Chapter 3 — Atoms And Molecules

Introduction: The laws of chemical combination describe how elements combine to form compounds. They are empirical rules based on experiments and are essential for writing and balancing chemical equations.

1. Law of Conservation of Mass (Lavoisier): "Mass is neither created nor destroyed in a chemical reaction." The total mass of reactants equals the total mass of products. This explains why chemical equations must be balanced.

Example (molecular equation): 2H2 + O2 → 2H2O. If 4 g of H2 react with 32 g of O2, the total reactant mass = 36 g and mass of 2 moles of H2O = 36 g.

2. Law of Definite Proportions / Constant Composition (Proust): A given chemical compound always contains its constituent elements in fixed definite proportions by mass, independent of source or preparation method.

Example: Water (H2O) always contains hydrogen and oxygen in mass ratio H : O = 2 : 16 = 1 : 8. That is, 1 g of H combines with 8 g of O in water. Percent composition formula: % of element = (mass of element in formula / molar mass of compound) × 100. For H2O: %H = 2/18 × 100 = 11.11%, %O = 16/18 × 100 = 88.89%.

3. Law of Multiple Proportions (Dalton): When two elements form more than one compound, the different masses of one element that combine with a fixed mass of the other are in ratios of small whole numbers.

Example: Carbon and oxygen form CO and CO2. For a fixed 1 g of C, oxygen combined in CO = 16/12 ≈ 1.333 g; in CO2 = 32/12 ≈ 2.667 g. The ratio 1.333 : 2.667 = 1 : 2, a small whole-number ratio (1:2).

Notes and limits: These laws apply to stoichiometric compounds. Some solid compounds (non-stoichiometric or variable composition compounds, often metal oxides) show small deviations from definite proportions due to crystal defects or variable oxidation states.

Importance: These laws provide the foundation for writing balanced chemical equations, finding empirical formulas, computing percent composition, and understanding stoichiometry.

Dalton's Atomic Theory

Introduction: John Dalton (early 19th century) proposed a simple atomic theory to explain chemical reactions and laws of chemical combination. It laid the foundation for modern chemistry and explained empirical laws such as the law of conservation of mass, law of definite proportions and law of multiple proportions.

Dalton’s Postulates:

1. All matter is made of extremely small particles called atoms, which are indivisible and indestructible (Dalton’s indivisible particles model).
2. All atoms of a given element are identical in mass and properties.
3. Atoms of different elements differ in mass and properties.
4. Compounds are formed when atoms of different elements combine in simple whole-number ratios.
5. Chemical reactions involve rearrangement of atoms; atoms are neither created nor destroyed (explains conservation of mass).

How Dalton’s Theory Explains Key Laws:

• Law of Conservation of Mass: Atoms are neither created nor destroyed during chemical reactions, so total mass remains constant.
• Law of Definite Proportions: A given compound always contains the same elements in the same fixed mass ratio because it is made of a fixed type and number of atoms.
• Law of Multiple Proportions: When two elements form more than one compound, the masses of one element that combine with a fixed mass of the other are in ratios of small whole numbers (because different whole-number combinations of atoms form different compounds).

Experimental Evidence (basic): Dalton used quantitative chemical data (mass relationships in reactions and compounds) to support his ideas. For example, analysis of compounds like water and carbon dioxide showed fixed mass ratios of elements.

Limitations (and later modifications):

• Atoms are not indivisible: they are made of subatomic particles (electrons, protons, neutrons).
• Atoms of the same element can have different masses (isotopes), so Dalton’s statement that all atoms of an element are identical in mass is not always correct.
• Atoms can be transformed in nuclear reactions (contradicting absolute indivisibility in extreme cases).

Modern View: Dalton’s picture was replaced by atomic models that include subatomic structure and quantum behavior, but his key concepts—matter made of atoms, fixed ratios in compounds, and conservation in chemical reactions—remain foundational.

Summary: Dalton’s atomic theory provided a clear, testable framework for chemistry: atoms are the basic units of matter, different elements have different atoms, and chemical changes are rearrangements of these atoms.

Dalton's Atomic Theory (brief)
John Dalton (early 1800s) proposed that matter is made of tiny indivisible particles called atoms. His main points: atoms are indivisible and indestructible, all atoms of an element are identical in mass and properties, atoms of different elements differ in mass and properties, compounds are formed by combination of atoms in fixed whole‑number ratios, and chemical reactions rearrange atoms.

