication by E Oxford: Blackwell Science. ISBN 0-632-03583-8. p.  41. Electronic version.
  2. ^ a b International Union of Pure and Applied Chemistry. The International Union of Pure and Applied Chemistry ( IUPAC) (aɪjuːpæk or ay-yoo-pec) is an international Non-governmental organization "relative molar mass". Compendium of Chemical Terminology Internet edition. Compendium of Chemical Terminology (ISBN 0-86542-684-8 is a book published by IUPAC containing internationally accepted definitions for terms in Chemistry.
  3. ^ a b Bureau International des Poids et Mesures (2006). The International Bureau of Weights and Measures ( Bureau international des poids et mesures, in French) is an international Standards organization, one The International System of Units (SI) (8th Edn). ISBN 92-822-2213-6.  p.  126.
  4. ^ a b CODATA value: atomic mass constant. NIST. Retrieved on 2007-10-14. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1066 - Norman Conquest: Battle of Hastings - In England on Senlac Hill seven miles from Hastings, the forces
  5. ^ a b International Union of Pure and Applied Chemistry Commission on Isotopic Abundances and Atomic Weights (2006). The International Union of Pure and Applied Chemistry ( IUPAC) (aɪjuːpæk or ay-yoo-pec) is an international Non-governmental organization "Atomic Weights of the Elements 2005". [[[Pure and Applied Chemistry|Pure Appl. Chem. ]] 78: 2051–66. doi:10.1351/pac200678112051. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.  
  6. ^ Mohr, Peter J. ; Taylor, Barry N. (2005). "CODATA recommended values of the fundamental physical constants: 2002". Rev. Mod. Phys. 77: 1–107. The Reviews of Modern Physics is a journal of the American Physical Society. doi:0034-6861/2005/77(1)/1(107). A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.  
  7. ^ {{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. The International Union of Pure and Applied Chemistry ( IUPAC) (aɪjuːpæk or ay-yoo-pec) is an international Non-governmental organization Polym. Sci. , Polym. Lett. Ed. | volume = 22 | pages = 57}} Metanomski, W. V. (1991). Compendium of Macromolecular Nomenclature, pp.  47–73. ISBN 0-63202-847-5.  
  8. ^ 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. Carbon-12 is the most abundant of the two stable Isotopes of the element Carbon, accounting for 98 The simpler definition given here is equivalent to the full definition because of the way the molar mass constant is itself defined. The molar mass constant, symbol M u is a Physical constant which relates Atomic weight and Molar mass.
  9. ^ Atomic Weights and Isotopic Compositions for All Elements. NIST. Retrieved on 2007-10-14. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1066 - Norman Conquest: Battle of Hastings - In England on Senlac Hill seven miles from Hastings, the forces
  10. ^ Author Guidelines – Article Layout. RSC Publishing. The Royal Society of Chemistry (RSC is a Learned society ( Professional association) in the United Kingdom with the goal of "advancing the Retrieved on 2007-10-14. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1066 - Norman Conquest: Battle of Hastings - In England on Senlac Hill seven miles from Hastings, the forces
  11. ^ Greenwood, N. N. ; Earnshaw, A. (1997). Chemistry of the Elements, 2nd Edition, Oxford:Butterworth-Heinemann. ISBN 0-7506-3365-4.  
  12. ^ See, eg, Weast, R. C. (Ed. ) (1972). Handbook of Chemistry and Physics (53rd Edn. ). Cleveland: Chemical Rubber Co.

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