## What is Avogadro’s law?

Avogadro’s law statement – Under constant temperature and pressure, the relationship between the volume of gas and the number of moles is direct. This law is also known as Avogadro’s Principle or Avogadro’s hypothesis. This hypothesis was first published by Amadeo Avogadro in the year 1811.

### Avogadro’s law with a modern definition is stated as follows

For a specific mass of an ideal gas, the volume and number of moles of the gas are directly proportional, at constant pressure and temperature.

## Avogadro’s law formula

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 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

N_{A }= 6.023 × 10^{23}.

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= 10^{25} Pa

Temperature at STP = 273.15K

V=R(nt/T)

⇒V=8.314*273.15*10^{-5}

⇒V=22.710981 L

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=m/M

Where **m** = mass of gas under investigation

**M** = molar mass

By Avogadro’s law,

n = km/M

m = m/v = d

Where d is the density of the gas.

Form the above equation we can also deduce that the density of a gas is directly proportioned to the molar mass of the gas. The above equation is useful in the identification of a gas from the calculation of its molar mass. This law is useful while comparing the same substance under two different conditions. For example: at constant temperature and pressure, if the volume and number of moles of gas changes from V_{1} to V_{2} and N_{1} to N_{2}respectively. This can be expressed as,

V_{1}/n_{1}=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.

### Solved example:

**1.** A 6 lt sample consists of 0.5 moles of gas at a temperature of 25°C and pressure of 2 atm. Calculate the final volume if we add 0.25 moles of gas at the same temperature and same pressure.

**Sol: **Consider Avogadro’s law – V_{1}/n_{1}=V_{2}/n_{2}

Given date:

V_{1} = 6 lt

n_{1 }= 0.5 mol

n_{2 }= 0.5 + 0.25 = 0.75 mol

V_{2} = ?

To find the value of V_{2}:

Consider the equation:

V_{2} = V_{1} *(n_{1}/n_{2})

Insert the values of V_{1}, n_{1}, n_{2}

V_{2} = 6 * (0.75/0.5)

V_{2} = 9.0 lt

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