Limitations of Dalton's Theory

• Atoms are divisible: Dalton said atoms are indivisible. Discovery of electrons (Thomson), protons and neutrons, and later quarks, showed atoms have internal structure.
• Atoms of an element are not identical: Dalton assumed identical mass/properties for all atoms of an element. Isotopes (same Z, different neutrons) have different masses (e.g., H: protium, deuterium, tritium) though chemical properties are nearly same.
• Atoms of different elements can have nearly same mass: Different elements can have atoms with similar masses (isobars), contradicting the simple mass distinction Dalton suggested.
• Atoms can be created/destroyed in nuclear reactions: Dalton held atoms indestructible. Nuclear reactions convert mass to energy (E = mc^2) or change one element to another (radioactivity, fission, fusion).
• Some elements exist as molecules: Dalton often pictured elements as single atoms; many elements are diatomic or polyatomic in nature (O2, N2, P4, S8). Thus elemental form is not always single atoms.
• Ions and charges: Dalton assumed atoms are neutral indivisible particles. Atoms can lose or gain electrons to form ions (Na+ , Cl−), so chemical behavior depends on electrons.
• Atomic mass is not always an integer for naturally occurring samples: Natural atomic mass is an average of isotopic masses weighted by abundance, so it may be non‑integral (e.g., Cl ≈ 35.45 u), unlike Dalton's expectation of fixed integer masses.

Modern View (how Dalton's ideas were revised)

• Atoms have structure: Atoms consist of a tiny dense nucleus (protons and neutrons) and electrons arranged in shells around the nucleus. Most of the atom's mass is in the nucleus; most of its volume is electron cloud.
• Isotopes: Atoms of the same element have same number of protons (atomic number Z) but can have different numbers of neutrons, giving different mass numbers (A). Chemical properties are governed mainly by electrons; nuclear properties differ.
• Ions and electron arrangement: Atoms can gain/lose electrons to form ions; chemical bonding (ionic, covalent, metallic) arises from electron transfer/sharing. Electronic configuration explains periodic chemical behavior.
• Molecules and stoichiometry: Compounds are made of atoms combined in definite whole‑number ratios (molecules or extended ionic lattices). Laws like definite and multiple proportions are explained by discrete numbers of atoms in molecules.
• Mass–energy relation and nuclear changes: In chemical reactions mass is conserved to very high accuracy, but in nuclear reactions mass can change and convert to energy (E = mc^2).

Summary: Dalton's atomic theory was a crucial step in chemistry but needed revision. Modern atomic theory keeps the idea of atoms as basic units but adds internal structure (protons, neutrons, electrons), isotopes, ions, and quantum ideas about electrons, explaining exceptions Dalton could not.

Definition: An atom is the smallest particle of an element that can exist independently and retain the chemical properties of that element. Atoms are composed of a tiny central nucleus (containing protons and neutrons) surrounded by electrons in discrete energy levels or shells.

Basic structure:

• Protons (p+): positively charged particles in the nucleus. The number of protons = atomic number (Z).
• Neutrons (n0): neutral particles in the nucleus. Protons + neutrons = mass number (A).
• Electrons (e–): negatively charged particles in shells around the nucleus. In a neutral atom, number of electrons = number of protons (Z).

Symbolic representation: An atom is commonly represented as AZX or X_Z^A, where X is the chemical symbol of the element, Z is the atomic number (number of protons), and A is the mass number (protons + neutrons).

Example: 12₆C or ¹²₆C means carbon with A = 12 and Z = 6. It has 6 protons and (12 − 6) = 6 neutrons. In a neutral atom it also has 6 electrons.

Isotopes: Atoms of the same element (same Z) with different mass numbers (different number of neutrons) are called isotopes. Example: ³⁵₁₇Cl and ³⁷₁₇Cl are isotopes of chlorine.

Ions (brief): If an atom gains or loses electrons it becomes an ion. A cation (e.g., Na+) has fewer electrons than protons; an anion (e.g., Cl−) has more electrons than protons. The symbolic notation sometimes shows charge as superscript, e.g., Na⁺.

Important notes for Class 9 level: Use the symbolic notation to find protons, neutrons and electrons quickly: protons = Z, neutrons = A − Z, electrons = Z for neutral atoms (or Z ± charge for ions).

Definition: A molecule is the smallest particle of a substance that can exist independently and retain the chemical properties of that substance. It is formed when two or more atoms are chemically bonded together. Molecules may contain atoms of the same element or of different elements.

