Avogadro Law

In 1811, the Italian scientist Amedeo Avogadro combined Dalton's atomic theory with Gay-Lussac's law of combining volumes to propose what is now called Avogadro's law: equal volumes of any gases, measured at the same temperature and pressure, contain equal numbers of molecules. Equivalently, at fixed temperature and pressure, the volume of a gas sample depends only on the number of molecules present (i.e. on the amount, $n$, of gas), so $V \propto n$, or $V = k_4n$ -- the volume per mole ($V/n$) is the same constant for every ideal gas at given $T,P$. Because the volume of a gas is directly proportional to the number of moles, one mole of ANY gas, at STP, occupies the same molar volume: $22.414$ L mol$^{-1}$ under the old STP convention (1 atm, 273.15 K), or $22.71$ L mol$^{-1}$ under the current IUPAC STP convention (1 bar, 273.15 K). Combining $V = k_4n$ with $n = m/M$ gives $V = k_4 m/M$, i.e. $M = k_4(m/V) = k_4 d$ (since $d = m/V$), so …