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Avogadro’s Law

Avogadro’s Law describes the link between the volume of a gas and the number of molecules it contains. It was created in 1811 by an Italian physicist named Amedeo Carlo Avogadro. He discovered that equal amounts of different gases have an equal number of particles through a series of studies. 

In other words, Avogadro’s number law asserts that the volume of an ideal gas is precisely proportional to the number of moles it contains if the temperature and pressure are kept constant. It means that the number of moles also grows when the volume increases. Similarly, when volume decreases, the number of moles decreases as well. 

The law is also known as Avogadro’s number law, Avogadro’s hypothesis, and Avogadro’s principle. It is only valid for ideal gases and offers a rough estimate for actual gases. Compared to gases with heavy molecules, gases with light molecules, such as helium and hydrogen, obey Avogadro’s Law more precisely.

At constant temperature and pressure, Avogadro’s number law asserts the total number of atoms/molecules in a gas (i.e., the amount of gaseous material) is directly proportional to the volume occupied by the gas.

Avogadro’s Law is strongly connected to the ideal gas equation because it relates temperature, pressure, volume, and amount of material for a particular gas.

Avogadro’s Law and Its Consequences

The fact that the law is correct has a few significant repercussions:

  • At 0 °C and 1 atmosphere of pressure, the molar volume of all ideal gases is 22.4 litres.
  • When gas pressure and temperature remain constant, the volume increases as the number of gas molecules increases.
  • When gas pressure and temperature remain constant, the volume falls as the number of gas moles drops.
  • Every time you blow up a balloon, you demonstrate the Avogadro constant.

Avogadro’s Law Formula

You may represent Avogadro’s number law using the following formula under constant pressure and temperature:

V ∝ n

V/n = k

Where V signifies the gas volume, n is the gaseous material (typically represented in moles), and k is a constant. 

You may use the following formula to compute the increase in the volume occupied by the gas when the quantity of gaseous material increases.

V1/n1 = V2/n2 ( = k, as per Avogadro’s number law).

Derivation of Avogadro’s Law

The ideal gas equation, represented as below, is the source of Avogadro’s number law:

PV = nRT 

P denotes the pressure exerted by a gas on the container wall.

V indicates the volume occupied by the gas.

n refers to the entire amount of gaseous material or the number of moles of the gas.

R stands for the universal gas constant.

T is the gas’ absolute temperature.

Therefore,

V/N = (RT)/P 

after rearranging the ideal gas equation, where (RT)/P is constant since the temperature and pressure are maintained constant, and the product of two or more constants is a constant. 

Hence, 

V/N = k.

Molar Volume of a Gas

According to Avogadro constant, the volume and quantity of gaseous material are constant under constant pressure and temperature. k represents this constant.

k = (RT)/P determines this constant.

T = 273.15 K and P = 101.325 kilopascals at normal temperature and pressure

As a result, at STP, the volume of one-mole gas is 

(8.314 J.mol-1.K-1) (273.15K)/(101.325kPa) = 22.4 litres.

As a result, at STP, one mole of any gas takes up 22.4 litres of volume. [STP = Standard temperature and pressure]

Examples of Avogadro’s Law

  1. The process of breathing well illustrates Avogadro’s Law. An increase in the lung’s volume when humans inhale (expansion of the lungs) accompanies the rise in the molar quantity of the air in the lungs.
  2. The deflation of automotive tyres is another use of Avogadro’s rule. The number of moles of air in the tyre reduces when air trapped inside the tyre exits. The volume filled by the gas decreases. As a result, it was causing the tyre to lose its shape and deflate.
  3. The action of a bicycle pump illustrates Avogadro’s number law. The pump draws air from the surrounding environment and forces it into a deflated item. As the amount of gas molecules increases, the object’s form channels. Avogadro’s number law describes the relationship between the number of air molecules and the volume.
  4. A soccer ball has a bladder and a stiff outer shell. When the ball deflates, the bladder loses its form and becomes deflated. It causes the ball to lose its capacity to bounce. By forcing air into the bladder with an air pump, you may raise the volume of air inside the bladder. The number of air molecules in a given volume of air is proportional to the number of air molecules in that volume. As a result, pumping air into a soccer ball is a clear example of Avogadro’s Law in action.

Solved Examples on Avogadro’s Law

Example 1

An empty balloon filled with one mole of helium gas has a capacity of 3.0 litres. (Assume that the temperature and pressure do not change.) what would the balloon’s volume be if you added 5.0 moles of helium gas to it?

Given,

The initial helium concentration (n1) = 1 mol

The balloon’s initial volume (V1) is 3.0 L.

Helium (n2) final quantity = 1 mol + 5.0 mol = 6.0 mol

V1/n1 = V2/n2 , according to value of avogadro number

As a result, the balloon’s ultimate volume (V2) = (V1n2)/n1 = (3.0L*6.0mol)/1mol = 18.0 L.

When filled with 6.0 moles of helium gas, the balloon will have a capacity of 18.0 litres.

Example 2

Due to a puncture, a tyre having 20 moles of air and occupying a volume of 80L loses half of its volume. What would be the quantity of air in a deflated tyre if the pressure and temperature remain constant?

Given,

The initial volume of air (n1) is equal to 20 mol.

The tyre’s initial volume (V1) is 80 L.

The tyre’s ultimate volume (V2) is 40 L.

According to Avogadro’s Law, the ultimate quantity of air in the tyre (n2) = (V2n1)/V1 = 10 moles.

There would be 10 moles of air in the deflated tyre.

Conclusion

Avogadro’s Law only offers relationships for actual gases, even though it is entirely applicable to all ideal gases. At more significant pressures and lower temperatures, the divergence of actual gases from ideal behaviour tends to rise. Compared to heavier molecules, gaseous molecules with smaller molecular weights, such as hydrogen and helium, follow the value of the Avogadro number to a large extent.