How molecules form (brief): Atoms form molecules by sharing (covalent bonding) or transferring electrons (ionic bonding leads to formula units; for simple molecular substances we focus on covalent bonding). The bonded group of atoms behaves as a single neutral entity — a molecule.

Classification of molecules:

• Based on composition:
  • Homoatomic (elementary) molecules: made of atoms of the same element. Examples: O2, N2, S8, P4.
  • Heteroatomic (compound) molecules: made of atoms of different elements. Examples: H2O, CO2, NH3, CH4.
• Based on atomicity (number of atoms in a molecule):
  • Monoatomic: single-atom species treated as molecules for noble gases (He, Ne, Ar).
  • Diatomic: two atoms (either same or different). Common element diatomics: H2, N2, O2, Cl2; also CO is a heterodiatomic example.
  • Triatomic: three atoms, e.g., H2O, CO2, O3 (ozone).
  • Polyatomic: more than three atoms, e.g., CH4 (4), NH3 (4 atoms total), S8 (8), C6H12O6 (glucose).

Key points to remember:

• Atomicity is the number of atoms present in one molecule of an element or compound.
• Elementary molecules contain only one type of atom; compound molecules contain more than one type.
• Noble gases are monoatomic gases (exist as single atoms) and are often referred to as monoatomic molecules in simple discussions.

Example calculations (conceptual): To find the relative molecular mass (Mr) of a molecule, add the relative atomic masses of atoms present. For H2O: Mr = 2(1) + 16 = 18. For CO2: Mr = 12 + 2(16) = 44.

Relation to amount of substance: 1 mole of any substance contains Avogadro's number (NA = 6.022 × 10^23) of molecules. This links molecular mass (in g mol^-1) to mass of a sample.

Simple conceptual diagrams that help: ball-and-stick models for shape, structural formulae (H-O-H for water), and classification tree diagrams showing the split into homoatomic/heteroatomic and by atomicity.

What is Atomic Mass (Relative Atomic Mass)?

Atomic mass (more precisely, relative atomic mass) of an element is the average mass of the atoms of the element compared with 1/12th of the mass of an atom of carbon-12. It is a dimensionless number often expressed in unified atomic mass units (u), where 1 u = 1/12 mass of a carbon-12 atom.

Definition of 1 u: 1 u (also written as 1 amu) = mass of one-twelfth of a carbon-12 atom ≈ 1.660539 × 10^-27 kg.

Why 'relative' and why an average? Most elements exist as a mixture of isotopes (atoms with the same atomic number but different mass numbers). The atomic mass shown in the periodic table is the weighted average of the masses of all naturally occurring isotopes of that element, weighted by their relative abundances. Because it is an average compared to the carbon-12 standard, it is called the relative atomic mass.

How to calculate relative atomic mass

• List isotopes with their masses (in u) and their percentage (or fractional) abundances.
• Multiply each isotope mass by its fractional abundance.
• Sum the results to get the weighted average (the relative atomic mass).

Simple worked example (Chlorine): Chlorine has two common isotopes: 35Cl (mass ≈ 35 u) and 37Cl (mass ≈ 37 u). If their abundances are 75% and 25% respectively, the relative atomic mass is

Atomic mass = 35 × 0.75 + 37 × 0.25 = 26.25 + 9.25 = 35.5 u

This is why the atomic mass of chlorine in the periodic table is about 35.5 u, even though no single chlorine atom has mass 35.5 u.

Relation with mass number and particles: For a given isotope, mass number A = number of protons (Z) + number of neutrons (N). The mass of an isotope in u is roughly equal to its mass number (because protons and neutrons each have mass ≈ 1 u), but small differences arise due to nuclear binding energy and the mass of electrons.

Practical importance: Relative atomic mass is used to find molar mass (g per mole) in chemistry calculations: the relative atomic mass in u is numerically equal to the mass of one mole of that element in grams (approx). For example, chlorine's relative atomic mass ≈ 35.5 u → 1 mole of Cl atoms ≈ 35.5 g.

Molecular Mass (Relative Molecular Mass) and Formula Mass

Relative atomic mass (Ar) of an element is the average mass of its atoms compared to 1/12th of the mass of a carbon-12 atom. It is a relative, unitless number (e.g., Ar(H) ≈ 1, Ar(O) ≈ 16).

Relative molecular mass (Mr) is the sum of the relative atomic masses of all atoms present in a molecule. It is used for covalent molecules (like H₂O, CO₂). Mr is also called molecular mass or molecular weight (dimensionless, but often given in atomic mass units (u) or daltons, where 1 u ≈ 1 Da).

