Noesis
1.1.9 · D5Matter, Measurement & the Mole

Question bank — Law of definite proportions (Proust)

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The law in one breath: a pure compound always holds its elements in the same fixed ratio by mass, whatever its source or method of making. Keep that sentence in your head — most traps are just it being bent the wrong way.

The symbols this page uses

Before the traps, we nail down every letter so no reveal makes you guess. Picture a single molecule of a two-element compound as a little cluster of coloured bricks.

Figure — Law of definite proportions (Proust)

The picture above shows why the ratio survives no matter how many molecules you scoop up: stack identical molecules and both the red-brick pile and the blue-brick pile grow by the same factor , so dividing one by the other, cancels.

Figure — Law of definite proportions (Proust)

True or false — justify

A compound made in a lab and the same compound found in a rock have identical mass ratios.
True — the ratio is set by atom counts and atomic masses, both of which are constants of nature, so source cannot change them.
If two samples of a substance have different element mass ratios, they cannot be the same pure compound.
True — a single pure compound is locked to one ratio, so a genuine difference in ratio means different compounds, a mixture, or measurement error.
The law says every substance on Earth has a fixed composition.
False — it applies only to pure compounds; mixtures like air or brass can vary continuously in composition.
and having different C:O ratios violates the law of definite proportions.
False — each of them individually has one fixed ratio; the difference between them is described by the Law of Multiple Proportions, a separate law.
Adding excess oxygen to a hydrogen–oxygen reaction makes the resulting water richer in oxygen.
False — the excess oxygen stays as leftover reactant; every water molecule formed still obeys the oxygen-to-hydrogen mass ratio (derived above from ).
The law of definite proportions and the law of conservation of mass are the same statement.
False — conservation says total mass is unchanged in a reaction; definite proportions says the ratio inside a compound is fixed. Different claims.
Because the ratio is "by mass," it depends on how large a sample you take.
False — mass of over mass of has the sample count cancel out, so any sample size gives the same ratio.
Isotopes could, in principle, make two samples of the same compound show slightly different mass ratios.
True at the fine level — differing isotope abundance shifts the average atomic mass slightly, which is why the law is stated with ordinary (average) atomic masses and is treated as exact at the chemistry level.

Spot the error

"Salt water is a compound because salt and water always taste the same, so it has definite proportions."
Error: salt water is a mixture, not a compound — you can dissolve any amount of salt, so its composition varies and the law does not apply.
"Since air is roughly nitrogen everywhere, air is a compound obeying definite proportions."
Error: air's ratio is only approximately stable and is not fixed by chemical bonding; a variable, unbonded ratio marks a mixture, not a compound.
"Water is O:H, so if I have g of hydrogen I must be able to combine all of it with any oxygen I have."
Error: you also need at least g of oxygen. If oxygen is short, some hydrogen stays as excess — the ratio dictates a strict demand, not a guarantee that all reactant is used.
"Proust discovered that different compounds of the same elements come in whole-number ratios."
Error: that whole-number-multiples insight is the Law of Multiple Proportions (Dalton). Proust's law is about one compound having one fixed ratio.
"A molecule of water could have 2.3 hydrogen atoms if it forms in unusual conditions."
Error: atoms combine in whole numbers (Dalton's Atomic Theory); you cannot have a fraction of an atom, which is precisely why the mass ratio is quantized and fixed.
"If the mass ratio of two samples matches, they are guaranteed to be the exact same compound."
Partly wrong: matching ratio is necessary but not always sufficient — two different compounds can coincidentally share a mass ratio, so a match is strong evidence, not absolute proof.
"The percentage composition of a compound can drift if you make more of it."
Error: percentage by mass is a direct consequence of the fixed ratio, so it is constant no matter how much you synthesize.

Why questions

Why must the mass ratio be a fixed number and not just "usually" fixed?
Because each molecule contains a fixed integer count of each atom () and each atom has a fixed mass (), so is built entirely from constants.
Why does the sample size not affect the ratio?
For molecules, element contributes mass and contributes ; dividing, the cancels, leaving a ratio independent of how big the sample is.
Why does the law fail for mixtures?
In a mixture the components are not chemically bonded in fixed whole-number counts, so their proportions are free to vary — nothing "locks in" a ratio.
Why is Dalton's atomic theory needed to explain Proust's law?
It supplies the reason the counts are whole numbers and fixed; without indivisible atoms combining in set ratios, there would be no mechanism forcing a constant mass ratio.
Why can excess reactant never change a compound's composition?
The compound forms only in its fixed atom ratio; any reactant beyond what that ratio can consume simply remains unreacted and separate, leaving the product's ratio untouched.
Why do we say the law makes composition "quantized"?
Because you can only add elements one whole atom at a time, composition jumps in discrete steps rather than sliding smoothly — like Lego bricks that cannot be halved.
Why is percentage composition a "direct consequence" of this law?
If the mass ratio of elements is fixed, then each element's fraction of the total mass is also fixed, giving a constant percentage for every element.

Edge cases

Does the law apply to a compound with three or more elements, like ?
Yes — the reasoning holds for any number of elements; each has a fixed atom count, so every pairwise (and overall) mass ratio is constant.
What happens to the "ratio" if a compound has zero atoms of some element?
Mathematically the ratio needs a nonzero denominator, so we simply do not form a pairwise ratio with an element whose count is — it isn't part of the compound. The law constrains ratios only among elements actually present (); a -to-nonzero "ratio" is not defined and never needed.
Can a single pure element (like ) obey the law of definite proportions?
The law is about ratios between different elements, so with only one element there is no such ratio to fix — the law is vacuously satisfied and not really the point.
If real experimental masses give instead of exactly , is the law broken?
No — the small gap is measurement error; the law is exact in principle, and real data is judged by whether it rounds to the fixed ratio within experimental uncertainty.
Two compounds of iron and oxygen give Fe:O mass ratios and (mass of Fe divided by mass of O). Does either break definite proportions?
Neither — each is internally fixed (that is definite proportions); e.g. gives and gives . Their differing from each other is the domain of the Law of Multiple Proportions.
Does dissolving a compound in water change its element mass ratio?
No — dissolving forms a mixture with water but the compound's own molecules keep their fixed internal ratio; you've changed the surroundings, not the compound.
Could a compound with variable composition (a "non-stoichiometric" solid) exist?
At an advanced level yes — some crystals (e.g., certain metal oxides) have slight lattice defects and mildly variable ratios, which is exactly why the law is stated for idealized pure compounds.
Recall One-line stress test

If you can explain, without notes, why adding excess oxygen never changes water's ratio, you have internalized the whole law: composition is quantized by whole atoms, so extras just sit aside.

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