Avogadro's law (sometimes referred to as Avogadro's hypothesis or Avogadro's principle) is an experimental gas law relating volume of a gas to the amount of substance of gas present. A modern statement of Avogadro's law is:

For a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant.

which can be written as: $V \propto n\,$

or $\frac{V}{n}=k$

where:

V is the volume of the gas
n is the amount of substance of the gas (measured in moles).
k is a constant.

This law explains how, under the same condition of temperature and pressure, equal volumes of all gases contain the same number of molecules. For comparing the same substance under two different sets of conditions, the law can be usefully expressed as follows: $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

The equation shows that, as the moles of gas increases, the volume of the gas also increases in proportion. Similarly, if the number of moles of gas is decreased, then the volume also decreases. Thus, the number of molecules or atoms in a specific volume of ideal gas is independent of their size or the molar mass of the gas.

The law is named after Amedeo Avogadro who, in 1811, hypothesized that two given samples of an ideal gas, of the same volume and at the same temperature and pressure, contain the same number of molecules. As an example, equal volumes of molecular hydrogen and nitrogen contain the same number of molecules when they are at the same temperature and pressure, and observe ideal gas behavior. In practice, real gases show small deviations from the ideal behavior and the law holds only approximately, but is still a useful approximation for scientists.

## Mathematical definition

Avogadro's law is stated mathematically as: $\frac{V}{n} = k$

Where:

V is the volume of the gas(es).
n is the amount of substance of the gas.
k is a proportionality constant.

The most significant consequence of Avogadro's law is that the ideal gas constant has the same value for all gases. This means that: $\frac{p_1\cdot V_1}{T_1\cdot n_1}=\frac{p_2\cdot V_2}{T_2 \cdot n_2} = constant$

Where:

p is the pressure of the gas in the cell
T is the temperature in kelvin of the gas

## Ideal gas law

A common rearrangement of this equation is by letting R be the proportionality constant, and rearranging as follows: $pV = nRT$

This equation is known as the ideal gas law.

## Molar volume

Taking STP to be 101.325 kPa and 273.15 K, we can find the volume of one mole of a gas: $V_{\rm m} = \frac{V}{n} = \frac{RT}{p} = \frac{(8.314 \mathrm{ J} \mathrm{ mol}^{-1} \mathrm{ K}^{-1})(273.15 \mathrm{ K})}{101 325 \mathrm{ Pa}} = 22.41 \mathrm{ dm}^3 \mathrm{ mol}^{-1}$

For 100.000 kPa and 273.15 K, the molar volume of an ideal gas is 22.712 dm3mol-1.