Atoms and Molecules

The reaction is:

Mass of reactants:

Mass of sodium carbonate (Na₂CO₃) = 5.3 g

Mass of acetic acid (CH₃COOH) = 6.0 g

Total mass of reactants = 5.3 + 6.0 = 11.3 g

Mass of products:

Mass of CO₂ = 2.2 g

Mass of H₂O = 0.9 g

Mass of sodium acetate (CH₃COONa) = 8.2 g

Total mass of products = 2.2 + 0.9 + 8.2 = 11.3 g

Since mass of reactants = mass of products = 11.3 g, these observations are in agreement with the Law of Conservation of Mass, which states that matter is neither created nor destroyed in a chemical reaction.

Given: H₂ and O₂ combine in the ratio 1 : 8 by mass to form water (H₂O).

This means 1 g of hydrogen requires 8 g of oxygen.

Therefore, 3 g of hydrogen will require:

24 g of oxygen gas is required to react completely with 3 g of hydrogen gas.

The following postulate of Dalton's atomic theory is the result of the law of conservation of mass:

"Atoms are indivisible particles which cannot be created or destroyed in a chemical reaction."

Since atoms are neither created nor destroyed, the total mass of atoms (and hence matter) remains the same before and after a chemical reaction. This is exactly what the law of conservation of mass states.

The following postulate of Dalton's atomic theory explains the law of definite proportions:

"The relative number and kinds of atoms are constant in a given compound."

This means that any given chemical compound always contains the same elements combined in the same fixed ratio by number (and hence by mass). For example, water (H₂O) always contains 2 hydrogen atoms for every 1 oxygen atom, regardless of how the water was produced or where it was obtained.

The atomic mass unit (u or amu) is defined as one-twelfth (1/12) of the mass of one atom of carbon-12 (¹²C).

The atomic mass unit provides a convenient scale for expressing the masses of atoms and molecules. For example, one atom of hydrogen has a mass of approximately 1 u, and one atom of oxygen has a mass of approximately 16 u.

It is not possible to see an atom with the naked eye because atoms are extremely small — their size is of the order of 10⁻¹⁰ m (0.1 nm or 1 Angstrom).

For comparison, the smallest object visible to the naked eye is about 0.1 mm (10⁻⁴ m), which is one million times larger than an atom.

Even the most powerful optical microscopes (which use visible light) cannot resolve individual atoms because the wavelength of visible light (~400–700 nm) is much larger than the size of an atom (~0.1 nm). According to the principles of optics, you cannot see objects smaller than the wavelength of light used to observe them.

Individual atoms can only be imaged using specialized instruments like the Scanning Tunnelling Microscope (STM) or Atomic Force Microscope (AFM), which work on quantum mechanical principles rather than visible light.

To write the formulae, we use the valency (combining capacity) of each element/ion and apply the criss-cross method:

(i) Sodium oxide — Na⁺¹ and O⁻²

(ii) Aluminium chloride — Al⁺³ and Cl⁻¹

(iii) Sodium sulphide — Na⁺¹ and S⁻²

(iv) Magnesium hydroxide — Mg⁺² and OH⁻¹

(i) Al₂(SO₄)₃ — Aluminium sulphate

(ii) CaCl₂ — Calcium chloride

(iii) K₂SO₄ — Potassium sulphate

(iv) KNO₃ — Potassium nitrate

(v) CaCO₃ — Calcium carbonate

A chemical formula is a symbolic representation of the composition of a compound (or element). It shows:

1. The types of atoms (elements) present in the compound.

2. The number of atoms of each element in one molecule (or formula unit) of the compound.

Examples:

H₂O — One molecule of water contains 2 hydrogen atoms and 1 oxygen atom.

CO₂ — One molecule of carbon dioxide contains 1 carbon atom and 2 oxygen atoms.

NaCl — One formula unit of common salt contains 1 sodium ion and 1 chloride ion.

H₂SO₄ — One molecule of sulphuric acid contains 2 hydrogen, 1 sulphur, and 4 oxygen atoms.

The chemical formula also allows us to calculate the molecular mass of a compound by adding the atomic masses of all atoms present.

(i) H₂S (Hydrogen sulphide):

Number of hydrogen atoms = 2

Number of sulphur atoms = 1

Total atoms = 2 + 1 = 3 atoms

(ii) PO₄³⁻ (Phosphate ion):

Number of phosphorus atoms = 1

Number of oxygen atoms = 4

Total atoms = 1 + 4 = 5 atoms

H₂ (Hydrogen): 2 × 1 = 2 u

O₂ (Oxygen): 2 × 16 = 32 u

Cl₂ (Chlorine): 2 × 35.5 = 71 u

CO₂ (Carbon dioxide): 12 + (2 × 16) = 12 + 32 = 44 u

CH₄ (Methane): 12 + (4 × 1) = 12 + 4 = 16 u

C₂H₆ (Ethane): (2 × 12) + (6 × 1) = 24 + 6 = 30 u

C₂H₄ (Ethene): (2 × 12) + (4 × 1) = 24 + 4 = 28 u

NH₃ (Ammonia): 14 + (3 × 1) = 14 + 3 = 17 u

CH₃OH (Methanol): 12 + (3 × 1) + 16 + 1 = 12 + 3 + 16 + 1 = 32 u

ZnO (Zinc oxide):

Na₂O (Sodium oxide):

K₂CO₃ (Potassium carbonate):

Given:

Mass of 1 mole of carbon atoms = 12 g

1 mole contains Avogadro's number of atoms = 6.022 × 10²³ atoms

The mass of one carbon atom is approximately 1.993 × 10⁻²³ g.

