Describe the mole concept (comparison of the mole with other units of measurements and molar quantities of substances)

The Mole Concept

Introduction

When we buy groceries, we often purchase items in groups—a dozen eggs, a pair of shoes, or a gross of pencils. In chemistry, we also need a convenient way to count extremely tiny particles like atoms and molecules. The mole is the SI unit that solves this problem by representing a specific number of particles.

What is a Mole?

A mole (mol) is the amount of substance that contains exactly 6.02 × 10²³ particles. This number is called Avogadro's constant (symbol: L or Nₐ).

$1\text{ mol} = 6.02 \times 10^{23}\text{ particles}$

The particles can be atoms, molecules, ions, or electrons. For example:

• 1 mole of water (H₂O) contains 6.02 × 10²³ water molecules
• 1 mole of sodium (Na) contains 6.02 × 10²³ sodium atoms
• 1 mole of sodium chloride (NaCl) contains 6.02 × 10²³ ion pairs

Comparing the Mole with Other Units

Just as we use familiar units to count objects, the mole allows chemists to count particles. Here are some common comparisons:

Unit	What it represents
Pair	2 items
Dozen	12 items
Gross	144 items
Mole	6.02 × 10²³ particles

The mole is unique because it connects the tiny world of atoms to measurable quantities like mass and volume.

Molar Mass

Molar mass (M) is the mass of exactly one mole of a substance, expressed in grams per mole (g/mol). Numerically, molar mass equals the relative atomic mass (Ar) or relative molecular mass (Mr).

Examples:

• Molar mass of sodium (Na) = 23 g/mol
• Molar mass of water (H₂O) = 18 g/mol (H: 1 × 2 + O: 16)
• Molar mass of carbon dioxide (CO₂) = 44 g/mol (C: 12 + O: 16 × 2)

Calculating Number of Moles

The number of moles (n) in a sample is calculated by dividing the mass (m) by the molar mass (M):

$n = \frac{m}{M}$

Where:

• n = number of moles (mol)
• m = mass (g)
• M = molar mass (g/mol)

Worked Example 1: Calculate the number of moles in 180 g of carbon (C).

Given: m = 180 g, M = 12 g/mol

$n = \frac{180\text{ g}}{12\text{ g/mol}} = 15\text{ mol}$

Worked Example 2: Calculate the number of moles in 88 g of carbon dioxide (CO₂).

Molar mass of CO₂ = 12 + (16 × 2) = 44 g/mol

$n = \frac{88\text{ g}}{44\text{ g/mol}} = 2\text{ mol}$

Number of Particles in a Substance

To find the total number of particles (N) in a given amount of substance:

$N = n \times L$

Where:

• N = number of particles
• n = number of moles
• L = Avogadro's constant (6.02 × 10²³ mol⁻¹)

Worked Example: Calculate the number of atoms in 0.5 mole of calcium (Ca).

Given: n = 0.5 mol, L = 6.02 × 10²³ mol⁻¹

$N = 0.5 \times 6.02 \times 10^{23} = 3.01 \times 10^{23}\text{ atoms}$

Molar Volume of Gases

At standard temperature and pressure (STP), where temperature is 0°C (273 K) and pressure is 1 atm (760 mm Hg), one mole of any gas occupies 22.4 dm³ (or 22.4 liters). This is called molar volume (Vm).

$V_m = 22.4\text{ dm}^3\text{/mol at STP}$

Worked Example: What volume does 2 moles of oxygen gas (O₂) occupy at STP?

Given: n = 2 mol, Vm = 22.4 dm³/mol

$V = n \times V_m = 2 \times 22.4 = 44.8\text{ dm}^3$

Real-life application

In Tanzania, a shopkeeper at a local duka (store) might weigh 500 grams of salt for a customer using a balance scale. Understanding moles helps the shopkeeper appreciate that this 500 g of salt (NaCl, molar mass = 58.5 g/mol) actually contains about 5.13 × 10²³ sodium chloride formula units—a massive number, just as a carton of water sold in Dar es Salaam contains dozens of individual bottles, each containing countless molecules of water.