Dalton's atomic theory — postulates and limitations: Foundations

Before you read a single postulate, you need to be fluent with a handful of symbols the parent note quietly assumes: what a ratio is, what a subscript like $B_{x}$ means, what the summation sign $\sum$ does, and what $E = m c^{2}$ is even asking. We build each one from nothing.

1. The atom — the "indivisible lump"

Every idea on the parent page rests on one picture: matter is not a smooth paste, it is a pile of identical little balls.

Figure — Dalton's atomic theory — postulates and limitations

Look at the figure. On the left is the pre-Dalton idea — matter as a smooth, infinitely divisible smear (keep cutting forever). On the right is Dalton's idea — matter as discrete balls you eventually cannot cut. The whole theory lives on the right.

Why the topic needs this: if matter were a smear, you could combine "0.37 of it" with "0.63 of another" — any fraction at all. Only discrete balls force the whole-number recipes the mass laws demand.

2. Counting and the counting number $N$

To say "a recipe uses whole numbers," you must first be able to count the balls.

3. Mass $m$ and the mass of one atom $m_{i}$

Counting balls is not enough; the mass laws weigh them. So we need mass.

In the figure each blue ball has the same mass $m_{i}$ (postulate 2: atoms of an element are identical). So a pile of $N_{i}$ of them weighs exactly $N_{i} m_{i}$ — no surprises, because every ball is a perfect copy.

Why the topic needs this: the parent's mass-conservation formula multiplies a count by a per-atom mass. Without separating "how many" ( $N$ ) from "how heavy each" ( $m_{i}$ ), you cannot write that formula.

4. The ratio and the colon `:`

The mass laws are stated in ratios like $1 : 8$ and $1 : 2$ . What does that even mean?

The figure shows two water samples — small and large. The bars for H and O grow together, keeping the same height ratio $1 : 8$ . Simplifying a ratio means dividing both sides by their common factor until no smaller whole numbers work: $16 : 32 \to 1 : 2$ (divide both by 16). That is the move Example 1 makes.

5. Subscripts in formulas: $A B_{x}$

The parent writes compounds like $A B_{x}$ and $C O_{2}$ . The little number below the line is doing real work.

Why the topic needs this: postulate 4 says atoms combine in whole-number ratios — the subscripts $x, y$ are those whole numbers. When the parent computes $\frac{x m _{B}}{y m _{B}} = \frac{x}{y}$ , it is comparing two subscripts.

6. The summation sign $\sum$

The parent's mass-conservation formula uses $\sum_{i} N_{i} m_{i}$ . This symbol scares people; it is just "add up a list."

Why the topic needs this: total mass = every atom's mass added up. Since a reaction changes neither any $N_{i}$ nor any $m_{i}$ (postulates 3 and 2), the whole sum is frozen — that is conservation of mass in one symbol.

7. The equation $E = m c^{2}$ — reading it, not solving it

The parent lists nuclear reactions as a limitation, invoking $E = m c^{2}$ . You only need to read what it claims.

Why the topic needs this: Dalton swore atoms are never created or destroyed. In nuclear reactions a sliver of mass does disappear — but it isn't gone, it became energy via this equation. That single fact breaks postulate 3. See Mass–Energy Equivalence (E=mc²) for the full story.

You cannot cut the ball into a smaller piece of the same element.

Why must the count

N

always be a whole number?

Half an atom is not an atom of that element — you can only have whole balls.

What is the difference between

m

and

m_{i}

m

is a whole sample's mass;

m_{i}

is the mass of a single atom of type

i

What does the ratio

1 : 8

actually claim about water?

For every 1 gram of hydrogen there are 8 grams of oxygen (so H is

\frac{1}{9}

of the total).

How do you simplify the ratio

16 : 32

Divide both sides by their common factor 16, giving

1 : 2

What does the subscript

2

C O_{2}

mean?

Two oxygen atoms bonded to one carbon atom.

Read

\sum_{i} N_{i} m_{i}

in plain words.

Add up, over every atom type, its count times its per-atom mass — i.e. the total mass.

E = m c^{2}

, why is the released energy so large?

A tiny mass gets multiplied by

c^{2}

, an enormous number.

What stays the same in an isotope pair, and what differs?

Same element (proton count / name), different mass (neutron count).

What stays the same in an isobar pair, and what differs?

Same mass number, different element.

Connections

Parent topic
Laws of Chemical Combination
Discovery of the Electron (Thomson)
Isotopes and Isobars
Mass–Energy Equivalence (E=mc²)
Mole Concept and Stoichiometry
Modern Atomic Theory

Foundations — Dalton's atomic theory — postulates and limitations