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Avogadro’s law is a gas law and is also referred to as Avogadro’s hypothesis or Avogadro’s principle. It states that the total number of molecules or atoms of a gas is directly proportional to the volume that the gas occupies at a constant temperature and pressure. This law is much related to the ideal equation of the gas because it links the temperature, volume, pressure and the amount of substance for a gas.

This law is named after Amedeo Carlo Avogadro, an Italian scientist, who had suggested that two different gases that occupy the same amount of volume at constant pressure and temperature must have equal numbers of atoms or molecules.

At constant pressure and temperature, the Avogadro’s law is expressed as follows:

V ∝ n

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

Here, V is the volume of the gas

n is the amount of gaseous substance expressed in moles, and

k is constant

When the amount of the gaseous substance is allowed to increase, the increase in the volume that is occupied by the gas is calculated as follows:

$\frac{V_1}{n_1}$ = $\frac{V_2}{n_2}$ = k , according to Avogadro’s law

It is graphically represented as follows.

Here, the straight line that indicates that both the quantities are directly proportional tends to pass through the origin, which implies that zero moles of gas occupy zero volume.

Avogadro’s law is derived from the ideal gas equation, which is expressed as follows:

PV = nRT

Where in,

P refers to the pressure exerted by a gas on its container wall

V refers to the volume occupied by gas

n is the total amount of gaseous substance or number of moles of the gas

R refers to the universal gas constant, and

T refers to the absolute temperature of the gas

After rearranging the ideal gas equation,

$\frac{V}{n}$ = $\frac{(RT)}{P}$  in which,

the value of $\frac{(RT)}{P}$ is constant because the temperature and pressure are kept constant and the product of two or more constants is a constant. Hence,

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

### Molar Volume of a Gas

According to Avogadro’s law, the ratio of the volume and amount of gaseous substance is constant at constant pressure and temperature and is denoted by k. This constant is determined by

k = $\frac{(RT)}{P}$

Under standard temperature and pressure,

T = 273.15 K and P = 101.325 kiloPascals

Hence, the volume of one-mole gas at STP is,

$\frac{(8.314 J.mol-1.K-1)(273.15 K)}{(101.325 kPa)}$ = 22.4 litres

Hence, one mole of any gas occupies 22.4 litres volume at STP.

The respiration process is an example of Avogadro’s law. When we inhale, there is an increase in the molar quantity of the air in our lungs. This leads to an increase in the lungs volume. Take a look at the image below.

Even though it is perfectly applicable to all the ideal gases, Avogadro’s law only provides the relationships for the real gases. The deviation of the real gases from the ideal behaviour tends to increase at higher pressures and lower temperatures. Gaseous molecules that have lower molecular masses like hydrogen and helium follow Avogadro’s law to a good extent when compared to the heavier molecules.

### Solved Example on Avogadro’s Law

Example 1: A tyre that consists of 10 moles air and occupies 40L volume loses half of the volume because of a puncture. What is the amount of air left in the deflated tyre at STP?

Solution:

Initial amount of air  n1 is 10 mol

Initial volume of tyre V1 is 40 L

Final volume of tyre V2 is 20 L

the amount of air left in the deflated tyre,

n2 = $\frac{V_{2}n_{1}}{V_1}$  = 5 moles

Hence, the deflated tyre contains 5 moles air