Atomic Foundations of Matter
Pour salt into water and weigh the beaker before and after — the reading does not change. Burn baking soda with vinegar in a sealed balloon and weigh again — still no change, even though a gas hisses out and the mixture fizzes. Yet burn the same baking soda in an open dish and the balance seems to lose mass, because the carbon dioxide simply escapes into the room. Same atoms, same universe, different bookkeeping. This chapter builds the accounting rules that let you track matter through any change, physical or chemical, without ever losing count of a single atom. You will meet two founding laws of chemistry, discovered a few years apart in eighteenth-century France. Antoine Lavoisier weighed reactants and products with unprecedented care and found that mass is neither created nor destroyed in a chemical reaction — the Law of Conservation of Mass. Joseph Proust then showed that a compound always contains its elements in the same fixed ratio by mass, wherever the sample comes from — the Law of Constant Proportions. John Dalton then asked why these two laws should be true at all, and answered with an atomic theory so good that most of it still stands: atoms are indivisible in chemical reactions, atoms of one element are identical, and atoms combine in small whole-number ratios. From there the chapter turns practical. How do atoms actually combine — by sharing electrons or by trading them outright? What do we call the particle that results, and how do we name it and write its formula? And once you can write a formula, how heavy is one unit of the substance? By the end you will be able to verify a reaction obeys the conservation law, write and name covalent and ionic compounds correctly, and calculate molecular mass and formula unit mass from atomic masses alone.
- Law of Conservation of Mass (Lavoisier, 1789): in a chemical reaction, total mass of reactants equals total mass of products — matter is neither created nor destroyed.
- Mass only appears to change in an open system because a gas escapes unseen; in a closed system the balance reading never moves.
- Law of Constant Proportions (Proust): a compound's elements always combine in the same fixed mass ratio, regardless of source — water is always hydrogen and oxygen in the ratio 1:8 by mass.
- Dalton's Atomic Theory explains both laws: atoms are indivisible in chemical reactions, atoms of one element are identical, and atoms combine in simple whole-number ratios to form compounds.
- Atoms combine in two ways to become stable (complete octet or duplet): sharing electrons forms a covalent bond; transferring electrons forms an ionic bond, creating a positive cation and a negative anion.
- A molecule is an electrically neutral group of atoms held together covalently that can exist independently; ionic compounds instead form a repeating crystal lattice, so we speak of a formula unit.
- Chemical formulae use valency: for covalent compounds the valencies criss-cross as subscripts; for ionic compounds the ion charges criss-cross and simplify to the smallest whole-number ratio.
- Molecular mass (covalent) and formula unit mass (ionic) are both found the same way — add the atomic masses of every atom shown in the formula.
- Ionic compounds are generally soluble in water and conduct electricity only when molten or dissolved (never as a solid); most covalent compounds show the opposite pattern.
- Key idea: mass is conserved and elements combine in fixed ratios because matter is made of indivisible atoms that only rearrange by sharing or transferring electrons, and every chemical formula and every molecular or formula unit mass follows directly from that ratio and those atomic masses.
Mass is conserved in every chemical reaction and elements always combine in the same fixed ratio because matter is built from indivisible atoms that merely rearrange by sharing electrons (covalent bonds) or transferring them (ionic bonds), and this atomic bookkeeping is exactly what a chemical formula, molecular mass and formula unit mass record.
What this chapter covers
The chapter builds in four connected stages. First come two experimental laws describing how much matter is involved in a change: Conservation of Mass (total mass stays the same across a reaction) and Constant Proportions (a compound's elements always combine in the same fixed mass ratio). Second, Dalton's Atomic Theory explains why both laws hold, by proposing atoms are indivisible, identical within an element, and combine in small whole-number ratios. Third, the chapter asks how atoms combine — sharing electrons (covalent bonding, molecules) or transferring electrons (ionic bonding, cations, anions and crystal lattices) — and how to name and write formulae. Fourth, once a formula is known, the chapter shows how to compute molecular mass (covalent) or formula unit mass (ionic) from atomic masses. Carry two numbers throughout: the atomic mass unit (u), where hydrogen is about 1 u and oxygen about 16 u, and the octet rule — atoms are stable with eight electrons in their outermost shell (two, for the innermost K-shell).
