Avogadro Law (Volume - Amount Relationship)

Equal volumes, equal numbers of molecules

In 1811, the Italian scientist Amedeo Avogadro combined ideas from Dalton's atomic theory with Gay Lussac's law of combining volumes (Unit 1) to state what is now known as Avogadro's Law: equal volumes of all gases, under the same conditions of temperature and pressure, contain equal numbers of molecules. In other words, once temperature and pressure are fixed, a gas's volume depends only on how many molecules (moles, $n$) of it are present:

The number of molecules in one mole of any substance is Avogadro's constant, $6.022\times10^{23}$ — the same number you met when "mole" was first defined (Unit 1).

Standard conditions and molar volume

Because volume is directly proportional to moles, one mole of any gas at standard temperature and pressure (STP) occupies the same volume. Modern STP is defined as $273.15\,\text{K}$ ($0\,^{\circ}\text{C}$) and $1\,\text{bar}$ (exactly $10^{5}$ Pa) — chosen to approximate water's freezing point and sea-level atmospheric pressure. At STP, the molar volume of an ideal gas (or a mixture of ideal gases) is 22.71098 L mol$^{-1}$. Table 5.2 lists the (very close to ideal) molar volumes of some real gases at STP:

Since the number of moles $n = \dfrac{m}{M}$ (where $m$ is mass and $M$ is molar mass):

so the density of a gas is directly proportional to its molar mass.

A gas that obeys Boyle's law, Charles' law and Avogadro's law exactly is called an ideal gas — a hypothetical gas with no intermolecular forces at all. Real gases follow these laws closely only when their intermolecular forces are practically negligible; otherwise they deviate from ideal behaviour, a topic taken up later in this unit. …