Chemistry

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Molar mass

• Molar mass definition
• Molar mass of nucleons
• Atomic molar mass
• List of atomic molar masses
• Molecular molar mass
• List of some molecular molar masses
• Ionic molar mass
• Molar mass of an ionic compound
• Calculate a molar mass
• Calculate a mass
• Calculate a quantity of matter

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 m_particle then the molar mass M of the chemical species is given by the following formula:

M =m_particle. N_A  (N_A is the Avogadro constant, N_A = 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)

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:
M_nucléon = m_nucléon.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

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
Meitnérium	268	Zirconium	91,2
Mendelevium	258,0
Mercury	200,6
Molybdenum	95,9
Neodymium	144,2

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 (H₂O) = 2.M (H) + M (O)
M (water) = 2.1.0 + 16.0
M (water) = 18.0 g / mol

Other examples

Glucose has the formula C₆H₁₂O₆:
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 C₈H₉NO₂:
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

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 CO₃^2-; its molar mass is:
M (CO₃^2-) = 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 (SO₄^2-)
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)

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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