Chapter 3: Mole Concept, Chemical Formula and Equation

Overview

The mole concept is one of the most fundamental and important topics in chemistry. It provides a bridge between the microscopic world of atoms and molecules and the macroscopic world we can measure in the laboratory. This chapter will guide you through understanding relative atomic and molecular masses, the mole concept itself, chemical formulas, and chemical equations. These concepts are essential for quantitative chemistry and will be used throughout your SPM Chemistry studies.

Learning Objectives

After studying this chapter, you should be able to:

Calculate relative atomic mass and relative molecular mass
Understand the mole concept and Avogadro's number
Write and interpret chemical formulas
Balance and interpret chemical equations
Perform stoichiometric calculations
Apply mole concept in practical laboratory situations

3.1 Relative Atomic Mass and Relative Molecular Mass

Understanding Atomic Mass Scale

Atomic masses are extremely small when expressed in grams, so we use a relative scale:

Carbon-12 Standard

Definition: One atom of carbon-12 is assigned exactly 12 atomic mass units (amu)
Purpose: Provides a standard reference for measuring atomic masses
Conversion: 1 amu = 1.66054 × 10⁻²⁴ grams

Relative Atomic Mass (Ar)

Definition: The average mass of an atom of an element compared to 1/12 the mass of a carbon-12 atom.

Calculation Method

For elements with isotopes:

A_r = \sum (\text{Isotope Mass} \times \text{Natural Abundance})

Example: Chlorine

Chlorine-35: 34.97 amu, 75.77% abundance
Chlorine-37: 36.97 amu, 24.23% abundance
$A_r$ = (34.97 × 0.7577) + (36.97 × 0.2423) = 35.45 amu

Common Relative Atomic Masses

Element	Symbol	Relative Atomic Mass
Hydrogen	H	1.008
Carbon	C	12.01
Nitrogen	N	14.01
Oxygen	O	16.00
Sodium	Na	22.99
Magnesium	Mg	24.31
Chlorine	Cl	35.45
Iron	Fe	55.85
Copper	Cu	63.55
Silver	Ag	107.87
Gold	Au	196.97
Lead	Pb	207.2

Relative Molecular Mass (Mr)

Definition: The sum of the relative atomic masses of all atoms in a molecule.

Calculation Formula

M_r = \sum (\text{Number of atoms} \times \text{Relative atomic mass})

Examples

Compound	Formula	Calculation	Mr
Water	$\text{H}_2\text{O}$	(2 × 1.008) + (1 × 16.00)	18.02
Carbon dioxide	$\text{CO}_2$	(1 × 12.01) + (2 × 16.00)	44.01
Sodium chloride	$\text{NaCl}$	(1 × 22.99) + (1 × 35.45)	58.44
Methane	$\text{CH}_4$	(1 × 12.01) + (4 × 1.008)	16.04
Glucose	$\text{C}_6\text{H}_{12}\text{O}_6$	(6 × 12.01) + (12 × 1.008) + (6 × 16.00)	180.16

Complex Compounds

For ionic compounds and complex molecules:

Compound	Formula	Calculation	Mr
Sulfuric acid	$\text{H}_2\text{SO}_4$	(2 × 1.008) + (1 × 32.07) + (4 × 16.00)	98.09
Calcium carbonate	$\text{CaCO}_3$	(1 × 40.08) + (1 × 12.01) + (3 × 16.00)	100.09
Ammonium sulfate	$(\text{NH}_4)_2\text{SO}_4$	2(14.01 + 4×1.008) + 32.07 + 4(16.00)	132.14

Key Terms

Relative Atomic Mass: Average mass of atoms compared to carbon-12
Relative Molecular Mass: Sum of relative atomic masses in a molecule
Atomic Mass Unit (amu): Unit of mass based on carbon-12 standard
Isotope: Atoms of same element with different masses

Did You Know?

If you had one mole of dollar bills and stacked them up, the pile would reach from the Earth to the Sun and back over 500 times! A mole represents 6.022 × 10²³ particles, an incredibly large number that makes the mole concept essential for working with atoms and molecules.

3.2 Mole Concept

What is a Mole?

Definition: A mole is the amount of substance that contains as many elementary entities (atoms, molecules, ions, or other particles) as there are atoms in exactly 12 grams of carbon-12.

Avogadro's Number

N_A = 6.022 \times 10^{23} \text{ particles/mol}

Significance: This is the number of particles in one mole of any substance.

