Question

State and explain Gay-Lussac’s law.

Answer 1

Hint: The Gay-Lussac’s law gives us a relation between the pressure and temperature of a gas at constant volume.
It also gives us the relation between the volumes of reactants used and the products obtained when two gases react.

Complete step by step solution:
Gay-Lussac’s law states that- “The pressure of a given mass of gas varied directly with the absolute temperature of the gas when the volume is kept constant.”
Mathematically, this law is given as- $\dfrac{P}{T}=k$
When we increase the temperature of a sample of gas in a fixed, rigid container the pressure of the gas increases too. This is due to the fact that an increase in temperature causes an increase in kinetic energy of the gas. Thus, the gas molecules strike the wall of the container with a higher force and result in increased pressure.
A graph of pressure-temperature helps us get a direct relationship on the cooling of a gas and the pressure. When we cool gas at a constant volume, the pressure is decreased till the gas condenses into a liquid.
Gay-Lussac’s law also gives us the law of combining volumes-
According to this law, when two gases react with each other to give us a new gas as a product, the volume of the reacting gas as well as the products bear a simple whole-number ratio. The condition is that the volume of both is measured under similar temperature and pressure conditions.
\[2{{H}_{2}}+{{O}_{2}}\to 2{{H}_{2}}O\]
2 volumes of hydrogen react with one volume of oxygen to give us two volumes of gaseous water.

Note: The Charles law and Gay-Lussac’s law are very similar. The only difference in them is the type of container. In Charles law, the container is flexible whereas in Gay-Lussac’s law the container is rigid. Also, the mathematical representation of both laws is similar-
\[\dfrac{{{P}_{1}}}{{{T}_{1}}}=\dfrac{{{P}_{2}}}{{{T}_{2}}}\]