Atoms, Molecules and Formulae

Read a formula as a description

A formula is a compact description, not a bag of letters to rearrange. In this lesson you will identify atoms, molecules and ions; read grouped formulae; build simple neutral ionic formulae from supplied charges; and calculate the mass represented by a formula.

Recall the previous lesson: an element, compound and mixture are composition categories. Here we add a second level of language about their constituent particles. Only whole-number counting, multiplication and simple signed sums are needed. Charges and atomic masses needed in questions are supplied. We will explain where charges come from in the next lesson; you do not need an unexplained shell diagram to begin.

1. Atom, molecule and ion do different jobs

An atom is a basic unit associated with an element. An element's identity is determined by its atoms' proton number, which the next lesson explains. Some elemental gases, such as helium, occur as separate atoms. Many other substances contain atoms bonded to other atoms.

A molecule is a discrete, electrically neutral group of two or more bonded atoms. O₂ contains two oxygen atoms, so it is a molecule of an element. CO₂ contains carbon and oxygen atoms, so it is a molecule of a compound. The number of atoms does not decide element versus compound; the number of different elements does. O₂ and O₃ both contain only oxygen, although their molecules differ.

An ion has a net electrical charge. A positive ion is a cation and a negative ion an anion. At this stage, treat the written charge as supplied information. For a simple atom, losing negatively charged electrons makes a positive ion; gaining them makes a negative ion. The detailed proton/electron accounting follows in the next lesson.

An ion may be a single atom, as in Na⁺ or Cl⁻, or a bonded group, such as NH₄⁺, NO₃⁻ or SO₄²⁻. A group carrying charge is a polyatomic ion, not a neutral molecule. NH₄⁺ has one nitrogen and four hydrogen atoms and a total charge of +1 on the group; it is not four separate hydrogen ions. The name chloride refers to Cl⁻, whereas chlorine names the element.

A compound need not contain separate molecules

In solid sodium chloride, sodium and chloride ions form an extended repeating crystal. NaCl states the simplest 1:1 ratio of Na⁺ to Cl⁻. A formula unit expresses that ionic composition ratio; it is not a tiny isolated NaCl molecule. A pure ionic compound can therefore contain more than one kind of ion while still being one chemical substance.

Figure CF2-V01. Four kinds of description

A cropped ionic pattern, continuing beyond its edges:

… Na⁺  Cl⁻  Na⁺  Cl⁻ …
… Cl⁻  Na⁺  Cl⁻  Na⁺ …
… Na⁺  Cl⁻  Na⁺  Cl⁻ …

The whole repeating pattern is the crystal model; do not isolate each adjacent Na⁺/Cl⁻ pair as a molecule. The two-dimensional sketch shows neither actual scale nor full three-dimensional coordination. The brackets around O₂ mark a discrete group; NaCl's formula unit is a composition ratio, not such a packet.

2. Learn what each position in the notation means

Symbols are case-sensitive. The first letter is uppercase and a second letter, if present, is lowercase. Co is cobalt; CO is a formula containing carbon and oxygen. Cl is chlorine's symbol; it must not be rendered as capital C followed by capital I.

A subscript is the small number below the line after an element or a bracketed group. No written subscript means one. A charge is written above the line, such as the 2− in SO₄²⁻; it is not an extra atom count. A coefficient is the ordinary-sized number before the entire formula, such as the 3 in 3CO₂.

Worked case CF02-A: amount versus identity

Compare 3CO₂, CO and C + O₂.

• One CO₂ molecule has one carbon and two oxygen atoms.
• 3CO₂ represents three such molecules: carbon count = 3×1 = 3; oxygen count = 3×2 = 6. The coefficient repeats the whole group.
• CO names a different compound, with a different carbon-to-oxygen atom ratio. Changing the subscript changes the described substance.
• C + O₂ lists separate substances. The plus sign does not by itself join atoms into CO₂.