For Sodium (Na):

Number of atoms of Na = 4.34 × 6.022 × 10²³ = 2.61 × 10²⁴ atoms

For Iron (Fe):

Number of atoms of Fe = 1.786 × 6.022 × 10²³ = 1.075 × 10²⁴ atoms

Since 2.61 × 10²⁴ > 1.075 × 10²⁴, 100 grams of sodium has more atoms than 100 grams of iron.

This is because sodium has a smaller atomic mass (23 u) compared to iron (56 u), so for the same mass, there are more moles (and hence more atoms) of sodium.

Total mass of sample = 0.24 g

Mass of boron = 0.096 g

Mass of oxygen = 0.144 g

The compound contains 40% Boron and 60% Oxygen by weight. Total = 40 + 60 = 100% (verified).

The Law of Conservation of Mass states: "In any physical or chemical change, matter is neither created nor destroyed; the total mass of the reactants is equal to the total mass of the products."

This law was given by Antoine Lavoisier in 1774.

Example: When hydrogen gas reacts with oxygen gas to form water:

4 g of H₂ + 32 g of O₂ = 36 g of H₂O. The total mass before (36 g) equals the total mass after (36 g), confirming conservation of mass.

The Law of Definite Proportions (or Law of Constant Proportions) states: "In a chemical compound, elements are always present in definite proportions by mass, regardless of the source or method of preparation of the compound."

This law was given by Joseph Louis Proust in 1799.

Example: Water (H₂O) always contains hydrogen and oxygen in the mass ratio of 1:8.

Whether water is obtained from a river, formed by the combustion of hydrogen, or produced by any other method, it always contains:

Mass of H : Mass of O = 2 : 16 = 1 : 8

This ratio never changes, illustrating the law of definite proportions.

The mole is the SI unit for the amount of substance. One mole of any substance contains the same number of particles (atoms, molecules, ions, etc.) as there are atoms in exactly 12 grams of carbon-12.

Avogadro's Number (N_A): The number of particles in one mole of any substance is called Avogadro's number.

Key relationships of the mole concept:

1. 1 mole of atoms = 6.022 × 10²³ atoms = molar mass of the element (in grams)

2. 1 mole of molecules = 6.022 × 10²³ molecules = molecular mass (in grams)

3. 1 mole of a gas at STP = 22.4 litres (molar volume)

Examples: 1 mole of H₂O = 18 g of water = 6.022 × 10²³ molecules of water. 1 mole of NaCl = 58.5 g of salt.

Atomic mass of He = 4 u, so molar mass of He = 4 g/mol.

Part 1 — From mass:

Part 2 — From number of atoms:

Atomic mass of N = 14 u; Molar mass of N₂ = 28 g/mol; Molar mass of N (atom) = 14 g/mol.

(a) 0.5 mole of N₂:

(b) 0.5 mole of N atoms:

(c) 3.011 × 10²³ atoms of N:

(d) 6.022 × 10²³ molecules of N₂:

A polyatomic ion is a charged species (ion) that consists of two or more atoms covalently bonded together, carrying an overall positive or negative charge. They behave as a single unit in ionic compounds.

Examples:

(i) Sulphate ion: SO₄²⁻ — 1 sulphur atom + 4 oxygen atoms; charge = −2

(ii) Nitrate ion: NO₃⁻ — 1 nitrogen atom + 3 oxygen atoms; charge = −1

(iii) Ammonium ion: NH₄⁺ — 1 nitrogen atom + 4 hydrogen atoms; charge = +1

(iv) Carbonate ion: CO₃²⁻ — 1 carbon atom + 3 oxygen atoms; charge = −2

(i) Magnesium chloride: Mg²⁺ and Cl⁻

(ii) Calcium oxide: Ca²⁺ and O²⁻

(iii) Copper nitrate: Cu²⁺ and NO₃⁻

(iv) Aluminium chloride: Al³⁺ and Cl⁻

(v) Calcium carbonate: Ca²⁺ and CO₃²⁻

Ions are electrically charged atoms or groups of atoms. An ion is formed when an atom (or group of atoms) gains or loses one or more electrons.

Cation (Positive Ion):

Formed when an atom loses one or more electrons. It carries a positive charge.

Examples:

Na⁺ (sodium ion) — Na loses 1 electron

Ca²⁺ (calcium ion) — Ca loses 2 electrons

Al³⁺ (aluminium ion) — Al loses 3 electrons

NH₄⁺ (ammonium ion) — a polyatomic cation

Anion (Negative Ion):

Formed when an atom gains one or more electrons. It carries a negative charge.

Examples:

Cl⁻ (chloride ion) — Cl gains 1 electron

O²⁻ (oxide ion) — O gains 2 electrons

S²⁻ (sulphide ion) — S gains 2 electrons

SO₄²⁻ (sulphate ion) — a polyatomic anion