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Molar mass

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Molar mass definition

Definition: The molar mass of a chemical species (atomic, molecular or ionic) corresponds to the mass of a mole of this chemical species.

It is a quantity that can be noted M (always in capital letter to distinguish it from the mass) and which may be accompanied by the name or the empirical formula of the chemical species concerned placed in parentheses or in subscript.
According to that definition, if we know the mass of a microscopic particle mparticle then the molar mass M of the chemical species is given by the following formula:

M =mparticle. NA  (NA is the Avogadro constant, NA = 6,022.1023)

It can be expressed as the ratio of the mass "m" of the sample of a chemical species to the quantity of matter "n" contained in that sample. This relation can be expressed by the following formula:

M = m : n
M: molar mass of the chemical species in grams per mol (g / mol or g.mol-1)
m: mass of the sample in grams (g)
n: quantity of sample matter in mol (mol)

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Molar mass of nucleons

Reminder: nucleons are the particles that make up the atomic nucleus, there are two kinds that are the protons and the neutrons.
Protons and neutrons have very close masses:
the proton has a mass of 1,672.10-27 kg
the neutron has a mass of 1.675.10-27 kg
If we limit ourselves to a precision of 3 significant digits then we can consider that a nucleon (a neutron or a proton) has a mass of 1.67.10-27 kg.
In this case, the molar mass of the nucleons is:
Mnucl閛n = mnucl閛n.NA
= 1.67.10-27. 6.02-1023 kg
= 1.00-10-3 kg / mol
= 1.00 g / mol

The molar mass of a nucleon is 1 g / mol

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Atomic molar mass

By definition, the molar mass of an atomic chemical species corresponds to the mass of one mole of atoms, besides each atom is composed of electrons and a nucleus made of nucleons. If the atomic number of an atom is Z and its number of nucleons is A then it is composed of:

Z electrons
Z protons
A - Z neutrons

The mass of the atom can be considered as the sum of masses of these particles but we can make the following approximations:
the mass of electrons (9.109.10-31kg) is negligible compared to the mass of nucleons (1.67.10-27 kg), especially if we limit ourselves to a precision of 3 significant digits, at 0.01. 10-27 kg.
the mass of a proton and a nucleon is the same, the mass of a nucleon is about 1.67.10-27 kg

Thus we can consider the approximation that the mass of an atom is the mass of the nucleons in its nucleus and as a nucleon has a molar mass of 1.00 g / mol then an atomic chemical species whose number of nucleons is A thus has a molar mass of A=1.00 g / mol.

The number of nucleons A (also called mass number) of an atomic chemical species also corresponds to its molar mass expressed in g / mol

Examples

The molar mass of carbon 12 is 12 g / mol
That of oxygen 16 is 16 g / mol
That of phosphorus 31 is 31 g / mol
etc.

To know the molar mass of an atomic chemical species, it is sufficient to consult the periodic table and locate the number of its nucleons.

Note

The periodic table often provides decimal expressions of the number of nucleons because it refers to the average number of nucleons of a chemical element in a natural sample that is generally composed of a mixture of isotopes.

List of atomic molar masses

 Element molar masses (g/mol) Element molar masses (g/mol) Actinium 227,0 Neon 20,2 Aluminum 27,0 Neptunium 237,0 Americium 243,0 Nickel 58,9 Antimony 121,8 Niobium 92,9 Silver 107,9 Nobelium 259,0 Argon 39,9 Osmium 190,2 Arsenic 74,9 Gold 197,0 Astatine 210,0 Oxygen 16,0 Azote 14,0 Palladium 106,4 Barium 137,3 Phosphor 31,0 Berkelium 247,0 Platine 195,1 Beryllium 9,0 Plumb 207,2 Bismuth 209,0 Plutonium 244 Bohrium 264 Polonium 209,0 Bore 10,8 Potassium 39,1 Brome 79,9 Praseodymium 140,9 Cadmium 112,4 Promethium 145,0 Calcium 40,1 Protactinium 231,0 Californium 251,0 Radium 226,0 Carbone 12,0 Radon 222,0 Cerium 140,1 Rhenium 186,2 Cesium 132,9 Rhodium 102,9 Chlorine 35,5 Rubidium 85,5 Chrome 52,0 Ruthenium 101,1 Cobalt 58,9 Rutherfordium 261 Copper 63,5 Samarium 150,4 Curium 247,0 Scandium 45,0 Darmstadtium 281 Seaborgium 266 Dubnium 262 Selenium 79,0 Dysprosium 162,5 Silicon 28,1 Einsteinium 254,0 Sodium 23,0 Erbium 167,3 Strontium 87,6 pewter 118,7 Sulfur 32,1 Europium 152,0 tantalum 180,9 Iron 55,8 Technetium 98,9 Fermium 257,0 Tellurium 127,6 Fluor 19,0 Terbium 158,9 Francium 223,0 Thallium 204,4 Gadolinium 157,3 Thorium 232,0 Gallium 69,7 Thulium 168,9 Germanium 72,6 Titan 47,9 Hafnium 178,5 tungsten 183,9 Hassium 277 Ununbium 285 Helium 4,0 Ununhexium 292 Holmium 164,9 Ununoctium 294 Hydrogen 1,0 Ununpentium 288 Indium 114,8 Ununquadium 289 Iodine 126,9 Ununseptium 292 Iridium 192,2 Ununtrium 284 Krypton 83,8 Ununium 280 Lanthane 138,9 Uranium 238,0 Lawrencium 260,0 Vanadium 50,9 Lithium 6,9 Xenon 131,3 Lutetium 175,0 Ytterbium 173,0 Magnesium 24,3 Yttrium 88,9 Manganese 54,9 Zinc 65,4 Meitn閞ium 268 Zirconium 91,2 Mendelevium 258,0 Mercury 200,6 Molybdenum 95,9 Neodymium 144,2