The core ideas
The Law of Conservation of Mass
Antoine Lavoisier is remembered as the father of modern chemistry because he insisted on weighing everything. Dissolve salt in water and the solution's mass equals the sum of salt and water — a physical change conserves mass. The same holds for chemical changes, provided nothing enters or escapes the vessel: baking soda reacted with vinegar in an open dish loses mass as carbon dioxide bubbles away, but the identical reaction sealed in a flask with a balloon shows no change at all.
where: the equation only holds for a closed system, one that exchanges no matter with its surroundings. This is the Law of Conservation of Mass: matter can neither be created nor destroyed in a chemical reaction, only rearranged.
The Law of Constant Proportions
Soon after Lavoisier, Joseph Proust asked whether two elements combining into a compound must always combine in the same ratio. He found that they must: purified water from a river, a borewell or the ocean always breaks down into hydrogen and oxygen in the same mass ratio.
where: the ratio 1:8 is fixed by the compound's identity; 9 g of water always yields 1 g of hydrogen and 8 g of oxygen. This is the Law of Constant Proportions (also the Law of Definite Proportions, or Proust's Law). It applies only to pure compounds, never to mixtures — sugar and water mix in any ratio, but "water" cannot be made with hydrogen and oxygen in any ratio other than 1:8.
Dalton's Atomic Theory
John Dalton, teaching in Manchester in the early 1800s, realised both laws above follow automatically from a simple picture of matter. His postulates: matter is made of tiny, indivisible atoms; atoms can be neither created nor destroyed in a chemical reaction, only rearranged (explaining conservation of mass); atoms of a given element are identical in mass and properties, while atoms of different elements differ; and atoms combine in small whole-number ratios fixed for a given compound (explaining constant proportions). Twentieth-century physics later showed atoms can be split in nuclear reactions, but Dalton's picture remains essentially correct for every ordinary chemical reaction.
How atoms combine to become stable
Atoms with a full outer shell (eight electrons, or two for a K-shell) are stable, as you saw with helium and neon earlier. Atoms with an incomplete outer shell reach that stable count in two ways, both lowering the system's total energy, so the resulting chemical bond is more stable than the separate atoms.
Sharing electrons gives a covalent bond. Two hydrogen atoms, each needing one more K-shell electron, share one electron each, forming a stable hydrogen molecule, a single bond written H—H. Chlorine (seven valence electrons) shares similarly to give Cl—Cl. Oxygen (six valence electrons) shares two electrons each, giving a double bond, O=O. Hydrogen and chlorine, each needing one electron, share one pair to give the covalent compound hydrogen chloride (HCl).
Transferring electrons gives an ionic bond. Sodium has one lone valence electron; losing it leaves 11 protons but only 10 electrons, a positively charged sodium cation, Na⁺. Chlorine needs only one electron to complete its octet; gaining it gives 18 electrons against 17 protons, a negatively charged chloride anion, Cl⁻. Cations and anions together are ions, and the electrostatic attraction between oppositely charged Na⁺ and Cl⁻ is the ionic bond holding sodium chloride together. Unlike covalent compounds, ionic compounds do not exist as separate molecules; cations and anions instead pack into a repeating crystal lattice, each sodium ion surrounded by six chloride ions and vice versa.
