Law of definite proportions (Proust)

WHAT is it?

The key word is compound. This is not about mixtures — a mixture (like salt stirred into water) can have any proportions. A compound has chemically bonded atoms in whole-number counts.

WHY is it true? (First-principles reasoning)

Let a compound have $n_A$ atoms of element $A$ (atomic mass $m_A$ ) and $n_B$ atoms of $B$ (atomic mass $m_B$ ) per molecule.

$\frac{\text{mass of }A}{\text{mass of }B} = \frac{n_A\, m_A}{n_B\, m_B}$

Every term on the right is a constant — $n_A, n_B$ are fixed small integers, $m_A, m_B$ are fixed atomic masses. So the ratio is a fixed number. That is the law.

HOW to use it (the workflow)

Find the mass ratio of elements from one sample.
Because the law says this ratio is constant, predict the masses in any other sample.
If the numbers don't match a fixed ratio → you're not looking at a pure compound (or the data is a mixture / experimental error).

Figure — Law of definite proportions (Proust)

Common Mistakes (Steel-manned)

Recall Feynman: explain to a 12-year-old

Imagine every "water Lego" is made of exactly 2 red bricks (hydrogen) and 1 blue brick (oxygen) snapped together. You can never make a water Lego with 2.5 red bricks — bricks don't split! So no matter how many water Legos you build, the pile of red bricks vs blue bricks always weighs in the same proportion. That's why water from anywhere is always $8$ grams oxygen for each $1$ gram hydrogen.

Active Recall

State the Law of Definite Proportions.

A pure compound always contains the same elements in the same fixed ratio by mass, regardless of source or method of preparation.

Who proposed it and when?

Joseph Proust, 1799.

Why is the mass ratio of a compound constant?

Each molecule has a fixed whole number of atoms of each element, and each atom has a fixed mass, so

m_A/m_B = n_A m_A^{atom}/n_B m_B^{atom}

is a constant.

Does the law apply to mixtures?

No — only to pure compounds; mixtures can have any proportions.

Water is 8:1 O:H by mass. How much O combines with 2.5 g H?

8 \times 2.5 = 20

g oxygen.

CO and CO₂ contain the same elements but different ratios — does this violate the law?

No. Each compound individually has a fixed ratio. Different compounds differing is the Law of Multiple Proportions.

If you add excess oxygen to hydrogen, does water's composition change?

No; the excess O is leftover reactant. Formed water stays 8:1.

Two Cu-oxide samples give Cu:O = 4.00 and 4.00. Same compound?

Yes — identical fixed mass ratios indicate the same compound.

Connections

Dalton's Atomic Theory — the atomic basis (fixed atom counts) that explains this law.
Law of Conservation of Mass — Lavoisier's law; mass is conserved and fixed in ratio.
Law of Multiple Proportions — the sister law for different compounds of the same elements.
The Mole Concept — mass ratios lead to mole ratios and formulas.
Empirical and Molecular Formula — fixed ratios let us deduce chemical formulas.
Percentage Composition — direct consequence: fixed % by mass of each element.

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, Law of Definite Proportions ka matlab simple hai: koi bhi pure compound hamesha apne elements ko ek fixed mass ratio mein rakhta hai — chahe wo compound kahin se bhi aaye ya kaise bhi banaya jaaye. Jaise paani (water) hamesha $8$ gram oxygen aur $1$ gram hydrogen ke ratio mein hota hai. Rain ka ho, lab ka ho, ya iceberg ka — ratio $8:1$ hi rahega. Yeh law Joseph Proust ne 1799 mein diya tha.

Iske peeche ki reason bahut pyaari hai. Har molecule fixed number of atoms se banta hai — water hamesha $2$ H aur $1$ O. Aadha atom hota hi nahi! Aur har atom ka mass fixed hai. Toh mass ka ratio automatically constant ho jaata hai: $m_A/m_B = n_A m_A^{atom} / n_B m_B^{atom}$ , jismein sab constants hain. Isliye ratio kabhi change nahi hota.

Ek important galti yeh hoti hai ki students sochte hain "zyada oxygen daal do toh water zyada oxygen-rich ho jayega." Nahi! Woh extra oxygen sirf leftover (excess reactant) ban ke padi rahegi — bane hue water molecules toh $8:1$ hi rahenge. Aur yaad rakho — yeh law sirf compounds pe lagta hai, mixtures pe nahi (mixture mein ratio kuch bhi ho sakta hai).

Yeh concept क्यों important hai? Kyunki isi se hum chemical formula, percentage composition, aur mole calculations samajhte hain. Jab tum ek sample se ratio nikaal lete ho, to kisi bhi doosre sample ke masses predict kar sakte ho — bina experiment kiye. Exam mein "kitna oxygen chahiye" type questions isi trick se solve hote hain: ratio pakdo, scale karo, ho gaya.

WHAT is it?

WHY is it true? (First-principles reasoning)

HOW to use it (the workflow)

Worked Examples

Common Mistakes (Steel-manned)

Active Recall

Connections

Concept Map

Hinglish (regional understanding)

Go deeper — visual, from zero

Test yourself — Matter, Measurement & the Mole

Connections