3.1 Mole

Introduction

Stoichiometry is an integral part of the chemical industry and has a wide range of practical applications. For example, the chemical composition of everyday products such as soap, detergent, toothpaste, shampoos, cosmetics, medicines, and fertilizers is determined by stoichiometry.

Stoichiometry comes from the Greek word "Stoichen" meaning element and the word "Metron" which means measure. The study of relative amounts of the substances involved in the chemical reaction is known as stoichiometry. It helps in the application of balanced chemical equations for the calculation of the quantities of the reactants and the products. It is based on a balanced chemical equation that shows the mole-to-mole quantity of the reactants and products.

Definition

Mole: The atomic mass, formula mass, and molecular mass of a substance expressed in grams is called a mole.

The mole is the SI unit to express the amount of a substance. It is symbolized as mol.

In simple words: A mole is a counting unit in chemistry, just like "dozen" means 12 items. One mole of any substance contains the same number of particles (Avogadro's number, 6.022 × 10²³), and its mass in grams equals its atomic mass, molecular mass, or formula mass.

Main Idea

• The mole is the SI unit for the amount of a substance.
• One mole of any substance contains 6.022 × 10²³ particles (atoms, molecules, ions, or formula units).
• The mass of one mole of a substance in grams is equal to its atomic mass, molecular mass, or formula mass.
• Balanced chemical equations tell us the mole ratios of reactants and products.
• Moles can easily be converted into mass of reactants/products.

Core Concept

A balanced chemical equation gives the mole-to-mole ratio of reactants and products. Once we know the moles of one substance, we can find the moles of any other substance in the reaction using this ratio.

Simple explanation: If a recipe says "2 cups of flour + 1 cup of sugar → 2 cakes," then the ratio is 2:1:2. Similarly, a chemical equation like 2H₂ + O₂ → 2H₂O tells us that 2 moles of hydrogen react with 1 mole of oxygen to produce 2 moles of water.

Detailed Explanation

What is a Mole?

The atomic mass, formula mass, and molecular mass of a substance expressed in grams is called a mole.

Examples:

Key point: One mole of any substance has a mass in grams equal to its atomic mass, molecular mass, or formula mass.

Mole Ratios in Stoichiometric Calculations

Let's look at the following chemical reaction:

2H_2(g) + O_2(g) → 2H₂O_(g)

What does this chemical equation tell us?

- 2 moles of hydrogen + 1 mole of oxygen → 2 moles of water.

Key point: Any chemical reaction can be interpreted in terms of moles. Moles can easily be converted into the mass of reactants/products. A balanced chemical equation will tell you the ratio of the reactants/products to the mole.

The Mole as a Unit

• The mole is the SI unit to express the amount of a substance.
• It is symbolized as mol.
• One mole = 6.022 × 10²³ particles (Avogadro's number).
• The mass of one mole of a substance = its molar mass (in g/mol).

Formula:

Number of moles = Mass of substance (g)Molar mass (g/mol)

n = mM

Where:

• n = number of moles
• m = mass of substance in grams
• M = molar mass in g/mol

Intermediate Level

The mole as a bridge:

- Balanced equation → mole ratio → moles of substance → mass of substance

Key formula:

n = mM

Steps for solving mole problems:

• Write the balanced chemical equation.
• Identify the mole ratio between the given substance and the required substance.
• Convert the given mass to moles (if needed) using n = m/M.
• Use the mole ratio to find the moles of the required substance.
• Convert moles to mass (if needed) using m = n × M.

Example: For 2H₂ + O₂ → 2H₂O:

• 2 moles H₂ : 1 mole O₂ : 2 moles H₂O
• If you have 4 moles H₂, you need 2 moles O₂, and you get 4 moles H₂O.

Formula / Mathematical Form

n = mM

Where:

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

Mole ratio from a balanced equation:

For the reaction:

aA + bB → cC + dD

The mole ratio is:

a : b : c : d

Example:

2H₂ + O₂ → 2H₂O

Mole ratio:

2 : 1 : 2

Solved Example

Example 3.1

Methanol burns according to the following equation:

2CH₃OH + 3O_2(g) → 2CO_2(g) + 4H₂O_(g)

If 3.50 moles of methanol are burnt in oxygen, calculate:

(a) How many moles of oxygen are used? (b) How many moles of water are produced?

Solution (a)

Given: Moles of methanol = 3.50\ moles

Required: Moles of oxygen = ?

Formula (from balanced equation):

2\ moles of CH₃OH = 3\ moles of O₂

1\ mole of CH₃OH = 32\ moles of O₂

Substitution:

3.50\ moles of CH₃OH = 3.50 × 32\ moles of O₂

Calculation:

= 10.502 = 5.25\ moles of O₂

Final Answer: The number of moles of O₂ consumed = 5.25\ moles

Solution (b)

Given: Moles of methanol = 3.50\ moles

Required: Moles of water = ?