Naming and writing chemical formulae
Covalent compounds are named with prefixes that count atoms: mono- (1, dropped for the first element), di- (2), tri- (3), tetra- (4), penta- (5), hexa- (6), the second element's name ending in -ide. So CO is carbon monoxide, CO2 is carbon dioxide, N2O5 is dinitrogen pentoxide; hydrogen never takes a prefix, so H2S is hydrogen sulfide, not dihydrogen sulfide. Ionic compounds are named cation first, then anion, simple anions ending in -ide (sodium chloride), many polyatomic anions not (sulfate, nitrate, hydroxide, carbonate). To write a covalent formula, criss-cross each element's valency as a subscript — carbon (valency 4) and chlorine (valency 1) give CCl4. To write an ionic formula, write the cation symbol first, criss-cross the numerical charges (without signs) as subscripts, and simplify by any common factor — magnesium (2+) and oxide (2−) give Mg2O2, simplified to MgO. When two or more polyatomic ions of one kind are needed, enclose that ion in brackets with the subscript outside, as in Mg(OH)2 or Al2(SO4)3.
Two worked derivations
The goal here is to show that the Law of Constant Proportions is not a separate rule of nature but a direct, calculable consequence of Dalton's atomic theory once a compound's formula and atomic masses are known — and to see exactly how the familiar 1:8 hydrogen-to-oxygen ratio in water falls out of nothing more than counting atoms and multiplying by standard atomic mass in atomic mass units (u), where hydrogen is assigned 1 u and oxygen 16 u.
Step 1. Start from Dalton's postulate: a compound has a fixed, whole-number ratio of atoms of each element, and every atom of an element has the same fixed mass. Water's formula, from two hydrogen atoms sharing electrons with one oxygen atom, is H2O — always two hydrogen atoms per one oxygen atom.
Step 2. Convert the atom count into a mass count. Two hydrogen atoms contribute 2 times 1 u, which is 2 u; one oxygen atom contributes 1 times 16 u, which is 16 u. Every water molecule anywhere has this same atom count and therefore this same mass split.
Step 3. Form the ratio: 2 u to 16 u, simplifying (divide both by 2) to 1 to 8 — precisely the ratio Proust measured experimentally, decades before atoms could be counted directly.
Step 4. Generalise and check. Since 1:8 depends only on the fixed formula H2O and fixed atomic masses, it cannot change regardless of where the water was collected from. If 9 g of pure water is decomposed, hydrogen is 1 out of 9 parts (1 g) and oxygen is 8 out of 9 parts (8 g), matching the chapter's stated result. Verified: 2 times 1 u plus 1 times 16 u equals 18 u total, split as 2 u hydrogen to 16 u oxygen, ratio 1 is to 8; 1/9 of 9 g is 1 g while 8/9 of 9 g is 8 g.
Go deeper · Derivation B · 2 minDeriving the criss-cross rule for ionic formulae from charge neutrality
The goal here is to justify, rather than just apply, the criss-cross shortcut used to write ionic formulae — to show algebraically why swapping the numerical values of a cation's charge and an anion's charge and using them as subscripts is guaranteed to produce an electrically neutral compound, the one physical requirement every real ionic compound must satisfy, since a charged lump of matter would instantly attract opposite charge until neutral.
Step 1. Set up the general case. Let the cation A carry charge m+ and the anion B carry charge n−, with m and n positive whole numbers (m = 3 for Al three-plus, n = 2 for O two-minus, say). Let a formula unit contain x atoms of the cation and y of the anion, written A subscript x, B subscript y.
Step 2. Apply the neutrality condition. Total positive charge is x times m, total negative charge is y times n. For overall neutrality these must be equal, giving x times m equals y times n.
Step 3. Solve for the smallest whole-number x and y. Choosing x equal to n and y equal to m satisfies the equation automatically, since n times m equals m times n — exactly the criss-cross rule, the anion's charge becoming the cation's subscript and vice versa. If m and n share a common factor, x and y are divided by it, which is why Mg2O2 is written as MgO.
Step 4. Check against two chapter examples. For aluminium (m = 3) and oxide (n = 2), x = 2, y = 3, so Al2O3, with charge balance 2 times 3+ equal to 3 times 2− equal to 6. For magnesium (m = 2) and hydroxide (n = 1, polyatomic), x = 1, y = 2, so Mg(OH)2, balance 1 times 2+ equal to 2 times 1− equal to 2. Both confirm neutrality as predicted. Verified: for Al3+ and O2- the criss-cross gives Al2O3 with charge balance 2 times 3 equal to 3 times 2 equal to 6; for Mg2+ and OH- it gives Mg(OH)2 with charge balance 1 times 2 equal to 2 times 1 equal to 2.