Formula mass is the sum of the relative atomic masses of the atoms in the simplest formula (formula unit) of an ionic compound (like NaCl, CaCl₂). For ionic substances we do not have discrete molecules, so we use the formula unit mass (also reported as a dimensionless number or in u).

How to calculate

1. Write the chemical formula and identify each element and its count (subscript).
2. Look up Ar of each element from the periodic table.
3. Multiply Ar by the number of atoms of that element and add all contributions: Mr or formula mass = Σ(Ar × number of atoms).

Important notes

• Mr and formula mass are relative and usually written without units. When needed, you can express them as atomic mass units (u) or convert to kilograms using 1 u = 1.66053906660×10⁻²⁷ kg.
• Molar mass (g mol⁻¹) is the mass in grams of one mole of that substance and numerically equals Mr (e.g., Mr(H₂O)=18 → molar mass = 18 g mol⁻¹).
• Use Mr for molecules (covalent). Use formula mass for ionic compounds (formula units).

Worked example (stepwise)

Calculate Mr of water (H₂O):

• Ar(H) = 1, Ar(O) = 16
• Number of H atoms = 2, number of O atoms = 1
• Mr(H₂O) = 2×Ar(H) + 1×Ar(O) = 2×1 + 16 = 18

Calculate formula mass of sodium chloride (NaCl):

• Ar(Na) = 23, Ar(Cl) = 35.5
• Formula mass = 23 + 35.5 = 58.5

Connections to real life

• Pharmacy and medicine: doses and drug formulation use molar masses to calculate how much substance to give (later taught when mole concept is introduced).
• Cooking and nutrition labeling: molecular/formula masses underlie how chemists convert between numbers of particles and masses.
• Materials and industry: knowing formula mass helps compute quantities for reactions in manufacturing and lab work.

Summary sentence: Molecular (relative molecular) mass = sum of atomic masses in a molecule; formula mass = sum of atomic masses in the simplest formula (used for ionic compounds). Both are calculated by adding Ar × atom count for every element in the formula.

Definition: Valency (or combining capacity) of an element is the number of hydrogen atoms (or monovalent atoms/groups) that one atom of the element can combine with or displace. It equals the number of electrons an atom loses, gains or shares to achieve a stable (often noble gas) electronic configuration.

Why it matters: Valency explains how atoms form molecules and determines the simplest formula of compounds (e.g., H2O, CO2, NaCl).

Determining valency (simple rules):

• Find the number of valence electrons from electronic configuration (for main-group elements).
• For metals (typically groups 1–3): valency ≈ group number (they lose electrons). Example: Na (1 valence e–) → valency 1; Mg (2 valence e–) → valency 2.
• For nonmetals (typically groups 4–7): valency ≈ 8 − group number (they gain electrons to complete octet). Example: O (6 valence e–) → 8−6 = 2 → valency 2; Cl (7 valence e–) → 8−7 = 1 → valency 1.
• Elements with 4 valence electrons (like C, Si) commonly show valency 4 (they share electrons).

Electronic-configuration method (quick): Valency = number of electrons lost or gained to reach nearest noble gas. Examples: C (2,4) → needs 4 to complete octet → valency 4; P (2,8,5) → gains 3 → valency 3 (common), or can show valency 5 in some compounds.

Writing formulas using valency (criss-cross rule for ionic compounds): If A has valency m and B has valency n, formula is A_nB_m. Practically, write charges and cross the magnitudes: Al3+ and O2− → Al2O3.

Examples of common valencies: H = 1, O = 2, N = 3 (commonly), C = 4, Na = 1, Mg = 2, Cl = 1, Al = 3.

Difference from oxidation state (brief): Valency is a combining capacity concept (usually a positive integer); oxidation state can be positive, negative or fractional and depends on electron bookkeeping in a compound.

Key points students should remember:

• Valency is determined by how many electrons are gained, lost or shared to obtain a stable electronic configuration.
• Use group number for quick estimation: metals → group number; nonmetals → 8 − group number (main-group elements).
• Criss-cross magnitudes to write ionic formulas: A^m+ and B^n− → A_nB_m.
• Some elements show variable valency (transition elements or some p-block elements like P, S).

Worked examples inside explanation:

• Carbon (Z = 6): config 2,4 → needs 4 electrons → valency = 4 → methane CH4.
• Oxygen (Z = 8): config 2,6 → 8−6 = 2 → valency = 2 → water H2O.
• Sodium (Z = 11): config 2,8,1 → loses 1 → valency = 1 → sodium chloride NaCl.