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Molecular molar mass

By definition, it corresponds to the mass of one mole of molecules belonging to the same chemical species. Since a molecule is composed of atoms bonded together, it can be obtained by adding the atomic molar masses of each of its constituents.

For example, a water molecule of formula H2O is composed of an oxygen atom linked to two hydrogen atoms, therefore one mole of water molecules contains one mole of oxygen atoms and two moles of hydrogen.

Therefore, the molar mass of water is equal to the sum of the molar mass of oxygen and twice that of hydrogen, which can be expressed by the following relationship:

M (water) = M (H
2O) = 2.M (H) + M (O)
M (water) = 2.1.0 + 16.0
M (water) = 18.0 g / mol

Other examples

Glucose has the formula C
6H12O6:
M (C6H12O6) = 6.M (C) + 12.M (H) + 6.M (O)
M (C6H12O6) = 6.12.0 + 12.1.0 + 6.16.0
M (C 6 H 12 O 6) = 180.0 g / mol

Paracetamol has the formula C
8H9NO2:
M (C8H 9NO2) = 8.M (C) + 9.M (H) + M (N) + 2.M (O)
M (C8H 9NO2)= 8.12.0 + 9.1.0 + 14.0 + 2.16.0
M (C8H 9NO2) = 151.0 g / mol

List of some molecular molar masses

 Chemical species Formula Molnar mass (g/mol) Acetic acid C2H4O2 60,0 Benzene C6H6 78,0 Butane C4H10 58,0 Caffeine C8H10N4O2 194,0 Hydrogen chloride hcl 36,5 dinitrogen N2 28;0 Dichloride Cl2 71,0 Dihydrogen H2 2,0 Iodine I2 253,8 Carbon dioxide CO2 44,0 Dioxygen O2 32,0 Water H2O 18,0 Ethane C2H6 30,0 Ethanol C2H6O 46,0 Ibuprofen C13H18O2 206,0 Methane CH4 16,0 Ozone O3 48,0 Paracetamol C8H9NO2 151,0 Pentane C5H12 72,0 Propane C3H8 44,0

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Ionic molar mass

A monoatomic ion differs from an atom only by a defect or an excess of one or more electrons, besides the mass of these electrons is neglected when calculating an atomic molar mass, therefore we can make the approximation that the molar mass of a monoatomic ion is the same of the atom from which it derives.

Example

The sodium ion Na +: its atomic molar mass of sodium (23.0 g / mol)
Cu2+ copper ion: its atomic molar mass of copper (63.5 g / mol)
etc.

We can make the same approximation for the molar mass of a polyatomic ion, it is the sum of the atomic molar masses of its elements.

Examples
The carbonate ion has the chemical formula CO32-; its molar mass is:
M (CO32-) = M (C) + 3.M (O)
= 12 + 3.16
= 60 g / mol

The acetate ion has the chemical formula
C2H3O2-; its molar mass is:
M (C2H3O2-) = 2.M (C) + 3.M (H) + 2.M (O)
= 2.12 + 3.1.0 + 2.16
= 59 g / mol

Molar mass of an ionic compound

An ionic compound is a solid chemical species at room temperature that results of the combination of a cation (a positive ion) and an anion (a negative ion)
Its molar mass can be obtained:

- By adding the molar mass of the cation and the anion if they are known
- By adding the atomic molar mass of each element as one could for a molecule.

Examples

The molar mass of copper sulfate (CuSO4) can be obtained by adding the molar mass of the copper ion and the sulfate ion:
M (CuSO4) = M (Cu2+) + M (SO42-)
It can also be determined by adding the molar mass of copper, sulfur and 4 molar masses of oxygen:
M (CuSO4) = M (Cu) + M (S) + 4.M (O)

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Calculate a molar mass

If the nature and formula of a chemical species are known, then it is possible to determine and to calculate the molar mass of this species from the atomic molar masses indicated in the periodic table (following the methods of the preceding paragraphs).

Moreover, if the mass (m) and the quantity of matter (n) of a sample of a pure chemical species are known then the molar mass can be calculated by the relation which defines the molar mass as the ratio:

M = m : n

Calculate a mass

It is also possible to modify the relation between molar mass (M), mass (m) and quantity of material (n) in order to express mass :

m = M.n

This relation may, for example, be useful for determining the mass of reagents that must be used to be in the stoichiometric conditions of a chemical transformation.

Calculate a quantity of matter

The relation which defines the molar mass M of a chemical species as the ratio of the mass m of a sample of matter divided by the quantity of matter "n" can be modified to express the quantity of matter:
This relation can, for example, be useful for determining the amount of matter obtained during a chemical synthesis (or during any chemical transformation in general).

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