Worked examples
Board level - Verifying the Law of Conservation of Mass (NCERT Example 9.1, extended)
Students place 4.0 g of calcium carbonate with 2.92 g of hydrochloric acid in a closed container. After the reaction, they measure 1.76 g of carbon dioxide, 0.72 g of water, and 4.44 g of calcium chloride. Verify the Law of Conservation of Mass, and state what would happen to the reading if the same reaction were done in an open beaker instead.
Step 1. Add the reactant masses: 4.0 g plus 2.92 g gives 6.92 g.
Step 2. Add the product masses: 1.76 g plus 0.72 g plus 4.44 g gives 6.92 g.
Step 3. Compare the two totals — 6.92 g equals 6.92 g, so the law is obeyed in this closed container.
Step 4. In an open beaker, carbon dioxide gas would bubble away instead of staying trapped, so the reading would fall below 6.92 g by roughly the 1.76 g of escaped gas. The law itself is not violated — mass has simply left the system being weighed. Answer: 6.92 g equals 6.92 g, so the law is obeyed; in an open beaker the reading would appear to drop by about 1.76 g as the gas escapes, even though no mass is truly lost.
Board level - Using the Law of Constant Proportions to scale a reaction (NCERT Example 9.3, extended)
Sodium chloride (NaCl) contains sodium and chlorine in the fixed mass ratio 23:35.5. If 46 g of sodium reacts completely with chlorine, find the mass of chlorine required, and the total mass of sodium chloride formed.
Step 1. Write the fixed ratio as a proportion: mass of chlorine over mass of sodium always equals 35.5 over 23, whatever quantity of sodium is used, since the ratio is fixed by the compound's identity.
Step 2. Scale to the given mass: mass of chlorine equals (35.5 / 23) times 46 g, giving 71 g.
Step 3. Apply conservation of mass: mass of sodium chloride formed equals 46 g plus 71 g, giving 117 g. Answer: 71 g of chlorine is required, and 117 g of sodium chloride is formed.
Higher-order thinking (HOTS / olympiad-style) - From electronic configuration to formula unit mass in one chain
Element A has electronic configuration 2, 8, 2 and element B has configuration 2, 8, 7. Predict the bond type formed when A and B combine, write and name the compound's formula, and calculate its formula unit mass. Take atomic mass of A as 24 u and B as 35.5 u.
Step 1. Read the valence electrons. A has 2 outer electrons, so it loses both to reach a stable octet, becoming a cation of charge 2+ (matches magnesium). B has 7 outer electrons, so it gains 1, becoming an anion of charge 1− (matches chlorine).
Step 2. Since A loses electrons and B gains them, this is electron transfer, so an ionic bond forms between cation A2+ and anion B−.
Step 3. Criss-cross: the cation's charge, 2, becomes the anion's subscript, and the anion's charge, 1 (not written), becomes the cation's subscript, giving AB2 — magnesium chloride, MgCl2.
Step 4. Formula unit mass: one atomic mass of A plus two of B, which is 24 u plus 2 times 35.5 u, giving 24 u plus 71 u, which is 95 u. Answer: an ionic bond forms; the compound is AB2 (magnesium chloride, MgCl2); its formula unit mass is 95 u. Timing note: aim for under three minutes. The chain is configuration to valence electrons to ion charge to bond type to formula to formula unit mass — each step feeds the next, so identify A and B correctly first before touching the arithmetic; a wrong charge at Step 1 wrecks every later step.
