A mole is the SI base unit used to measure the amount of substance. It represents a fixed number of specified particles, just as a dozen represents 12 items. In chemistry, this fixed number is much larger and is called Avogadro’s constant. The particles being counted may be atoms, molecules, ions, electrons, formula units, or other specified entities, depending on the substance. ^[1–4]

The mole concept connects the microscopic world of atoms, molecules, and ions with quantities that can be measured in the laboratory. Chemical equations describe how particles react with one another, but in experiments, substances are usually measured in grams, liters, or concentrations. The mole acts as a bridge between these two scales.

Avogadro’s Constant

Avogadro’s constant or Avogadro’s number is represented by N_a. Its approximate value is: ^[1–6]

6.022 x 10²³ mol^–1

It means that 1 mole of any substance contains 6.022 x 10²³ specified particles of that substance.

For example, 1 mol of carbon contains 6.022 x 10²³ carbon atoms. Similarly, 1 mol of water contains 6.022 x 10²³ H₂O molecules, and 1 mol of sodium ions contains 6.022 x 10²³ Na⁺ ions.

Thus, the number remains constant, while the type of particle depends on the substance.

The relationship between the number of particles and moles is:

N = n x N_a

Where

N: Number of particles of the substance

N: Number of moles of the substance

N_a: Avogadro’s constant 

Rearranging this equation:

n = N / N_a 

Therefore, one can calculate the number of moles from the given number of particles.

Worked Example

How many molecules are present in 0.25 mol of CO₂?

Answer:

Since CO₂ is a molecular substance, the particles being counted are CO₂ molecules.

Using the formula:

N = n x N_a

Substitute the values:

N = 0.25 x 6.022 x 10²³

N = 1.5055 x 10²³

Therefore, 0.25 mol of CO₂ contains 1.51 x 10²³ CO₂ molecules.

Role of Moles in Balanced Chemical Equations

A balanced chemical equation shows the ratio in which substances react and form products. These ratios are expressed in moles, not in grams. The numbers written before chemical formulas are called coefficients, and they indicate how many moles of each substance take part in the reaction. ^[1–6]

For example:

2 H₂ + O₂ → 2 H₂O

This equation shows that 2 mol of H₂ react with 1 mol of O₂ to form 2 mol of H₂O. Therefore, the mole ratio of H₂ to O₂ to H₂O is:

2 : 1 : 2

If the amount of one substance is known, this mole ratio can be used to calculate the amount of another substance in moles. To compare masses, the mole ratio is used first, and then the values are converted between moles and grams using molar mass.

Molar Mass

Molar mass is the mass of 1 mole of a substance. It is commonly expressed in grams per mole, written as g/mol. Because each mole contains the same number of particles, molar mass tells us the mass of that fixed amount for a particular substance. ^[1–6]

Different substances have different molar masses because their particles have different masses:

Element: The molar mass is usually taken from its atomic mass on the periodic table and expressed in g/mol. For example, the molar mass of sodium is 22.99 g/mol and that of potassium is 39.10 g/mol.

Compound: The molar mass is calculated by adding the atomic masses of all the atoms present in its chemical formula. For example, water has the formula H₂O. Using the rounded atomic masses H = 1 and O = 16, its molar mass is:

2 x 1 + 16 = 18 g/mol

So, 1 mol of H₂O has a mass of 18 g.

Molar mass allows conversion between mass and moles using the relationship:

n = m / M

Where, 

m: Mass of the substance

n: Number of moles of the substance
M: Molar mass

Although 1 mole of any substance contains the same number of particles, different substances do not have the same mass. For example, using rounded atomic masses, 1 mol of H₂O has a mass of 18 g, while 1 mol of CO₂ has a mass of 44 g.

The mass of a molecule or formula unit is commonly expressed in u. For molecular substances, it is called molecular mass. For ionic compounds and other substances represented by formula units, it is better called formula mass.

Worked Example 

How many moles are present in 11 g of CO₂?

Answer:

First, find the molar mass of CO₂.

Molar mass of carbon = 12 g/mol

Molar mass of oxygen = 16 g/mol

Molar mass of CO₂: 12 + 2 x 16 = 44 g/mol

Now, use the formula:

n = m / M

Substitute the values:

n = 11 / 44

=> n = 0.25 mol

Therefore, 11 g of CO₂ contains 0.25 mol of CO₂.

Mole and Gas Volume

For gases, moles can be related to volume only when temperature and pressure are specified. This is because equal numbers of ideal gas particles occupy equal volumes under the same conditions of temperature and pressure.

Under the commonly used older school convention of 0 °C and 1 atm, 1 mole of an ideal gas occupies about 22.4 L. This volume is called the molar volume of the gas under those conditions.

Under the IUPAC definition of STP, which is 273.15 K and 100 kPa, 1 mole of an ideal gas occupies about 22.7 L. Therefore, the temperature and pressure conditions should always be stated when using molar gas volume.

The relationship between moles, gas volume, and molar volume is:

n = V / V_m

Worked Example

How much volume would 44.8 L of a gas be at 0°C and 1 atm?

Answer:

At 0°C and 1 atm, 22.4 L of a gas is equal to 1 mol.

n = V / V_m

44.8 L will be:

44.8 / 22.4 = 2 mol

Multiple Choice Questions

Question 1. The mass of 2 moles of H₂O is:

A. 12 grams
B. 24 grams
C. 36 grams
D. 48 grams

Answer:

Molar mass of H₂O: 2 x 1  + 16 = 18 g/mol

Using the formula:

m = n × M

Substitute the values:

m = 2 x 18 = 36 g

The correct answer is C. 36 grams.

Question 2: How many hydrogen atoms are present in 1 mol of H₂O molecules?

A. 1.2044 x 10²²
B. 1.2044 x 10²⁴
C. 1.2044 x 10²⁶
D. 1.2044 x 10²⁸

Answer:

Each H₂O molecule contains 2 hydrogen atoms.

Therefore, 1 mol of H₂O molecules contains 2 mol of hydrogen atoms.

Number of hydrogen atoms:

2 x N_a = 2 x 6.022 x 10²³ = 1.2044 x 10²⁴ hydrogen atoms

The correct answer is B. 1.2044 x 10²⁴.