Chapter 4: Measurement of Matter
Comprehensive chapter summary with detailed explanations and examples.
Grade 9 Learning: Chapter 4: Measurement of Matter
Introduction
In previous studies, we learned about atoms and molecules as the fundamental building blocks of matter. Chemistry often involves transformations where substances react to form new ones. How can we measure and quantify these changes? This chapter delves into the fundamental laws governing chemical combinations, introduces the concept of the mole for counting particles, and explains how to determine and use chemical formulae.
Laws of Chemical Combination
Early experiments by scientists like Antoine Lavoisier and Joseph L. Proust led to the formulation of key laws that govern how elements combine to form compounds.
Law of Conservation of Mass
Proposed by Antoine Lavoisier (often called the father of modern chemistry), this law states:
"In a chemical reaction, the total mass of the reactants is equal to the total mass of the products."
This means that matter is neither created nor destroyed during a chemical reaction; it simply changes form. For example, if you react calcium chloride (CaCl₂) solution with sodium sulphate (Na₂SO₄) solution, a white precipitate of calcium sulphate (CaSO₄) forms along with sodium chloride (NaCl) solution. If you carefully measure the total mass before and after the reaction in a closed system, you will find the mass remains unchanged.
Law of Constant Proportions
Proposed by the French chemist J.L. Proust, this law states:
"In a chemical compound, the constituent elements are always present in definite proportions by mass, irrespective of the source or method of preparation."
For example, water (H₂O) always consists of hydrogen and oxygen combined in a fixed mass ratio of 1:8. Whether you get water from a river, synthesize it in a lab, or extract it from a fruit, this ratio remains constant. 9 grams of water will always contain 1 gram of hydrogen and 8 grams of oxygen.
Atoms: Size, Mass, and Valency
Atomic Size and Mass
Atoms are incredibly small. Their size is measured in nanometers (1 nm = 10⁻⁹ m). The mass of an atom is concentrated in its nucleus (protons + neutrons). Since absolute atomic masses are tiny, we use a relative scale.
Atomic Mass Unit (u): The standard unit is the unified atomic mass unit (u), defined as 1/12th the mass of a Carbon-12 atom. (1 u ≈ 1.66 × 10⁻²⁷ kg).
Atomic Mass:The relative mass of an atom compared to 1/12th the mass of a Carbon-12 atom. Examples: H ≈ 1 u, O ≈ 16 u, Na ≈ 23 u.
Valency
Valency is the combining capacity of an element. It represents the number of electrons an atom loses, gains, or shares to achieve a stable electron configuration (usually a full outer shell).
- Elements that lose electrons (metals) have positive valency (e.g., Na⁺, valency 1; Mg²⁺, valency 2).
- Elements that gain electrons (non-metals) have negative valency (e.g., Cl⁻, valency 1; O²⁻, valency 2).
- Some elements share electrons (covalent bonding), and valency relates to the number of bonds formed (e.g., C in CH₄, valency 4).
Variable Valency: Some elements, particularly transition metals, can exhibit different valencies in different compounds (e.g., Iron: Fe²⁺ (ferrous, valency 2) and Fe³⁺ (ferric, valency 3); Copper: Cu⁺ (cuprous, valency 1) and Cu²⁺ (cupric, valency 2)).
Molecules and Molecular Mass
A molecule is the smallest particle of an element or compound that can exist independently and retain the properties of the substance. It consists of two or more atoms chemically bonded together (e.g., O₂, H₂O, CO₂, NaCl - formula unit for ionic compounds).
Molecular Mass: The molecular mass of a substance is the sum of the atomic masses of all atoms in one molecule (or formula unit) of the substance. It is expressed in atomic mass units (u).
Calculating Molecular Mass of H₂SO₄
Atomic masses: H=1 u, S=32 u, O=16 u
Formula: H₂SO₄
Molecular Mass = (2 × Atomic mass of H) + (1 × Atomic mass of S) + (4 × Atomic mass of O)
= (2 × 1 u) + (1 × 32 u) + (4 × 16 u)
= 2 u + 32 u + 64 u = 98 u
The Mole Concept
Since atoms and molecules are too small to count individually, chemists use a unit called the mole to relate the macroscopic amount of a substance (mass) to the number of microscopic particles (atoms/molecules).