Figure CF2-V02. The outside number repeats the whole group

3CO₂ → [CO₂] [CO₂] [CO₂]

The coefficient is the outside 3; the subscript is the small 2 inside CO₂. The molecule count and atom count are different quantities.

For an ionic compound, the same coefficient rule counts represented formula units. It still does not claim that each formula unit is a physically separate molecule.

3. Build ionic formulae by cancelling charge

A neutral ionic compound has total positive charge equal in magnitude to total negative charge. Write the cation first, then the anion. Choose the smallest whole-number ratio of those ions that makes the total zero.

A compact reference set for this lesson is: Na⁺ and K⁺; Mg²⁺ and Ca²⁺; Al³⁺; Cl⁻, O²⁻ and N³⁻; OH⁻, NO₃⁻, CO₃²⁻, SO₄²⁻ and NH₄⁺. These are identities and charges used here, not an unbounded memorisation list. New or variable charges must be supplied in a question.

Worked case CF02-B: neutral first, shortcut second

You are given Mg²⁺ and N³⁻. A magnesium ion contributes +2; a nitride ion contributes −3.

Try before the answer: One of each gives +2−3 = −1. What small total could both charge magnitudes reach?

Resolved: Six. Three Mg²⁺ ions give +6 and two N³⁻ ions give −6. Thus the ratio is 3:2 and the formula is Mg₃N₂. Check: 3×(+2) + 2×(−3) = 0.

Now change the supplied anion to O²⁻. One Mg²⁺ and one O²⁻ already cancel, so the formula is MgO, not unreduced Mg₂O₂. The 2:2 counts have zero charge but are not the smallest ratio.

Crossing charge magnitudes can be a convenient memory aid for the numbers, but it comes after understanding neutrality. Reduce a common factor and recheck the charge. Do not cross signs into a neutral formula. This method handles the stated ions; it is not a universal method for predicting every compound that could exist.

Worked case CF02-C: keep a polyatomic group intact

You are given Ca²⁺ and OH⁻. One calcium ion needs two hydroxide ions: +2 + 2×(−1) = 0. Write Ca(OH)₂. The parentheses show that the whole OH group occurs twice.

One formula unit represents Ca = 1, O = 2 and H = 2. For 2Ca(OH)₂, the leading coefficient doubles the entire inventory: Ca = 2, O = 4 and H = 4. Writing CaOH₂ would fail to repeat the O with the H and would not preserve two hydroxide groups.

Figure CF2-V03. Charge ledger, then atom ledger

Then count what the formula represents:

Ion count, charge total and atom count have their own labels. Do not add them as though they were the same quantity.

4. Valency is not the same as signed charge

Valency means combining capacity in the elementary model and is written as a nonnegative number. An ion's charge has a sign. The number of valence electrons is another quantity; it will be explained with atomic structure. Do not treat all three as interchangeable.

Using supplied simple valencies, oxygen's combining capacity 2 and hydrogen's 1 are consistent with H₂O: one oxygen combines with two hydrogen atoms. This is useful for introductory formula patterns. It does not make valency a unique predictor of every molecular formula, structure or bond arrangement.

The reduction to a smallest ionic ratio has a strict limit. A supplied molecular formula H₂O₂ describes two hydrogen and two oxygen atoms in a molecule of hydrogen peroxide. Reducing its subscripts to HO would change the stated molecular formula. 'Always reduce every chemical formula' is therefore a false rule. You may recognise a simple ratio, but a molecular formula states the actual atom counts in the molecule.

No experiment or preparation is implied by these examples. We are interpreting chemical language.

5. Add the masses represented by the formula

The unit u is a very small mass unit useful for atoms and molecules. In the calculation exercises here, each atomic mass is supplied in u and school-rounded values are used. Follow those given values; do not substitute atomic number or mass number. The next lesson separates those quantities and explains noninteger tabulated atomic masses.

For a discrete molecule, the sum is its molecular mass. For an ionic compound, use formula-unit mass for the sum represented by its simplest formula unit. If the term relative atomic or molecular mass is used elsewhere, that is a ratio and has no unit; here we explicitly calculate masses in u.