What is a chemical formula? A chemical formula shows the kind and number of atoms of each element in a compound (e.g., H2O, NaCl). It is the simplest whole-number ratio of atoms (empirical formula) or the actual number in a molecule (molecular formula).

Key idea — Valency (combining capacity): Valency is the number of electrons an atom gains, loses or shares to attain a stable electronic configuration (usually an octet). For main-group elements you can use simple rules: group 1 → valency 1, group 2 → valency 2, group 13 → valency 3, group 14 → valency 4, group 15 → valency 3, group 16 → valency 2, group 17 → valency 1. Hydrogen has valency 1.

Steps to write the chemical formula (ionic compounds):

1. Write symbols of the combining elements (or ions) and find their valencies (or charges).
2. Use the criss-cross rule: write each element’s valency as the subscript of the other element.
3. Reduce subscripts to the simplest whole-number ratio.
4. If a polyatomic ion is used more than once, enclose it in parentheses and put the subscript outside.

Example of criss-cross: Aluminium (valency 3) + Oxygen (valency 2) → Al3 and O2 → criss-cross → Al2O3 (reduce if needed).

Polyatomic ions: Some groups of atoms carry a charge and act as a single unit (e.g., NO3− nitrate, SO4 2− sulfate, NH4+ ammonium). Use their charges as valencies and apply the criss-cross rule. When more than one polyatomic ion appears, use parentheses, e.g., (NH4)2SO4.

Covalent (molecular) compounds: Non-metals share electrons. Use prefixes to show numbers of atoms (mono-, di-, tri-, tetra-, etc.) in names, and write the formula with the correct subscripts: carbon dioxide → CO2; dinitrogen tetroxide → N2O4 (empirical formula NO2).

Variable valency (transition metals): Some elements have more than one valency (e.g., Fe2+, Fe3+). Indicate valency in names with Roman numerals: FeCl2 = iron(II) chloride, FeCl3 = iron(III) chloride.

Empirical vs molecular formula: Empirical formula is the simplest ratio (e.g., CH2O for glucose), whereas molecular formula gives the actual number of atoms in a molecule (C6H12O6 for glucose).

Tips and checks:

• Always ensure total positive charge = total negative charge for ionic compounds.
• Simplify subscripts to lowest terms (MgCl2 stays MgCl2; not Mg2Cl4).
• Remember to use parentheses for more than one polyatomic ion: Ca(NO3)2.

What it means
A chemical reaction is a process in which atoms are rearranged to form new substances (molecules or compounds). Representing reactions in terms of atoms and molecules explains how reactant molecules collide, bonds break, and new bonds form to produce product molecules while the total number of each type of atom remains the same.

Chemical equations and symbols
Chemical equations use chemical formulas to show reactants and products, and coefficients to show the number of molecules (or moles). Subscripts in formulas show the number of atoms in a molecule. Example: H₂O is one molecule of water containing 2 hydrogen atoms and 1 oxygen atom.

Balancing equations: conservation of atoms
Balancing a chemical equation means adjusting coefficients so that the number of atoms of each element is equal on both sides. This expresses the Law of Conservation of Mass at the particle level: atoms are neither created nor destroyed, only rearranged.

How to check balancing using atoms

• Write the unbalanced equation using formulas for all reactants and products.
• Count the number of atoms of each element on reactant and product sides.
• Change coefficients (not subscripts) to make the atom counts equal for every element.
• Re-check counts and reduce coefficients to smallest whole numbers if possible.

Example shown by atoms

Unbalanced: H2 + O2 -> H2O
Count atoms: Reactants: H = 2, O = 2  | Products: H = 2, O = 1
Balance by adding coefficient 2 before H2O:
2 H2 + O2 -> 2 H2O
Now: Reactants: H = 4, O = 2  | Products: H = 4, O = 2 (balanced)

State symbols and molecule-level view
You may also add (g), (l), (s), (aq) to indicate gaseous, liquid, solid, or aqueous states. At the molecule level, drawings (colored circles for different atoms) show how reactant molecules collide and rearrange to form product molecules but the count of each colored circle stays constant.

Why this is important
Representation in terms of atoms and molecules helps us: write correct balanced equations, predict amounts of products (stoichiometry), explain conservation of mass, and visualize reactions at the microscopic level.

