Avogadro's Law

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Equal volumes of two different ideal gases are compared at the same temperature and pressure, so what can be said about the number of molecules each volume contains?

RankGuru · Accepted Answer

This statement is Avogadro's hypothesis, presented in NCERT Class 11, Chapter 13 (Kinetic Theory), which follows directly from the ideal gas equation $PV = N k_B T$. Rearranging for the number of molecules gives $N = \frac{PV}{k_B T}$, an expression that contains only pressure, volume and temperature but no reference to the type of gas or its molecular mass. Therefore two gases held at the same pressure, the same volume and the same temperature must contain identical numbers of molecules, regardless of how heavy or light those molecules are. The option that the lighter gas has more molecules incorrectly injects mass dependence. The option that the heavier gas has more likewise wrongly links mass to count. The option involving molecular diameter confuses molecule size with molecule number. A plausibility check confirms the idea: since $N$ depends only on the macroscopic state variables $P$, $V$ and $T$, equal states must give equal molecule counts, which is exactly the physical content of Avogadro's law.

Avogadro's Law

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