2.3 Avogadro’s Hypothesis

In 1808, two big ideas landed on the scene.

Gay-Lussac noticed something cool: when gases react, their volumes mix in simple ratios — like 1:1, 1:2, or 2:3.

Dalton had his own idea: elements combine in simple whole-number ratios by atoms (think H₂O, not H₂O_0.5).

Then Berzelius mixed them. He guessed:

Uh-oh. When he tested this with hydrogen and oxygen, it led to a problem. For water formation, his idea forced oxygen and hydrogen to split into half-atoms. But Dalton’s theory said: No half-atoms allowed! 🔥

Enter Avogadro, the problem solver. He said: “You’re confusing two things.”

• Atom = the smallest part of an element that reacts (may not exist alone).
• Molecule = the smallest part of a substance that can exist freely.

With that, he fixed Berzelius’s idea into Avogadro’s Hypothesis:

Mystery solved. Half-atoms disappeared. Chemistry moved on. 🧪✨

e.g., if a litre of hydrogen, oxygen, nitrogen, or carbon dioxide is taken separately at NTP, then each of them contains the same number of molecules.

Where V = volume of gas; n = number of molecules.

At constant temperature and pressure, doubling the volume doubles the number of molecules, and vice versa.

The vapour density (V.D.) is the ratio of the mass of a given volume of a gas or vapour to the mass of the same volume of hydrogen, under the same conditions of temperature and pressure.

Let the chosen volume of the gas contain ‘n’ molecules. By Avogadro’s hypothesis, this number is the same for the gas and for hydrogen under identical conditions. Then:

The molecular mass of a compound/element is a number that shows how many times the molecule is heavier than one atom of hydrogen:

Dividing equation (2) by (1):

We know that:

Let us consider 1 litre of gas at NTP:

It has been found that the mass of 1 litre of hydrogen gas at NTP is 0.08986 g. So:

This volume (22.4 L) is called the gram molecular volume or molar volume of a gas at NTP.

Avogadro’s number (N_A) is the number of molecules present in one gram molecular mass (one mole) of any gas or substance. Its value is approximately 6.023 × 10²³ molecules per mole.

Let us consider H₂ gas to deduce this number.

We know the molecular mass of H₂ = 2, so 1 gram molecular mass of H₂ = 2 g.

Let w gram = mass of one hydrogen atom. Then 2w gram is the mass of one H₂ molecule, so 2 g contains 1/w H₂ molecules.

Since the mass of one hydrogen atom, w ≈ 1.67 × 10⁻²⁴ g:

i.e., 1 gram molecular mass of any gas contains Avogadro’s number of molecules (6.023 × 10²³).