What is atomicity? Atomicity of a substance is the number of atoms present in one molecule of that substance. For an element in its molecular form, atomicity tells how many atoms of that element are bonded together to make one particle (molecule or formula unit).

Atomicity of elements in nature

• Monoatomic (atomicity = 1): Single atoms exist independently. Example: noble gases — He, Ne, Ar, Kr, Xe (inert gases are monoatomic in nature).
• Diatomic (atomicity = 2): Two atoms of the same element form a molecule. Common diatomic elements: H2, N2, O2, F2, Cl2, Br2, I2. Many atmospheric and reactive gases are diatomic.
• Triatomic (atomicity = 3): Example: O3 (ozone) — three oxygen atoms bonded; important in the stratosphere.
• Polyatomic (atomicity > 3): Some elements form molecules containing more than three atoms. Typical examples: P4 (white phosphorus), S8 (sulfur), and many molecular allotropes and clusters.

Atomicity of compounds

For a chemical compound, atomicity is the total number of atoms in one molecule of the compound. Examples: H2O has atomicity 3 (2 H + 1 O); CO2 has atomicity 3 (1 C + 2 O); NH3 has atomicity 4.

Why atomicity matters

• Atomicity helps determine the molecular formula and calculate molecular mass (molar mass).
• Physical properties (e.g., boiling point, molecular interactions) depend on whether particles are monoatomic, diatomic or polyatomic.
• In stoichiometry and mole calculations, atomicity tells how many atoms are present per molecule and is used when counting atoms in reactions.

Common confusions

• Atomicity is not the same as valency. Atomicity counts atoms in a molecule; valency describes bonding capacity.
• Some elements exist as different allotropes with different atomicities (e.g., sulfur S8 vs polymeric sulfur).

Overview: This topic trains you to apply the mole concept and atomic/molecular masses to convert between mass, moles and number of particles (atoms, molecules, ions). Most problems require three steps: (1) find moles from mass, (2) use Avogadro's number to get number of particles, (3) adjust for atoms per molecule if needed.

Key ideas & method:

1. Avogadro's number (NA) = 6.022 × 10²³ particles per mole. One mole of any substance contains NA particles.
2. Molar mass (M) in g mol⁻¹ is numerically equal to the relative atomic/molecular mass. Example: M(H) = 1 g mol⁻¹, M(H₂O) = 18 g mol⁻¹.
3. Basic conversions:
   • moles (n) = mass (m, in g) / molar mass (M, in g mol⁻¹)
   • number of particles = n × NA
   • number of atoms in a sample = (number of molecules) × (atoms per molecule)
4. Mass of one atom or molecule: mass of one particle = (molar mass in g mol⁻¹) / NA (in g). Convert to kg by dividing by 1000.

Typical problem-solving steps:

1. Write the chemical formula and calculate its molar mass M (g mol⁻¹).
2. Compute moles: n = m / M.
3. Compute particles: particles = n × NA. If you need atoms, multiply molecules by atoms per molecule.
4. If asked mass of a single particle: mass_per_particle = M / NA (in g) → convert units if required.

Real-life examples:

• Counting molecules in a glass of water: a 250 mL glass (~250 g water) contains ~250/18 ≈ 13.9 mol → ≈ 8.37 × 10²⁴ water molecules and ≈ 2.51 × 10²⁵ atoms (since each water molecule has 3 atoms).
• Air in a small balloon: you can calculate the number of oxygen or nitrogen molecules in the balloon using its mass/volume, molar volume (or ideal gas law), and NA.
• Why 1 g of hydrogen contains enormously many atoms: 1 g H = 1 mol → 6.022 × 10²³ atoms, showing how small atoms are.

Common pitfalls:

• Confusing molecules and atoms (e.g., O₂ molecule has 2 atoms).
• For ionic solids (NaCl) treat formula unit as the particle (1 formula unit contains 2 ions: Na⁺ and Cl⁻). If asked atoms, multiply accordingly.
• Keep units consistent (grams for mass when using M in g mol⁻¹).

Worked mini-examples (in words):

1. How many molecules are in 18 g of water? M(H₂O)=18 g mol⁻¹. n=18/18=1 mol → molecules = 1 × NA = 6.022 × 10²³.
2. How many atoms are in 2 g of H₂? M(H₂)=2 g mol⁻¹. n=2/2=1 mol → molecules = NA, atoms = 2 × NA = 1.2044 × 10²⁴.

Use the formulas given below to solve standard numerical exercises and show each step clearly: list known, formula, substitution, calculation, final answer with units.