Molar Mass

Definition: The mass of one mole of a substance, expressed in grams per mole (g/mol).

Relationship

Molar mass in g/mol = Relative molecular/atomic mass in amu
Example: Water has Mr = 18.02, so molar mass = 18.02 g/mol

Examples

Substance	Formula	Molar Mass (g/mol)
Hydrogen	H	1.008
Oxygen	$O_2$	32.00
Water	$H_2$ O	18.02
Carbon dioxide	C $O_2$	44.01
Sodium chloride	NaCl	58.44
Glucose	$C_6H_{12}O_6$	180.16

Calculations Using Moles

Number of Particles

\text{Number of particles} = \text{Number of moles} \times N_A

Example: How many molecules are in 2 moles of water?

2 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} = 1.204 \times 10^{24} \text{ molecules}

Mass to Moles Conversion

\text{Number of moles} = \frac{\text{Mass (g)}}{\text{Molar mass (g/mol)}}

Example: How many moles are in 36.04 g of water?

\text{Moles} = \frac{36.04 \text{ g}}{18.02 \text{ g/mol}} = 2 \text{ mol}

Moles to Mass Conversion

\text{Mass (g)} = \text{Number of moles} \times \text{Molar mass (g/mol)}

Example: What is the mass of 0.5 moles of sodium chloride?

\text{Mass} = 0.5 \text{ mol} \times 58.44 \text{ g/mol} = 29.22 \text{ g}

Volume of Gases (STP)

Standard Temperature and Pressure (STP):

Temperature = 0°C (273 K)
Pressure = 1 atm (101.3 kPa)

Molar Volume at STP: 22.4 L/mol

\text{Volume (L)} = \text{Number of moles} \times 22.4 \text{ L/mol}

Example: What is the volume of 3 moles of oxygen gas at STP?

\text{Volume} = 3 \text{ mol} \times 22.4 \text{ L/mol} = 67.2 \text{ L}

Mole Calculations Summary

Given Required	Formula
Mass → Moles	$n = \frac{m}{M}$
Moles → Mass	$m = n \times M$
Moles → Particles	$N = n \times N_A$
Particles → Moles	$n = \frac{N}{N_A}$
Moles → Volume (gas)	$V = n \times 22.4$

Key Terms

Mole: Amount of substance containing 6.022 × 10²³ particles
Molar Mass: Mass of one mole of substance (g/mol)
Avogadro's Number: 6.022 × 10²³ particles/mol
STP: Standard Temperature and Pressure (0°C, 1 atm)

SPM Exam Tips

When doing mole calculations:

Always write down the formula before plugging in numbers

Pay attention to units and convert if necessary

For gas calculations, remember STP conditions

Double-check significant figures in your final answer

3.3 Chemical Formulas

Types of Chemical Formulas

Empirical Formula

Shows the simplest whole-number ratio of atoms in a compound
Example: $\text{CH}_3\text{O}$ for glucose (instead of $\text{C}_6\text{H}_{12}\text{O}_6$ )

Molecular Formula

Shows the actual number of atoms in a molecule
Example: $\text{C}_6\text{H}_{12}\text{O}_6$ for glucose

Structural Formula

Shows how atoms are connected in a molecule
Example: H-O-H for water

Writing Chemical Formulas

Rules for Writing Formulas

Determine the ions involved
Use charges to balance the formula
Write the positive ion first
Use subscripts to show the ratio

Common Ions

Positive Ions (Cations)	Negative Ions (Anions)	Formula Examples
Na⁺ (sodium)	Cl⁻ (chloride)	$\text{NaCl}$
K⁺ (potassium)	$O^2$ ⁻ (oxide)	$\text{K}_2\text{O}$
M $g^2$ ⁺ (magnesium)	$S^2$ ⁻ (sulfide)	$\text{MgS}$
A $l^3$ ⁺ (aluminum)	$\text{NO}_3^−$ (nitrate)	$\text{NO}_3$ ₃
F $e^2$ ⁺ (iron(II))	$\text{SO}_4^{2−}$ (sulfate)	$\text{FeSO}_4$
F $e^3$ ⁺ (iron(III))	$\text{PO}_4^{3−}$ (phosphate)	$\text{FePO}_4$

Writing Ionic Formulas

Method: Cross-multiply the charges (ignore signs)

Example: Aluminum oxide ( $\text{Al}^{3+}$ , $\text{O}^{2−}$ )

Write charges: $\text{Al}^{3+}$ $\text{O}^{2−}$
Cross-multiply: $\text{Al}_2\text{O}_3$
Check balance: (+3)×2 + (-2)×3 = 0