Worked case CF02-D: same counting method, different particle language

Ethanol's molecular formula is supplied as C₂H₆O. Its structure is not being derived here. Given C = 12 u, H = 1 u and O = 16 u:

• carbon contributes 2×12 = 24 u
• hydrogen contributes 6×1 = 6 u
• oxygen contributes 1×16 = 16 u
• molecular mass = 24 + 6 + 16 = 46 u

For ionic CaCO₃, given Ca = 40 u, C = 12 u and O = 16 u, formula-unit mass = 40 + 12 + 3×16 = 100 u. Calling it the mass of a separate 'CaCO₃ molecule' would give the wrong structural picture even if the addition were correct.

Figure CF2-V04. Mass comes from the atom inventory

C₂H₆O: molecular mass = 46 u. CaCO₃: formula-unit mass = 100 u. A subscript is a multiplier, not a mass to add directly. Do not label 46 u as 46 g without conversion. An individual particle's mass can be expressed in grams after a correct conversion, but this lesson does not require that conversion or the mole concept.

A four-step self-check

1. What is being described: atom, molecule, ion or an ionic formula ratio?
2. Which numbers are charges, inside subscripts, bracket subscripts or outside coefficients?
3. For a proposed ionic formula, is charge zero and is the ratio reduced without changing an ion?
4. For a mass calculation, did you count every represented atom and name the quantity appropriately?

Check your reasoning

Try these five questions before the explanations. They are free, untimed learning checks with no negative marking, not an official paper. Charges and masses supplied in the question take precedence over guessed memory.

1. Use these descriptions: helium has separate He atoms; oxygen has O₂ groups; NO₃⁻ carries a net negative charge; solid NaCl is an extended ionic crystal. Which complete interpretation is correct?

A. He: atom; O₂: molecule of an element; NO₃⁻: polyatomic ion; NaCl: formula giving an ionic ratio B. He: atom; O₂: molecule of a compound; NO₃⁻: polyatomic ion; NaCl: formula giving an ionic ratio C. He: atom; O₂: molecule of an element; NO₃⁻: neutral molecule; NaCl: formula giving an ionic ratio D. He: atom; O₂: molecule of an element; NO₃⁻: polyatomic ion; NaCl: an isolated molecule in this solid

2. In the formula expression 3Al(OH)₃, how many atoms of Al, O and H are represented in total?

A. Al = 3, O = 3, H = 3 B. Al = 1, O = 9, H = 9 C. Al = 3, O = 9, H = 9 D. Al = 3, O = 3, H = 9

3. Calcium ions are Ca²⁺ and oxide ions are O²⁻. Which neutral ionic formula expresses the smallest whole-number ratio of these ions?

A. Ca₂O₂ B. CaO C. CaO₂ D. Ca₂O

4. Given Al³⁺ and the intact sulfate ion SO₄²⁻, which formula is neutral and preserves the sulfate group?

A. Al₃(SO₄)₂ B. Al₂SO₄ C. Al(SO₄)₃ D. Al₂(SO₄)₃

5. Li₂O is an ionic compound. Use the supplied rounded atomic masses Li = 7 u and O = 16 u. Which result is correctly calculated and named?

A. Molecular mass = 30 u B. Formula-unit mass = 23 u C. Formula-unit mass = 30 u D. Formula-unit mass = 30 g

Answers and option diagnoses

1. A. He: atom; O₂: molecule of an element; NO₃⁻: polyatomic ion; NaCl: formula giving an ionic ratio

A respects all four supplied descriptions. B incorrectly calls O₂ a compound: both atoms belong to oxygen, so only one element is present. C removes the written negative charge from nitrate; NO₃⁻ is a group of atoms with net charge, not a neutral molecule. D turns a ratio in an extended crystal into a separate NaCl molecule. He can occur as separate atoms; not every elemental sample consists of multi-atom molecules.

