Gas Laws for Ideal Gas

If the gases are assumed to be ideal in nature, the following gas laws are applicable to them. The laws are defined to understand the ideal gases and their parameters like volume, pressure, etc. Let’s take a look at the laws,

Boyle’s Law

According to Boyle’s law, the volume of a given gas is inversely proportional to its pressure at a constant temperature. As this law is given by Robert A. Boyle in 1662, hence the name Boyle’s Law.

V ∝ 1/P

PV = Constant

For a given ideal gas,

P₁V₁ = P₂V₂

 

Charles’s Law

Charles’s law (named after Jacques Charles) states that at constant pressure, the volume of a gas is directly proportional to the absolute temperature of the gas. 

V ∝ T

V/T = Constant

Thus, for any given ideal gas,

V₁T₂ = V₂T₁

Pressure Law (Gay-Lussac’s Law)

Pressure Law or Gay-Lussac’s laws state that at constant volume, the pressure of a given gas is directly proportional to its absolute temperature. This law is named after Joseph-Louis Gay-Lussac who published this law in 1809.

P ∝ T

P/T = Constant

For any ideal gas,

P₁T₂ = P₂T₁

Avogadro’s Law

Avogadro’s Law or Avogadro-Ampere’s hypothesis states that an equal amount of volume of all gases under S.T.P. (Standard temperature and pressure) contain the same number of molecules i.e., one mole of any ideal gas at STP always has a volume of 22.4 liters.

V ∝  n

V/n = Constant

For any ideal gas,

V₁n₂ = V₂n₁

Graham’s Law of Diffusion of Gases

According to Graham’s law of diffusion of gases, the rate of diffusion of a gas is inversely proportional to the square root of the density of the gas. Therefore, the more the density of the gases slower will be its rate of diffusion.

r ∝ √(1/p)

Dalton’s Law of Partial Gases

According to this law, the net pressure applied by a mix of non-interacting gas is equivalent to the sum of the individual pressures.

P = P₁ + P₂ + P₃ +… P_n

The arithmetic mean of the speed of gas molecules is known as the average speed of molecules or the mean speed of the gas molecules. If there are  and are given by

Mean speed = v_mean = (v₁ + v₂ + v₃ +… v_n)/n

Formula for mean speed, v_mean = 

Similarly, there is another term known as the root mean square speed of gas molecules, it is defined as the root mean of the squares of speeds of gas molecules. The formula for the root mean speed is given as follows:

v_rms = √(3RT/M)

Similarly, there is a term known as the most probable speed of a gas molecule, which is defined as the speed obtained by the maximum number of gas molecules, and formula for the most probable speed is given as follows:

v_mp = √(2RT/M)

Kinetic Interpretation of Temperature

The overall average energy present in the molecules is directly proportional to the temperature. Therefore, average kinetic energy is formed by the measure of the average temperature of the gas. According to this, the average energy of the molecules is 0 when the temperature is 0. Therefore, the motion of the molecules stops at absolute 0. The formula for the average energy of the molecules is given as,

U = 3/2 RT

Kinetic Theory of Gases is a theoretical model which helps us understand the behavior of gases and their constituent particles. This theory suggests that gas is made up of a larger number of tiny particles which collide with each other and their surroundings and exchange kinetic energy between them. The kinetic theory of gases has various applications throughout physics, chemistry, and engineering and it is essential to understand many phenomena like diffusion, effusion, and Brownian motion.

In this article, we will learn about the assumptions of kinetic theory, its limitations, and others in detail.