Examples

Compound	Ions	Formula	Calculation
Sodium sulfide	Na⁺, $S^2$ ⁻	$\text{Na}_2\text{S}$	$\text{Na}_2\text{S}$
Magnesium nitrate	M $g^2$ ⁺, $\text{NO}_3^−$	$\text{Mg(NO}_3\text{)}_2$	$\text{Mg(NO}_3\text{)}_2$
Aluminum phosphate	$\text{Al}^{3+}$ , $\text{PO}_4^{3−}$	$\text{AlPO}_4$	$\text{AlPO}_4$
Iron(III) chloride	F $e^3$ ⁺, Cl⁻	$\text{FeCl}_3$	$\text{FeCl}_3$

Molecular Compounds

Covalent Compounds

Formed by sharing electrons between nonmetals
Use prefixes to indicate number of atoms

Prefixes:

1: mono-
2: di-
3: tri-
4: tetra-
5: penta-
6: hexa-

Examples

Name	Formula	Prefix System
Carbon monoxide	$\text{CO}$	mono + carbon + oxide
Carbon dioxide	$\text{CO}_2$	di + carbon + oxide
Dinitrogen trioxide	$\text{N}_2\text{O}_3$	di + nitrogen + tri + oxide
Phosphorus pentoxide	$\text{P}_4\text{O}_{10}$	tetra + phosphorus + deca + oxide

Balancing Chemical Formulas

Rules

Count atoms of each element on both sides
Use coefficients to balance (never change subscripts)
Start with the most complex molecule
Save elements that appear in one compound for last

Common Mistakes to Avoid

❌ Changing subscripts (this changes the compound)
❌ Forgetting to count polyatomic ions as a group
❌ Not checking the final balance

Did You Know?

Water ( $H_2$ O) is one of the few compounds where the molecular formula is the same as the empirical formula. Most compounds have different molecular and empirical formulas because their atoms combine in specific ratios that can be simplified.

3.4 Chemical Equations

Parts of a Chemical Equation

\text{Reactants} \rightarrow \text{Products}

2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}

Components

Reactants: Substances on the left (before arrow)
Products: Substances on the right (after arrow)
Coefficients: Numbers in front of formulas
States: (s) solid, (l) liquid, (g) gas, (aq) aqueous

Balancing Chemical Equations

Step-by-Step Method

Write the unbalanced equation
Count atoms of each element
Balance elements one at a time
Use coefficients, not subscripts
Check final balance

Examples

Example 1: Hydrogen + Oxygen → Water

Unbalanced: $\text{H}_2 + \text{O}_2 \rightarrow \text{H}_2\text{O}$
Count: H: 2 → 2, O: 2 → 1
Balance O: $\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$
Balance H: $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$
Check: H: 4 → 4, O: 2 → 2 ✓

Example 2: Methane + Oxygen → Carbon dioxide + Water

Unbalanced: $\text{CH}_4 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$
Count: C: 1 → 1, H: 4 → 2, O: 2 → 3
Balance H: $\text{CH}_4 + \text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}$
Balance O: $\text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}$
Check: C: 1 → 1, H: 4 → 4, O: 4 → 4 ✓

Complex Equations

Example 3: Iron oxide + Carbon → Iron + Carbon dioxide

Unbalanced: $\text{Fe}_2\text{O}_3 + \text{C} \rightarrow \text{Fe} + \text{CO}_2$
Count: Fe: 2 → 1, O: 3 → 2, C: 1 → 1
Balance Fe: $\text{Fe}_2\text{O}_3 + \text{C} \rightarrow 2\text{Fe} + \text{CO}_2$
Balance C: $\text{Fe}_2\text{O}_3 + 3\text{C} \rightarrow 2\text{Fe} + 3\text{CO}_2$
Check: Fe: 2 → 2, O: 3 → 6, C: 3 → 6 ✓

Types of Chemical Reactions

Synthesis/Combination

2\text{Mg} + \text{O}_2 \rightarrow 2\text{MgO}

Decomposition

2\text{HgO} \rightarrow 2\text{Hg} + \text{O}_2

Single Replacement

\text{Zn} + 2\text{HCl} \rightarrow \text{ZnCl}_2 + \text{H}_2

Double Replacement

\text{AgNO}_3 + \text{NaCl} \rightarrow \text{AgCl} + \text{NaNO}_3

Combustion

\text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}

Stoichiometric Calculations

Mole-Mole Relationships

From balanced equation: $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$

2 mol $H_2$ reacts with 1 mol $O_2$ to produce 2 mol $H_2$ O

Mole Ratio Method

\text{Moles of A} \times \frac{\text{Coefficient of B}}{\text{Coefficient of A}} = \text{Moles of B}

Example: How many moles of water are produced from 3 moles of hydrogen?