Defining the Mole
One mole (mole) is the amount of substance that contains as many elementary entities (atoms, molecules, ions, etc.) as there are atoms in exactly 12 grams of Carbon-12.
This specific number is called Avogadro's Number (N<0xE2><0x82><0x90>).
So, 1 mole of anything contains 6.022 × 10²³ particles of it.
- 1 mole of Carbon atoms = 6.022 × 10²³ Carbon atoms
- 1 mole of Water molecules = 6.022 × 10²³ Water molecules
Mole and Molar Mass
Crucially, the mass of one mole of a substance in grams is numerically equal to its atomic mass (for elements) or molecular mass (for compounds) in atomic mass units (u). This mass is called the Molar Mass (unit: g/mol).
- Atomic mass of C = 12 u → Molar mass of C = 12 g/mol
- Molecular mass of H₂O = 18 u → Molar mass of H₂O = 18 g/mol
- Molecular mass of O₂ = 32 u → Molar mass of O₂ = 32 g/mol
This provides a bridge between mass and moles:
And between moles and number of particles:
Example: Moles and Molecules in 44g of CO₂
1. Calculate Molar Mass of CO₂: C=12, O=16. M = 12 + (2 × 16) = 44 g/mol.
2. Calculate Moles: n = Given mass / Molar mass = 44 g / 44 g/mol = 1 mol.
3. Calculate Molecules: Number = n × N<0xE2><0x82><0x90> = 1 mol × 6.022 × 10²³ molecules/mol = 6.022 × 10²³ molecules.
So, 44 g of CO₂ is 1 mole and contains 6.022 × 10²³ molecules.
Radicals (Ions)
Atoms or groups of atoms that carry an electric charge are called radicals or ions
- Cations: Positively charged ions formed by loss of electrons (e.g., Na⁺, Ca²⁺, Al³⁺, NH₄⁺). These are also calledbasic radicalsas they often originate from bases.
- AnionsNegatively charged ions formed by gain of electrons (e.g., Cl⁻, O²⁻, SO₄²⁻, NO₃⁻). These are also calledacidic radicalsas they often originate from acids.
Radicals can be:
- Simple RadicalsConsist of a single charged atom (e.g., Mg²⁺, S²⁻).
- Compound/Composite RadicalsConsist of a group of bonded atoms with an overall charge (e.g., NH₄⁺ - ammonium, SO₄²⁻ - sulfate).
Chemical Formulae of Compounds
A chemical formula represents the composition of a compound using symbols and subscripts.
Steps to Write Chemical Formulae
- Step 1: Write the symbols of the radicals (cation first, then anion).
- Step 2: Write the valency below each radical.
- Step 3: Cross-multiply the valencies (ignoring the charges). These numbers become the subscripts for the opposite radical. Simplify the subscripts to the lowest whole number ratio if possible.
- Step 4: Write the final formula. Omit subscript '1'. Use parentheses around a compound radical if its subscript is greater than 1.
Example: Formula for Aluminum Sulphate
1. Symbols: Al (Aluminum), SO₄ (Sulphate)
2. Valencies: Al (3), SO₄ (2)
3. Cross-multiply: Al gets subscript 2, SO₄ gets subscript 3.
4. FormulaAl₂(SO₄)₃ (Parentheses needed for SO₄)
Example: Formula for Magnesium Oxide
1. Symbols: Mg (Magnesium), O (Oxide)
2. Valencies: Mg (2), O (2)
3. Cross-multiply: Mg gets 2, O gets 2. Simplify ratio 2:2 to 1:1.
4. FormulaMgOp>
Conclusion
Measurement of matter relies on fundamental laws like the conservation of mass and constant proportions. Understanding atoms, molecules, valency, and the mole concept allows us to quantify chemical substances and reactions. The ability to write chemical formulae correctly is essential for representing compounds and predicting how elements combine.