2. C. Al = 3, O = 9, H = 9

C is correct. One Al(OH)₃ formula unit represents Al₁O₃H₃; the coefficient 3 multiplies all of it, giving Al₃O₉H₉ in the total inventory. A ignores the bracket subscript. B forgets that the leading coefficient also multiplies Al. D applies the bracket multiplier only to H instead of the whole OH group. These are atom counts represented by the formula, not a claim that an ionic crystal contains isolated molecular packets.

3. B. CaO

B is correct: one Ca²⁺ and one O²⁻ give +2 + (−2) = 0, so the minimum ratio is 1:1. A has zero total charge for the stated ion counts, but 2:2 is not the smallest ratio; reduce it to 1:1. C gives +2−4 = −2 using the supplied oxide ions. D gives +4−2 = +2. Do not apply this reduction rule to an independently supplied molecular formula such as H₂O₂; this question is specifically about the simplest ionic ratio.

4. D. Al₂(SO₄)₃

D is correct. Two Al³⁺ ions give +6 and three SO₄²⁻ ions give −6. The formula is Al₂(SO₄)₃: the bracket repeats the whole sulfate ion three times. A has +9−4 = +5; B has +6−2 = +4; C has +3−6 = −3. None of A, B or C is neutral with the given ions. The 4 inside SO₄ stays fixed; changing it would no longer preserve sulfate.

5. C. Formula-unit mass = 30 u

C is correct: 2×7 + 16 = 30 u, and an ionic compound calls for formula-unit mass here. A gets the sum but wrongly describes a discrete molecule. B counts Li only once. D copies the number calculated in u and relabels it g without conversion. A particle mass can legitimately be expressed in grams after proper conversion, but 30 u is not 30 g.

Sources and scope

The RRB CEN 09/2025 official notice, §14.1, printed p.28, sets a Class 10 CBSE-level science boundary without naming this individual chapter. Formula language is a foundation for that level and for balancing equations later in this module; it is not a claim of separate RRB subtopic weightage.

Concept references: NCERT Exploration, Grade 9, Chapter 9, first edition April 2026, §§9.4–9.5 and 9.7–9.8, printed pp.169–180; Chapter 8, §8.4, pp.148–149, for symbols; and NIOS Secondary Science and Technology 212, Chapter 3, §§3.3 and 3.5, pp.56–57 and 61–64, edition not established. Supplied numerical values are independently checked rather than copied from older source tables. All prose, explained cases, visual designs and questions are original; these are not previous-year questions.

Analogy

Labelled building pieces help you keep an atom inventory. Three copies of one complete labelled model are like three packets with an unchanged packing list: the coefficient counts copies, while the formula fixes what each copy represents. The analogy does not show actual particle colour, size, shape, energy or bonding. In particular, an ionic formula unit is a composition ratio in a crystal, not a physical packet or separate molecule.

Quick reference

• Element/compound classify composition; atom/molecule/ion describe particles
• O₂: neutral molecule of an element; CO₂: neutral molecule of a compound
• Ion: net charge; cation positive, anion negative; a polyatomic ion is one charged group
• Solid NaCl: extended crystal with 1:1 ion ratio; no isolated NaCl molecule implied
• Symbols are case-sensitive: Co ≠ CO; Cl ≠ CI
• Subscript belongs to its symbol/group; charge is a superscript
• Coefficient multiplies the entire formula: 3CO₂ gives C = 3 and O = 6
• Neutral ionic formula: supplied charges → smallest cancelling ratio → preserve groups → recheck
• Ca(OH)₂ contains Ca = 1, O = 2, H = 2; 2Ca(OH)₂ contains Ca = 2, O = 4, H = 4
• Valency is combining capacity; charge has a sign; outer-electron count is distinct
• Do not reduce a given molecular formula such as H₂O₂ to HO
• Mass in u = sum of represented atom counts × supplied atomic masses
• Use molecular mass for molecules and formula-unit mass for ionic formula units
• Copying a numerical value from u to g without conversion is wrong