Formula (from balanced equation):

2\ moles of CH₃OH = 4\ moles of H₂O

1\ mole of CH₃OH = 42\ moles of H₂O

Substitution:

3.50\ moles of CH₃OH = 3.50 × 42\ moles of H₂O

Calculation:

= 14.002 = 7.00\ moles of H₂O

Final Answer: The number of moles of H₂O produced = 7.00\ moles

Concept Assessment Exercise 3.1

NH₃ is an important raw material in the manufacture of fertilizers. It is obtained by the combination of N₂ and H₂ as shown by the following balanced equation:

N_2(g) + 3H_2(g) → 2NH_3(g)

How many moles of the following are required to manufacture 8.0 moles of NH₃?

(a) Nitrogen (b) Hydrogen

Solution:

(a) Nitrogen:

From the equation:

1\ mole of N₂ = 2\ moles of NH₃

1\ mole of NH₃ = 12\ mole of N₂

8.0\ moles of NH₃ = 8.0 × 12 = 4.0\ moles of N₂

Answer: 4.0\ moles of N₂

(b) Hydrogen:

From the equation:

3\ moles of H₂ = 2\ moles of NH₃

1\ mole of NH₃ = 32\ moles of H₂

8.0\ moles of NH₃ = 8.0 × 32 = 12.0\ moles of H₂

Answer: 12.0\ moles of H₂

Example 3.2

Iron can be produced from iron ore Fe₂O₃ by reacting the ore with carbon monoxide (CO). What mass of iron can be formed from 425 g of iron ore?

Solution:

The balanced equation can be written as:

Fe₂O₃ + 3CO → 2Fe + 3CO₂

Given: Mass of iron ore = 425\ g

Molar mass of Fe₂O₃:

= (2 × 55.9) + (3 × 16) = 111.8 + 48 = 159.8\ g/mol

Number of moles of Fe₂O₃:

n = massmolar mass = 425159.6 = 2.66\ moles of Fe₂O₃

From the balanced equation:

1\ mole of Fe₂O₃ = 2\ moles of Fe

2.66\ moles of Fe₂O₃ = 2.66 × 2 = 5.32\ moles of Fe

Mass of Fe produced:

= no. of moles of Fe × Molar mass of iron

= 5.32 × 55.9

= 297.388\ g

Final Answer: Mass of iron produced = 297.388\ g

Important Points

• - Mole = atomic mass, formula mass, or molecular mass expressed in grams.
• - SI unit for amount of substance = mol.
• - 1 mole = 6.022 × 10²³ particles (Avogadro's number).
• - Molar mass = mass of 1 mole of a substance (g/mol).
• - Formula: n = mM.
• - Balanced equation gives the mole ratio.
• - Examples:
• - 1 mole of O = 16 g
• - 1 mole of O₂ = 32 g
• - 1 mole of H₂O = 18 g
• - 1 mole of Na⁺ = 23 g
• - 1 mole of NaCl = 58.5 g
• - Mole ratio from 2H₂ + O₂ → 2H₂O is 2 : 1 : 2.

Remember

• - Mole = amount of substance (SI unit: mol).
• - 1 mole = 6.022 × 10²³ particles.
• - Mass of 1 mole = atomic/molecular/formula mass in grams.
• - n = m / M.
• - Balanced equation → mole ratio.
• - Moles can be converted to mass and vice versa.
• - Stoichiometry uses mole ratios from balanced equations.

Common Mistakes

Quick Revision

Stoichiometry is the study of relative amounts of substances involved in chemical reactions. It is based on a balanced chemical equation that shows the mole-to-mole quantity of reactants and products.

Mole:

• The atomic mass, formula mass, and molecular mass of a substance expressed in grams is called a mole.
• The mole is the SI unit to express the amount of a substance (symbol: mol).
• Examples:
• 1 mole of O (atom) = 16 g
• 1 mole of O₂ (molecule) = 32 g
• 1 mole of H₂O (molecule) = 18 g
• 1 mole of Na⁺ (ion) = 23 g
• 1 mole of NaCl (formula unit) = 58.5 g

Mole Ratios in Stoichiometric Calculations:

• A balanced chemical equation tells us the mole ratio of reactants and products.
• Example: 2H₂ + O₂ → 2H₂O means 2 moles of H₂ + 1 mole of O₂ → 2 moles of H₂O.

Formula:

• n = mM

60-Second Revision

• Mole = SI unit for amount of substance (mol).
• 1 mole = 6.022 × 10²³ particles.
• Mass of 1 mole = atomic/molecular/formula mass in grams.
• Formula: n = m / M.
• Balanced equation → mole ratio.
• 1 mole O = 16 g; 1 mole O₂ = 32 g; 1 mole H₂O = 18 g.
• 2H₂ + O₂ → 2H₂O → ratio 2 : 1 : 2.
• Stoichiometry = study of relative amounts in reactions.
• ⚠️ Warning: always balance the equation before using mole ratios.