Common traps
Students often think the Law of Conservation of Mass fails whenever a reaction is done in the open, because the balance reading drops — the mass has not vanished, it left as an escaping gas that was never weighed. A related trap is applying the Law of Constant Proportions to mixtures: sugar dissolved in water can be made in any ratio, because a solution is a mixture, not a compound. In naming covalent compounds, students forget mono- is dropped for the first element but kept for the second (carbon monoxide, not monocarbon monoxide), and that hydrogen never takes a prefix. In ionic formulae, a common slip is leaving charge signs inside the final formula (Mg2+O2− instead of MgO) or forgetting to simplify criss-crossed subscripts. Students also mix up molecular mass (covalent, discrete molecules) with formula unit mass (ionic, a crystal lattice). Finally, many assume any water-soluble solid conducts electricity — sugar dissolves but does not ionise, while an ionic solid conducts only once dissolved or melted, never dry.
You should be able to…
- State the Law of Conservation of Mass and explain why an open system can appear to violate it even though it never truly does.
- State the Law of Constant Proportions and distinguish a compound (fixed ratio) from a mixture (any ratio).
- List Dalton's atomic theory postulates and explain how each accounts for one of the two mass laws.
- Decide whether a pair of atoms is more likely to share electrons (covalent) or transfer electrons (ionic), from valence electron count.
- Draw the electron-sharing or electron-transfer picture for simple molecules such as H2, Cl2, O2, HCl, H2O and NaCl.
- Name and write the formula of a covalent or ionic compound from valencies or charges, using the criss-cross method.
- Calculate the molecular mass of a covalent compound or the formula unit mass of an ionic compound, given atomic masses.
- Predict, from solubility and conductivity behaviour, whether an unknown compound is more likely to be ionic or covalent.
Ask the tutor: Want to work through a few more criss-cross formula and formula-unit-mass problems together, or check your own solved example against the Law of Conservation of Mass?
If I burn a piece of paper and the ash weighs much less than the paper, has the Law of Conservation of Mass been broken?
No. Burning paper is a chemical reaction between the paper and oxygen from the air, producing carbon dioxide and water vapour as well as ash. Those gaseous products drift away into the room instead of staying on your balance pan, so the ash alone will always weigh less than the original paper. If you could capture every gram of carbon dioxide and water vapour and weigh it along with the ash, the total mass would exactly equal the mass of the paper plus the oxygen it consumed. This is exactly the open-versus-closed-system idea from Activity 9.2.
Why is water always H2O and never, say, H3O in ordinary chemistry, if atoms can combine in different ratios?
Atoms combine in whichever ratio lets both reach a stable outer shell, and for hydrogen and oxygen that ratio is fixed by electron requirements: oxygen needs two more electrons to complete its octet, and each hydrogen atom can only supply one, so it takes exactly two hydrogen atoms to satisfy one oxygen atom. There is no stable way to satisfy oxygen's requirement with three hydrogen atoms, so H2O is the only stable neutral compound formed this way, and the Law of Constant Proportions then guarantees this 2 to 1 atom ratio, and its 1 to 8 mass ratio, in every sample of water anywhere.
Why do ionic compounds not have a molecular mass, and what is a formula unit mass instead?
Molecular mass only makes sense for a substance existing as discrete, independent molecules, each with a fixed, countable set of atoms bonded covalently, like a single H2O or CO2 unit. Ionic compounds like sodium chloride do not form such independent units; enormous numbers of Na+ and Cl− ions instead pack into one continuous crystal, with no natural boundary marking where "one molecule" ends. Chemists define a formula unit, the smallest whole-number ratio of ions shown in the formula (one Na+ for every Cl−), and the formula unit mass is found the same way molecular mass is, by adding atomic masses of everything shown in that formula.
How do I decide quickly whether a compound is ionic or covalent without drawing every electron?
A fast rule of thumb: a metal combined with a non-metal almost always forms an ionic compound, since metals lose their few valence electrons easily while non-metals gain electrons easily, favouring transfer — sodium chloride, magnesium oxide. Two non-metals combining, on the other hand, almost always share electrons rather than transfer them, since both want to gain and neither wants to lose, giving covalent compounds like carbon dioxide or water. You can also use the physical evidence from Activity 9.4 as a check: ionic compounds tend to dissolve in water and conduct electricity when dissolved or molten, while covalent compounds tend to dissolve in kerosene or petrol instead and do not conduct.