Q.Sample A of water is decomposed and found to contain $1\ \text{g}$ of hydrogen and $8\ \text{g}$ of oxygen. Sample B of water, obtained from a completely different source, is decomposed and found to contain $2\ \text{g}$ of hydrogen and $16\ \text{g}$ of oxygen. Show that these observations are consistent with the law of definite proportions.

Matter is anything that has mass and occupies space; its building blocks are atoms. Dalton's atomic theory (1808) was the first quantitative model: (1) matter is made of tiny indivisible atoms; (2) all atoms of a given element are identical in mass and properties, while atoms of different elements differ; (3) atoms combine in small whole-number ratios to form compounds; (4) in a chemical reaction atoms are only rearranged — never created, destroyed, or changed into another kind. These postulates explain the experimental laws of chemical combination, which are the heart of this concept.

1 — Law of conservation of mass (Lavoisier). In a chemical reaction the total mass of the products equals the total mass of the reactants — matter is neither created nor destroyed. So in 2 H₂ + O₂ → 2 H₂O, 4 g H₂ + 32 g O₂ gives exactly 36 g of water. The classic trap is an apparent mass loss when a gas escapes an open vessel (e.g. CO₂ from CaCO₃ → CaO + CO₂): mass is still conserved once the evolved gas is counted.

2 — Law of definite (constant) proportions (Proust). A pure compound always contains the same elements in the same fixed proportion by mass, no matter its source or how it was made. Water is always 1 : 8 hydrogen : oxygen by mass; CO₂ is always 3 : 8 carbon : oxygen. Given the fixed ratio in one sample you can find the mass of an element in any other sample of that compound.

3 — Law of multiple proportions (Dalton). When two elements form more than one compound, the masses of one element that combine with a fixed mass of the other are in a small whole-number ratio. Fixing 1 g of carbon: CO carries 1.33 g oxygen, CO₂ carries 2.67 g — a ratio of 1 : 2. This is the highest-yield JEE pattern: normalise to a fixed mass of the common element first, then take the ratio of the other element's masses; it should reduce to something like 1 : 2, 2 : 3, or 3 : 5. Works equally for the oxides of nitrogen (N₂O, NO, N₂O₃, NO₂, N₂O₅), the two chlorides of copper, etc.

4 — Law of reciprocal proportions (Richter). If elements A and B each combine separately with a fixed mass of a third element C, then the ratio of the masses of A and B that reacted with that fixed mass of C is the same as (or a simple whole-number multiple of) the ratio in which A and B combine directly with each other. It is the principle behind equivalent masses. Method: fix the mass of the common element C, read off the A : B masses, and compare with the direct A–B combining ratio.

5 — Gay-Lussac's law of combining volumes. When gases react, they do so in volumes that bear a simple whole-number ratio to one another and to the volumes of any gaseous products, all measured at the same temperature and pressure. In N₂ + 3 H₂ → 2 NH₃ the volumes combine as 1 : 3 : 2. Contrast with the mass laws — this one is about volumes of gases, not masses.

6 — Avogadro's law. Equal volumes of all gases, at the same temperature and pressure, contain equal numbers of molecules. This is what explains Gay-Lussac's law: because volume ∝ number of molecules (at fixed T, P), the whole-number volume ratios are really whole-number molecule (mole) ratios. Avogadro's law also lets you deduce a gaseous molecular formula from combining-volume data: if 1 volume of nitrogen + 3 volumes of hydrogen give 2 volumes of a product, the product must be NH₃ (and it resolved the early confusion between atoms and molecules of elemental gases like H₂, O₂, N₂).

Volume contraction. In a gaseous reaction the total gas volume usually changes because the number of gas molecules changes (and because a product like water may condense to a liquid at the measurement conditions). Track the gas volumes before and after: contraction = initial total gas volume − final total gas volume. Always state clearly whether a product is a gas or a liquid at the given T, P.

Modern limitations of Dalton's theory. Atoms are divisible (into protons, neutrons, electrons); atoms of the same element can differ in mass (isotopes), so "all atoms of an element are identical in mass" fails; some compounds are non-stoichiometric (e.g. certain oxides) and do not obey a strict fixed ratio; and isotopes/allotropes were unknown to Dalton. The laws, however, remain excellent working rules for ordinary chemistry.

How this concept is examined. JEE Main tests: identifying a Dalton postulate or its limitation; naming/stating each of the five laws; a conservation-of-mass calculation (including the escaping-gas trap); a definite-proportions ratio calculation; a multiple-proportions verification (the two-oxides pattern — normalise to a fixed common-element mass, then take the small whole-number ratio); a reciprocal-proportions check; a Gay-Lussac combining-volume calculation; a volume-contraction calculation; an Avogadro-law deduction of a gaseous molecular formula; and "which law does this data illustrate?" The habits that prevent most errors: count escaping gases before declaring mass lost, normalise to a fixed mass of the common element before comparing (multiple/reciprocal proportions), and keep the volume laws (Gay-Lussac, Avogadro) strictly at constant temperature and pressure.