Theory of Gases: Laws of Gases

Introduction

Gases have widely-spaced individual particles. They behave differently under different conditions. The laws of gas were developed in the late 1800s. Scientists got to know about the relationship between the volume, pressure, and temperature of a gas sample. Gas laws govern the physical properties of all gases. All gases show similar behaviour under normal conditions. These laws analyse the behaviour of gases under different conditions. They show the relationships between the changing temperature, pressure, and volume. 

Definition of Laws of Gases

There are some gas laws, depending on the different variables. These laws are mainly defined based on properties such as pressure, volume, etc., as a function of temperature. Boyle’s law, Charle’s law, Gay-Lussac’s law, and Avogadro’s law are some of them.

Boyle’s Law

Boyle’s law establishes the relationship between volume and pressure under constant temperature and mass. 

Boyle’s Law states that at a constant temperature, the volume of a given mass of a gas is inversely proportional to the pressure, that is,

V ∝ 1/P or PV= constant, k.

Here ‘V’ is the volume of the gas, ‘P’ is the pressure, and k is the constant.

In such a condition, the greater the pressure, the less the volume, and vice-versa. 

Therefore, under all circumstances, the product of the volume multiplied by the pressure remains constant. 

Boyle’s law applies to all gases regardless of their chemical properties. Therefore, we can write as below for a given mass of gas under two different sets of conditions at a constant temperature:

P1V1 = P2V2 = K

The pressure of a gas at a constant temperature increases by reducing its volume because gas molecules travel less distance between collisions at the walls due to the reduced volume. Therefore, the more the collisions, the more the pressure.

This is an isothermal process as the temperature remains the same.

Charles’s Law

Charles’s Law, or Law of Volume, states that at constant pressure, the volume of a given mass of a gas is directly proportional to its absolute temperature. 

That is, at constant pressure: 

V ∝ T or V/T= constant, k

Charles’s Law defines how the temperature and volume of a gas vary when the pressure remains constant.

With the increase in temperature, the volume increases, while with decreasing temperature, the volume decreases.

Jacques Charles calculated that the increase in volume with every degree equals 1/273.15 times the original volume.

The equation under constant pressure can be written as:  

V1/T1=V2/T2 = Constant

This is an isobaric process, as the pressure is constant with volume, and temperature changes accordingly.

Hence, Charle’s law establishes that the ratio of temperature to volume is constant.

Gay-Lussac’s Law

As per Gay-Lussac’s Law, or the Pressure Law, the pressure P of a provided mass of a gas is directly proportional to its absolute temperature T, given the volume V of the gas is kept constant.

That is,  P∝ T or P/T= a constant

Also, P1/T1= P2/T2

In other words, the ratio of pressure to temperature is constant.

Absolute temperature is the temperature measured from absolute zero on the Kelvin scale.

If the temperature is measured relative to absolute zero, the temperature is an absolute temperature; absolute zero is 0. 

So, according to Gay-Lussac’s law, gas at 0 °C (32 °F) is reduced by about 1/273 of its volume for every Celsius degree drop in temperature. 

This is an isochoric process, as the volume remains constant.

Avogadro’s Law

According to this law, under constant unchanged conditions of temperature and pressure, the volume of any gas is directly proportional to the number of molecules of that gas.

This law establishes the connection between gas volume and the number of moles. 

It can also be stated that equal amounts of all gases under standard temperature and pressure contain the same number of 6.023 x 1023 molecules.

1 mole of any gas at NTP occupies a volume of 22.4L.

Avogadro demonstrated this law by combining Dalton’s Atomic Theory and Gay-Lussac’s Law.

This law helps determine the relationship between the amount of gas (N) and the volume.

Let us now look at some application of these laws:

Graham’s Law

According to Graham’s law of diffusion of gases, the rate of diffusion of a gas is inversely proportional to the square root of its molecular mass.

That means, Rate of diffusion ∝ 1/sqrt(M).

M=molecular mass of gas

The gas diffusion rate is inversely proportional to its density vapour pressure or molecular weight square root.

The more the density of the gas, the more is the rate of diffusion.

Dalton’s Law of Partial Pressures

Dalton’s law of partial pressure is like an ideal gas law. 

It states that the total pressure of a mixture of gases equals the sum of the partial pressures of each gas.

It states that the total pressure exerted by the mixture of non-reactive gases equals the sum of the partial pressures of individual gases. 

This shows that, 

Ptotal= pa+pb+pc+……(at constant T, V).

Where pA, pb, Pc……….. = Partial pressures of gases.

Conclusion

The above laws of gas show us the relationship between various properties of gases at changed conditions of temperature, pressure, volume, and mass. These laws are applicable in our daily lives. 

For example:During the breathing process our lungs expand while inhaling and contract while exhaling.

Moreover,the application of these gas laws are also important for understanding future topics.