3 \text{ mol H}_2 \times \frac{2 \text{ mol H}_2\text{O}}{2 \text{ mol H}_2} = 3 \text{ mol H}_2\text{O}

Mass-Mass Calculations

\text{Mass A} \rightarrow \text{Moles A} \rightarrow \text{Moles B} \rightarrow \text{Mass B}

Example: How many grams of water are produced from 6 g of hydrogen?

6 \text{ g H}_2 \times \frac{1 \text{ mol H}_2}{2 \text{ g H}_2} \times \frac{2 \text{ mol H}_2\text{O}}{2 \text{ mol H}_2} \times \frac{18 \text{ g H}_2\text{O}}{1 \text{ mol H}_2\text{O}} = 54 \text{ g H}_2\text{O}

SPM Exam Tips

For balancing equations:

Always start with the most complex compound

Balance metals first, then nonmetals, then hydrogen/oxygen

Check your final answer by counting all atoms

Practice with various reaction types regularly

Laboratory Practical Exercise: Mole Concept Applications

Objective

To apply mole concept in laboratory calculations and preparations.

Materials Needed

Balance (0.01 g precision)
Various chemicals (NaCl, CuS $O_4$ , etc.)
Measuring cylinders
Safety equipment

Procedures

Exercise 1: Preparing Solutions

Calculate mass needed for 0.1 mol NaCl
Weigh and dissolve in 100 mL water
Verify concentration

Exercise 2: Reaction Stoichiometry

React known mass of magnesium with hydrochloric acid
Measure volume of hydrogen gas produced
Compare with theoretical yield

Expected Outcomes

Skill in mole-mass conversions
Understanding of reaction stoichiometry
Accuracy in laboratory measurements

Summary

This chapter has covered the essential mole concept and chemical calculations:

Relative Masses: Understanding atomic and molecular masses
Mole Concept: The mole as a counting unit for atoms/molecules
Chemical Formulas: Writing and interpreting compound formulas
Chemical Equations: Balancing and interpreting reactions
Stoichiometry: Quantitative relationships in chemical reactions

Mastering these concepts is crucial for success in SPM Chemistry and for understanding quantitative chemistry throughout your studies.

Practice Tips for SPM Students

Create a mole calculation formula sheet

Practice balancing equations daily

Memorize common ions and their charges
Work through stoichiometry problems step by step
Review laboratory applications of mole concept

Chapter 3: Mole Concept, Chemical Formula and Equation

Overview

Learning Objectives

3.1 Relative Atomic Mass and Relative Molecular Mass

Understanding Atomic Mass Scale

Carbon-12 Standard

Relative Atomic Mass (Ar)

Calculation Method

Common Relative Atomic Masses

Relative Molecular Mass (Mr)

Calculation Formula

Examples

Complex Compounds

Key Terms

3.2 Mole Concept

What is a Mole?

Avogadro's Number

Molar Mass

Relationship

Examples

Calculations Using Moles

Number of Particles

Mass to Moles Conversion

Moles to Mass Conversion

Volume of Gases (STP)

Mole Calculations Summary

Key Terms

3.3 Chemical Formulas

Types of Chemical Formulas

Empirical Formula

Molecular Formula

Structural Formula

Writing Chemical Formulas

Rules for Writing Formulas

Common Ions

Writing Ionic Formulas

Examples

Molecular Compounds

Covalent Compounds

Examples

Balancing Chemical Formulas

Rules

Common Mistakes to Avoid

3.4 Chemical Equations

Parts of a Chemical Equation

Components

Balancing Chemical Equations

Step-by-Step Method

Examples

Complex Equations

Types of Chemical Reactions

Synthesis/Combination

Decomposition

Single Replacement

Double Replacement

Combustion

Stoichiometric Calculations

Mole-Mole Relationships

Mole Ratio Method

Mass-Mass Calculations

Laboratory Practical Exercise: Mole Concept Applications

Objective

Materials Needed

Procedures

Exercise 1: Preparing Solutions

Exercise 2: Reaction Stoichiometry

Expected Outcomes

Summary

Related Topics