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# Quantities Related on mole concept and their Formulae

## Atomic and Molecular Mass

The atomic mass of an element is the mass of one atom of the element expressed in atomic mass units (amu). It accounts for the abundance of the various isotopes of the element and assigns an average value to the mass of one atom of the element.

For example, the atomic mass of carbon is 12.011 atomic mass units since carbon samples generally contain 98.89% of the carbon-12 isotope, 1.11% of carbon-13, and trace amounts of carbon-14. However, the atomic masses of these isotopes are different.

The atomic mass of a carbon-12 atom is 12 atomic mass units, but that of a carbon-13 atom is 13 amu. The atomic mass of an element is roughly equal to the sum of all the protons and neutrons present in its nucleus.

The molecular mass of an element is the sum of the atomic masses of all its constituent elements. This quantity is also represented in terms of atomic mass units. Therefore, the molecular mass of water is equal to the sum of the atomic masses of its constituents – hydrogen and oxygen.

The atomic mass of hydrogen is 1.00794 amu and that of oxygen is 15.9994. Since water molecules contain 2 hydrogen atoms and only one oxygen atom, the molecular mass of H2O is 18.0154 amu.

## Molar Mass

The molar mass of a substance is defined as the total mass of one mole of the substance. It is often represented in terms of ‘grams per mole’ (g/mol). However, the SI unit of this quantity is kg/mol. Molar mass can be represented by the following formula:

Molar mass of a Substance = (Mass of the Substance in grams)/(Number of Moles)

For example, the molar mass of water is approximately 18.015 g/mol, which is the mass of NA number of water molecules.

## Gram Atomic Mass and Gram Molecular Mass

The gram atomic mass of an element is the mass of one mole of that element. Similarly, the gram molecular mass of a compound refers to the mass of a single mole of the compound. Therefore, the gram atomic mass of hydrogen is approximately 1.007g and the gram molecular mass of water is approximately 18.015g.

## Related Formulae

The number of moles in a given sample of an element/compound can be calculated by dividing the total mass of the sample by the molar mass of the element/compound, as described by the following formula.

Number of Moles = (Mass of the Sample)/(Molar Mass)

The total number of atoms/molecules in a sample can be calculated by multiplying the number of moles with the Avogadro constant. This formula can be written as:

Number of Atoms or Molecules = (Number of Moles)*(6.022*1023)

The relationship between the atomic mass unit (amu) and the gram is given by:

1 amu = (1gram)/(6.022*1023) = 1.66*10-24 grams

Therefore, the mass of one mole of an element will be equal to its atomic mass in grams.

## Number of Electrons in a Mole of Hydrogen Molecule

The number of electrons in a mole of hydrogen molecule is

1 mole of H2 contains 6.023×1023 molecules and each molecule of H2 contains two electrons.

1 mole = 6.023×1023

Therefore the total no. of electrons in one mole of H2 are 12.046×1023.