Do equal masses of two gases contain the same number of molecules?
Short answer: Moles = mass/molar mass. 2 g H₂ = 1 mol; 2 g O₂ = 1/16 mol.
The trap
The wrong idea
“Equal masses of two gases contain the same number of molecules.”
It sounds reasonable, and a lot of JEE/NEET aspirants carry it into the exam. Here's a one-question check, then the explanation that makes it click.
Quick check
Try it before you peek
Which has more molecules: 2 g of H₂ or 2 g of O₂?
- H₂
- O₂
- Same
Show the answer
A. H₂
Moles = mass/molar mass. 2 g H₂ = 1 mol; 2 g O₂ = 1/16 mol.
The click
The number of molecules is set by the number of moles, not by mass: n = mass ÷ molar mass, and the number of molecules = n × N_A, where N_A ≈ 6.022 × 10²³ per mole. Different gases have different molar masses, so equal masses give different numbers of moles.
H₂ has a molar mass of 2 g/mol (2 × 1) and O₂ has 32 g/mol (2 × 16). So 2 g of H₂ = 2/2 = 1 mol ≈ 6.022 × 10²³ molecules, while 2 g of O₂ = 2/32 = 1/16 mol ≈ 3.76 × 10²² molecules. The hydrogen sample has 16 times as many molecules.
The idea in one line: each O₂ molecule is 16 times heavier than an H₂ molecule, so the same mass of oxygen contains 16 times fewer molecules.
The true statement this misconception is confused with is Avogadro's law: equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. It is about volume, not mass. At 0 °C and 1 atm, one mole of an ideal gas occupies about 22.4 L (about 22.7 L at 0 °C and 1 bar, the current IUPAC standard), so 2 g of H₂ would fill about 22.4 L while 2 g of O₂ would fill only about 1.4 L.
Got this one? The Knot Scan finds the misconception you don't know you have, in 8 questions.