# Mole Concept and Molar Mass

The mole concept fills in this disparity by equating the mass of a single atom or molecule (measured in a.m.u.) with the mass of a massive assembly of related molecules (measured in grams). Atomic mass refers to the mass of a single atom, whereas molecular mass refers to the mass of a group of atoms.

## Mole

We calculate the amount of substance (fundamental quantity) in mole. One mole of a substance is thus contains 6.02214076 * 1023 elementary particles. This number (also known as Avogadro’s constant) is commonly approximated as 6.022 * 1023. Thus, one mole of carbon contains 6.022 * 1023 carbon atoms. A mole of any substance is related with:

1. Mass of a substance;
2. Number of particle; and
3. Volume of gaseous substances.

### Mole in terms of mass of a substance

Moles in terms of mass is defined as the mass of substance which is expressed in gram.

1 mole of CaCO3 = 100 gm

Also, 1 mole of Na = 23 gm

1 mole of O2 gas = 32 gm

### Mole in terms of number of particles

A mole (gram mole) is the mass in grams of a collection of particles of substances (atoms, molecules, ions, electrons, protons, etc.) equal in number to the number of atoms present is 1 mole of C-12 isotopes i.e. 12 gms of C-12 isotope.

1 gm of atom of C-12 isotope (i.e. 12 gms of C-12 isotope) contains 6.022 * 1023 carbon atoms.

### Moles in terms of Volume

Mole in terms of volume is defined as the volume occupied by one mole of any gas at normal temperature and pressure.

This volume at N.T.P. or S.T.P. is molar or gram molecular volume which is equal to 22.4 liters. This applies only to a gaseous state.

Let us have a clear example from –

1 mole of H2 gas

2.016 gm of Hydrogen gas

22.4 litres at N.T.P.

22400 cc at N.T.P.

6.022 * 1023 hydrogen molecules

2 * 6.022 * 1023 hydrogen atoms

2 * 6.022 * 1023 electrons

The mole acts as a link between the laboratory (grams) and the atomic world (amu). It is possible to determine the number of molecules or atoms by weighing them. The International Prototype Kilogram, a block of Pt-Ir metal, and the selection of one carbon-12 atom as the reference for the atomic mass unit scale resulted in the numerical value of Avogadro’s number. A mole of C-12 weighs exactly 12 g by definition, and Avogadro’s number is calculated by counting the number of atoms. It is not so simple. Avogadro’s number is the fundamental constant with the least precision.

## Atomic mass unit (a.m.u.)

An element’s atomic mass unit (AMU or amu) is a unit of measurement for its atomic mass.

AMU is defined as one-twelfth the mass of a carbon-12 atom (12C).

The most abundant natural carbon isotope, 12C, accounts for more than 98% of all carbon found in nature. It has an 12 a.m.u. The AMU, also known as the dalton (Da) or the unified atomic mass unit (u), expresses both atomic and molecular masses.

1 a.m.u. = (1gm/No) = 1 Avogram = 1 Aston = 1 Dalton = 1.6 * 10-24 g

## Loschmidt number

The Loschmidt constant is also refer as the Loschmidt number. The Symbol n0 denotes the Loschmidt constant. It is the number of ideal gas molecules per unit volume. The unit of the Loschmidt constant is the reciprocal cubic meter.

Loschmidt constant at STP (P = 1 atm, T = 273.15 K) = 2.6867811 * 1025m-3

The constant is a measure of the density of numbers.

Johann Josef Loschmidt, an Austrian scientist, inspired the constant’s name. The Loschmidt constant is synonymous with Avogadro’s constant in German literature.

## Berzelius Hypothesis

​Berzelius a Swedish chemist, gave a hypothesis called Berzelius hypothesis which states that :

An equal volume of all gases under similar conditions of temperature and pressure contains an equal number of atoms.

This contradicts Dalton’s atomic theory, which holds that atoms are the ultimate particle of elements and are indivisible. As a result, this hypothesis is not applicable.

Avogadro’s law states, “An equal volume of all gases under the similar condition of temperature and pressure contain an equal number of molecules.”

• Determining the atomicity of the gases

Atomicity of an elementary substance is the number of atoms of the element present in 1 molecule of the substance in the calculation of atomicity.

For example:
The atomicity of oxygen is 2, while that of ozone is 3.

2n molecules(H) n molecules (O) 2n molecules (H2O)

By dividing the total by 2n,

1 molecule (H) 1/2 molecule (O) 1 molecule (H2O)
As a result, one molecule of water contains 1/2 molecules of oxygen. However, each molecule of water contains one atom of oxygen.

Hence 1/2 molecules = 1 oxygen molecule

1 molecule of oxygen = 2 oxygen atoms = 1 oxygen atom = 2

• To derive a relation; Molecular Mass = 2 * Vapour Density (V.D.)
• Determine the relationship between a gas’s mass and volume.

At STP, 22.4 liters of any gas weigh the same as the gas’s molecular mass expressed in grams. This is the gram molecular volume law.

## Atomic Mass

The weight of one atom makes up the atomic mass of an element. The atomic mass unit is abbreviated as a.m.u. One atomic mass unit (a.m.u.) is said to be one-twelfth the mass of a carbon-12 atom.

As a result, one a.m.u. is worth 1 g / NA = 1.66056 10-24 g.

The atomic mass unit is now referred to as a unified mass unit. As a result, a.m.u. has been replaced by u.

## Molar Mass

Calculating the atomic, molecular, and formula masses of atoms, molecules, and other compounds is fine, but because we can’t weigh individual particles, these masses are only of limited use. To make mass measurements useful, chemical quantities must be expressed at the macroscopic level. Molar mass, the mass in grams of one mole of a substance, is the link between the particulate and macroscopic levels. The units of molar mass are defined as grams per mole.

The defining equation of molar mass is mathematically;

Molar mass = mass/mole = g/mol

### Gram Molecular Mass (GMM)

Gram molecular mass is the mass of one mole of a molecular substance expressed in grams. It also has another name molar mass. This quantity of a substance is one gram molecule. The gram molecular mass of a substance is its molecular mass which is measure in grams.

No. of gram molecular mass = (Mass taken / Mol. mass)= no. of moles

For example, the molecular mass of oxygen is 32 grams; this is the relative molecular mass in grams. It is important to remember that relative atomic mass is always expressed as a ratio and has no units.

### Relative Molecular Mass (RMM)

Relative molecular mass is the molecular weight of an element or molecule. It is the number of times a single molecule of a substance retains a mass greater than one-twelfth that of a carbon atom (12C).

## Difference Between Atomic Mass and Molar Mass

### Methods of Determining Atomic Masses

• Dulong and Petit’s Method
• Specific Heat Method
• Volatile Chloride Formation Method
• Isomorphism Method

### Methods of Determining Molecular Masses

• Vapour Density Method
• From Graham’s Law
• Victor Meyer’s Method
• Colligative Properties

## References 