According to Gay Lussac’s theory, at constant volume, the pressure of a fixed amount of a gas varies directly with the temperature. Avogadro used the conclusions of Gay Lussac’s theory and Dalton’s atomic theory to derive a relationship between volume and the amount of a gas. According to Avogadro’s law, equal volumes of all gases under the same conditions of temperature and pressure contain an equal number of molecules.
Mathematically it can be stated as,

V ∝ n

Where,

V= volume of gas

n = number of moles

V= k n

Where k is the constant of proportionality.
The number of molecules in one mole is given by Avogadro’s constant, also known as Avogadro’s number

NA  6.023 × 1023.

Volume of one mole of gas can be calculated at STP (standard temperature and pressure) with the help of ideal gas equation,

Pressure at STP= 1025 Pa

Temperature at STP = 273.15K

$V\;=R\frac{nt}{p}$

$V=\frac{8.314*273.15}{10^{5}}$

$V=22.710981L$

Hence, according to Avogadro’s law, one mol of all gases at STP(standard temperature and pressure) will contain 22.710981 L of gas. Number of moles can be given in terms of molar mass as,

$n=\frac{m}{M}$

Where m = mass of gas under investigation

M = molar mass

$n=k\frac{m}{M}$

$m=\frac{m}{v}=d$

Where d is the density of the gas.

Form the above equation we can also deduce that density of a gas is directly proportioned to the molar mass of the gas. The above equation is useful in identification of a gas from the calculation of its molar mass. This law is useful while comparing same substance under two different conditions. For example: at constant temperature and pressure, if the volume and number of moles of gas changes from V1 to V2 and N1 to N2respectively. This can be expressed as,

$\frac{V_{1}}{N_{1}}=\frac{V_{2}}{N_{2}}$

Generally, only ideal gases are found to follow Avogadro’s law. However, real gases follow this law when forces of interaction between the gaseous molecules are practically negligible. This generally happens at very high temperature and low pressure.

#### Practise This Question

Which of the following sub atomic particle do you think will have no electrical charge and mass equal to the mass of hydrogen atom.