Mole

The mole is the fundamental SI unit of amount of substance, used to measure the quantity of entities such as atoms, molecules, ions, or other specified particles. It provides a bridge between the microscopic world of atoms and the macroscopic quantities that can be measured in laboratories. By defining a specific number of particles, the mole allows chemists to express chemical quantities in a practical and comparable form.

Definition

According to the International System of Units (SI) (2019 redefinition), one mole is defined as containing exactly:
6.02214076×10236.02214076 \times 10^{23}6.02214076×1023
specified elementary entities.
This number is known as the Avogadro constant (Nₐ). The entities may be atoms, molecules, ions, electrons, or other particles, depending on the context.
For example:

• 1 mole of hydrogen atoms = 6.022×10236.022 \times 10^{23}6.022×1023 atoms of hydrogen.
• 1 mole of water molecules = 6.022×10236.022 \times 10^{23}6.022×1023 molecules of H₂O.
• 1 mole of sodium chloride = 6.022×10236.022 \times 10^{23}6.022×1023 formula units of NaCl.

Thus, the mole acts as a counting unit, much like “dozen” represents twelve items, except that a mole represents an extraordinarily large number of particles.

Historical Background

The concept of the mole evolved from the early attempts of chemists to relate mass to number of atoms or molecules.

• In the early 19th century, Amedeo Avogadro (1776–1856) proposed that equal volumes of gases at the same temperature and pressure contain an equal number of molecules.
• The constant representing the number of entities per mole was later named the Avogadro number in his honour.
• By the mid-20th century, the mole was adopted as a base unit in the SI system (1971), standardising its definition and making it essential in chemical stoichiometry.

In 2019, the International Committee for Weights and Measures redefined the mole to fix the numerical value of the Avogadro constant rather than linking it to the mass of a specific substance (previously, one mole was the number of atoms in 12 grams of carbon-12). This change made the definition more precise and independent of material properties.

Relationship Between Mole, Mass, and Number of Particles

The mole establishes a direct relationship between the number of particles (N), amount of substance (n), and Avogadro constant (Nₐ):
n=NNan = \frac{N}{Nₐ}n=Na​N​
where:

• nnn = amount of substance (in moles),
• NNN = number of entities (atoms, molecules, ions, etc.),
• NaNₐNa​ = Avogadro constant (6.02214076×1023 mol−1)(6.02214076 \times 10^{23} \, \text{mol}^{-1})(6.02214076×1023mol−1).

It also connects mass and molar mass through the relation:
n=mMn = \frac{m}{M}n=Mm​
where:

• mmm = mass of the sample (in grams),
• MMM = molar mass (in g/mol).

Combining both gives:
N=m×NaMN = \frac{m \times Nₐ}{M}N=Mm×Na​​
This relationship is fundamental in stoichiometric calculations used in chemical reactions.

Molar Mass

The molar mass (M) of a substance is defined as the mass of one mole of its entities (atoms, molecules, or ions). It is numerically equal to the relative molecular mass (Mr) or atomic mass (Ar) expressed in grams per mole.
Examples:

• Molar mass of hydrogen (H₂) = 2.016 g/mol
• Molar mass of oxygen (O₂) = 31.998 g/mol
• Molar mass of water (H₂O) = 18.015 g/mol
• Molar mass of carbon dioxide (CO₂) = 44.01 g/mol

Hence, 18.015 g of water contains exactly 6.022×10236.022 \times 10^{23}6.022×1023 molecules.

The Concept of Molar Volume

At standard temperature and pressure (STP), defined as 0°C (273.15 K) and 1 atmosphere pressure, one mole of any ideal gas occupies a volume of 22.414 litres.
1 mol gas (at STP)=22.414 L1 \, \text{mol gas (at STP)} = 22.414 \, \text{L}1mol gas (at STP)=22.414L
At standard ambient temperature and pressure (SATP), defined as 25°C and 1 bar, one mole of an ideal gas occupies approximately 24.465 litres. This concept is widely used in gaseous stoichiometry and industrial gas calculations.

Applications in Chemistry

The mole concept is indispensable in nearly every branch of chemistry. It allows precise quantitative relationships between substances participating in chemical reactions.
Key applications include:

1. Stoichiometric Calculations: Determining reactant quantities and product yields in chemical equations.
2. Molar Concentration (Molarity): Expressing the concentration of solutions as moles of solute per litre of solution.
3. Chemical Analysis: Relating masses and volumes to the number of entities present.
4. Thermodynamics: Quantifying enthalpy, entropy, and Gibbs energy per mole of substance.
5. Kinetics: Expressing rate constants and reaction rates based on molar quantities.

Examples

1. Example 1: Calculate the number of water molecules in 9 grams of water.

   n=mM=918=0.5 moln = \frac{m}{M} = \frac{9}{18} = 0.5 \, \text{mol}n=Mm​=189​=0.5mol N=n×Na=0.5×6.022×1023=3.011×1023 moleculesN = n \times Nₐ = 0.5 \times 6.022 \times 10^{23} = 3.011 \times 10^{23} \, \text{molecules}N=n×Na​=0.5×6.022×1023=3.011×1023molecules

2. Example 2: Find the mass of 1 mole of oxygen atoms.
   Atomic mass of O = 16 g/molThus, 1 mole of oxygen atoms weighs 16 g.
3. Example 3: Determine the volume occupied by 2 moles of nitrogen gas at STP.

   V=n×22.414=2×22.414=44.828 LV = n \times 22.414 = 2 \times 22.414 = 44.828 \, \text{L}V=n×22.414=2×22.414=44.828L

Representation in Chemical Equations

In balanced chemical equations, coefficients represent the number of moles of substances participating in reactions.
Example:
2 H₂+O₂→2 H₂O2 \, \text{H₂} + \text{O₂} \rightarrow 2 \, \text{H₂O}2H₂+O₂→2H₂O
This means:

• 2 moles of hydrogen react with 1 mole of oxygen to produce 2 moles of water.
• At STP, 44.8 L of hydrogen react with 22.4 L of oxygen to yield 44.8 L of water vapour.

Importance in Modern Science

The mole forms a cornerstone of modern chemical metrology and quantitative analysis. It enables scientists to connect microscopic measurements (atomic masses and molecular counts) with macroscopic observations (mass, volume, and energy). The 2019 SI redefinition also improved the universality and precision of the mole, allowing its value to be constant and independent of any physical sample.
In addition to chemistry, the mole concept is vital in physics, materials science, biochemistry, and environmental science, wherever atomic-scale quantities must be linked to measurable macroscopic amounts.