Law of multiple proportions (Dalton)
WHAT is this law?
Contrast it with its sibling law so you don't confuse them:
| Law | Applies to | Says |
|---|---|---|
| Definite/Constant Proportions | ONE compound | Composition by mass is always the same |
| Multiple Proportions | TWO OR MORE compounds of the same two elements | Fixed-mass-of-A → masses of B are in a small integer ratio |
WHY is it true? (Derivation from atoms — first principles)
Dalton had no idea about grams-per-atom, but we can see exactly why it must work.
Step 1 — atoms are indivisible units of mass. Let one atom of A have mass and one atom of B have mass . These are fixed constants of nature.
Step 2 — compounds have integer atom counts. (Why? Because you cannot put half an atom into a molecule.) Compound 1 has formula ; Compound 2 has , where are integers.
Step 3 — write mass of B per fixed mass of A. In compound , mass of A , mass of B . So
Step 4 — fix the mass of A (take the ratio between the two compounds). (Why divide? "Fixed mass of A" means we normalise A away.)
Every letter here is an integer → the whole thing is a ratio of integers → a simple whole-number ratio.
Worked Examples
Common Mistakes (Steel-man + Fix)
Recall Feynman: explain it to a 12-year-old (hidden — try first!)
Imagine LEGO. Carbon is a red brick, oxygen is a blue brick. You can build "1 red + 1 blue" and also "1 red + 2 blue." Because you can only add whole blue bricks (never half a brick), the amount of blue in the second toy is exactly twice the first — a clean 1-to-2. Since atoms are tiny unbreakable bricks, the masses of oxygen come out in neat whole-number ratios. That neatness is proof that matter is made of tiny countable pieces.
Flashcards
State the law of multiple proportions
Who and when proposed it
What must you do BEFORE forming the mass ratio
In CO vs CO₂, oxygen ratio for fixed 12 g C
In SO₂ vs SO₃, oxygen ratio for fixed 32 g S
Deep WHY the ratio is integer
Difference from law of definite proportions
Can the raw masses be non-integers?
Connections
- Law of definite (constant) proportions — its sibling; one compound vs many.
- Law of conservation of mass (Lavoisier) — the other pillar Dalton built on.
- Dalton's atomic theory — this law is its strongest evidence.
- Mole concept and Avogadro number — turns mass ratios into atom counts.
- Empirical and molecular formula — integer atom ratios in practice.
- Law of reciprocal proportions (Richter) — the fourth combining-mass law.
Concept Map
Hinglish (regional understanding)
Intuition Hinglish mein samjho
Dekho, Law of Multiple Proportions ka core idea simple hai: jab do elements aapas mein ek se zyada compound banate hain, tab ek element ki mass ko fix karke dekho, to doosre element ki masses hamesha chhote whole numbers ke ratio mein aati hain — jaise 1:2, 2:3. Example: CO mein 12 g carbon ke saath 16 g oxygen, aur CO₂ mein 12 g carbon ke saath 32 g oxygen. Carbon fix (12 g), aur oxygen ka ratio 16:32 = 1:2. Bilkul saaf integer ratio!
Ye kyun hota hai? Kyunki atoms tootte nahi — aap aadha atom kisi molecule mein daal hi nahi sakte. Toh molecule mein har element ka whole number count hota hai. Jab masses ka ratio banate ho, wo actually atom-counts ka ratio ban jaata hai, isliye integer aata hai. Yahi baat Dalton ki atomic theory ka sabse strong proof hai — matter tiny countable bricks (atoms) se bana hai.
Exam trick: pehle ek element ki mass same karo dono compounds mein (zaroorat pade to scale karo, jaise ×2), phir doosre element ki masses ka ratio nikaalo aur lowest terms mein laao. Yaad rakho — raw masses non-integer ho sakti hain (jaise 5.14 g), sirf final reduced ratio chhote whole numbers hona chahiye. Aur confuse mat hona: Definite Proportions = ek compound ki fixed recipe; Multiple Proportions = do ya zyada compounds compare karna. Mantra: "FIX one, the OTHER goes in FULL steps."