The Law of Avogadro

Avogadro’s Law and its working principle

At constant temperature and pressure, Avogadro’s law, also known as Avogadro’s principle or Avogadro’s hypothesis, asserts that the total number of atoms/molecules in a gas (i.e. the amount of gaseous substance) is directly proportional to the volume occupied by the gas.

 Because it links temperature, pressure, volume, and amount of substance for a particular gas, Avogadro’s law is strongly related to the ideal gas equation.

The Law of Avogadro

Avogadro’s law is named after Amedeo Carlo Avogadro, an Italian scientist who proposed that two distinct ideal gases occupying the same volume at a given (constant) temperature and pressure must contain an equal number of molecules.

Avogadro’s law can be represented using the following formula under constant pressure and temperature:

n Vn

k = V/n

Where V signifies the gas volume, n the amount of gaseous substance (typically represented in moles), and k is a constant. The following formula can be used to compute the increase in the volume occupied by the gas when the amount of gaseous substance is increased:

Derivation

The ideal gas equation, which can be stated as follows, can be used to obtain Avogadro’s law:

nRT = PV

Where,

The pressure exerted by the gas on the walls of its container is denoted by ‘P,’ and the volume occupied by the gas is denoted by ‘V.’

‘n’ denotes the volume of a gaseous material (number of moles of gas)

The universal gas constant is ‘R.’

The absolute temperature of the gas is denoted by the letter ‘T.’

The following equation can be found by rearranging the ideal gas equation.

(RT)/P = V/n

Because the temperature and pressure are kept constant, and the product/quotient of two or more constants is always a constant, the value of (RT)/P is a constant. Therefore:

k = V/n

As a result, the proportionality between a gas’s volume and the number of gaseous molecules is established.

a gas’s molar volume

According to Avogadro’s law, the volume-to-amount ratio of a gaseous substance is constant (at constant pressure and temperature). The following equation can be used to calculate the value of this constant (k):

(RT)/P = k

The value of T equates to 273.15 Kelvin and the value of P corresponds to 101.325 kilo Pascals under standard temperature and pressure circumstances. As a result, one mole of a gas occupies the following volume at STP:

1 mole of gas occupies 22.4 litres = (8.314 J.mol-1.K-1)*(273.15 K)/(101.325 kPa)

At STP, one mole of any gaseous substance takes up 22.4 litres of space.

Avogadro’s Law Examples

Avogadro’s law is well illustrated by the process of respiration. The rise in the molar quantity of air in the lungs is accompanied by an increase in the volume of the lungs when humans inhale (expansion of the lungs). Below is an illustration of the volume change caused by an increase in the number of gaseous molecules.

Avogadro’s Law in Action

The deflation of automotive tyres is another common application of Avogadro’s law. The number of moles of air present in the tyre reduces when air trapped inside the tyre escapes. The volume occupied by the gas decreases as a result, causing the tyre to lose its shape and deflate.

Limitations of Avogadro’s Law

Avogadro’s law provides only approximate relationships for real gases, although being entirely applicable to ideal gases. At low temperatures and high pressures, the deviation of real gases from ideal behaviour rises.

It’s worth noting that gases with low molecular weights (such as helium and hydrogen) obey Avogadro’s law more than heavier molecules.

Example 1 

1 An empty balloon filled with one mole of helium gas has a volume of 1.5 litres. What would the balloon’s volume be if 2.5 moles of helium gas were added to it? (Assume that the temperature and pressure do not change.)

Ans-:

Given,

The initial helium concentration (n1) = 1 mol

The balloon’s initial volume (V1) is 1.5 L.

Helium (n2) final quantity = 1 mol + 2.5 mol = 3.5 mol

V1/n1 = V2/n2 according to Avogadro’s law

As a result, the balloon’s final volume (V2) = (V1n2)/n1 = (1.5L*3.5mol)/1mol = 5.25 L.

When filled with 3.5 moles of helium gas, the balloon will have a volume of 5.25 litres.

Example 2

Due to a puncture, a tyre having 10 moles of air and occupying a volume of 40 L loses half of its volume. What would be the amount of air in a deflated tyre if the pressure and temperature remained constant?

Given,

The initial volume of air (n1) is equal to 10 mol.

The tyre’s initial volume (V1) is 40 L.

The tyre’s final volume (V2) is 20 L.

The final amount of air in the tyre (n2) = (V2n1)/V1 = 5 moles, according to Avogadro’s law.

There would be 5 moles of air in the deflated tyre.

Conclusion 

The modern statement is: Avogadro’s law states that, “equal volumes of all gases, at the same temperature and pressure, have the same number of molecules.” 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.He concluded that the only way to explain Gay-Lussac’s observation was that, under identical conditions of temperature and pressure, for all ideal gases, any given volume must contain the same number of molecules.