Diffusion of Gases: Introduction, Meaning, Graham’s Law

The smell of food greets us as we enter the kitchen. Similarly, if someone uses perfume, the aroma is carried around the room. This is due to the fact that the aroma of the meal or perfume mixes with the air. In this article, we will explore this process which is called diffusion of gases.

Before understanding the concept of diffusion of gases, let us see the meaning of diffusion in general.

What is Diffusion?

Diffusion is the movement of a substance from an area of high concentration to an area of low concentration. This process happens in gases and liquids faster than solids because their particles can move randomly.

The term diffusion comes from the Latin word diffundere, which means to spread out.

Increasing the temperature or pressure increases the rate of diffusion.

Diffusion of Gases

The gases possess a remarkable property of spreading in the entire space available to them and of intermixing together even against gravity.

For example, if a bottle of ammonia is opened at one corner of a room, its smell can be felt at the other corner.

Let us understand with the help of an example how two gases intermix together even against gravity.

Suppose we have two gas jars, one containing colourless hydrogen gas and the other containing reddish-brown \({\text{N}}{{\text{O}}_2}.\) The two gases intermix when the jar containing hydrogen is inverted over the jar containing \({\text{N}}{{\text{O}}_2}\) and the cover in between the two jars is removed, and both jars look reddish-brown after some time.

\({\text{N}}{{\text{O}}_2}\) is heavier than hydrogen, yet it travels upwards while the lighter hydrogen gas travels downwards.

Thus, the intermixing of two gases even against gravity occurs due to the rapid movement of gas molecules and the presence of intermolecular spaces in a gas. Due to high velocity, the molecules of one gas penetrate into the intermolecular space of the other when brought in contact with each other. The velocities of the molecules are so high that they overcome the gravitational forces and mix up together even against gravity. The diffusion may be thus defined as-

The spontaneous intermixing of two or more gases even against gravity is called diffusion.

Examples of Diffusion of Gases in Daily Life

Diffusion of gases allows spreading the smell of various things quickly-

1. The fragrance of perfume can be smelled from a distance.
2. The smell of the burning incense stick can be smelled from a distance.
3. The aroma of the food while being cooked.

Graham’s Law of Diffusion

Thomas Graham studied the diffusion of various gases and established a relationship between the rate of diffusion and the density of a gas. This relationship is known as Graham’s law of diffusion. This law can be stated as follows-

At constant temperature and pressure, the rate of diffusion of a gas is inversely proportional to the square root of its density.

Mathematically, at constant temperature and pressure-

\({\text{r}} \propto \frac{1}{{\sqrt {\text{d}} }}\)

where \({\text{d}}\) is the density of the gas and \({\text{r}}\) is the rate of diffusion.

If \({{\text{r}}_1}\) and \({{\text{r}}_2}\) are the rates of diffusion of two gases at the same temperature and pressure, and \({{\text{d}}_1},{{\text{d}}_2}\) are their densities respectively, then according to this law-

\({{\text{r}}_1} \propto \frac{1}{{\sqrt {{{\text{d}}_1}} }}\)
\({{\text{r}}_2} \propto \frac{1}{{\sqrt {{{\text{d}}_2}} }}\)
\(\therefore \frac{{{{\text{r}}_1}}}{{{{\text{r}}_2}}} = \sqrt {\frac{{{{\text{d}}_2}}}{{{{\text{d}}_1}}}} \)

Since molecular mass of a gas is twice its vapour density i.e., \({\text{M}} = 2 \times {\text{d}},\) we have-

\(\frac{{{{\text{r}}_1}}}{{{{\text{r}}_2}}} = \sqrt {\frac{{{{\text{d}}_2}}}{{{{\text{d}}_1}}}} = \sqrt {\frac{{{{\text{M}}_2}}}{{{{\text{M}}_1}}}} \)

Where \({{\text{M}}_1}\) and \({{\text{M}}_1}\) are respectively the molecular masses of two gases under consideration. Thus, Graham’s law can also be stated as-

At constant temperature and pressure, the rate of diffusion of a gas is inversely proportional to the square root of its molecular mass.

The rate of diffusion of a gas is defined as the ratio of the volume of the gas diffused to the time taken in diffusion, i.e.,

\({\text{r}} = \frac{{\text{V}}}{{\text{t}}}\)

where \({\text{V}}\) is the volume of the gas diffused and \({\text{r}}\) is the time taken for diffusion. If \({{\text{V}}_1}\) and \({{\text{V}}_2}\) are the volume of two gases that undergo diffusion in time \({{\text{t}}_1}\) and \({{\text{t}}_2}\) respectively then we have-

\({{\text{r}}_1} = \frac{{{{\text{V}}_1}}}{{{{\text{t}}_1}}}\)
\({{\text{r}}_2} = \frac{{{{\text{V}}_2}}}{{{{\text{t}}_2}}}\)
\(\therefore \frac{{{{\text{r}}_1}}}{{{{\text{r}}_2}}} = \frac{{{{\text{V}}_1}/{{\text{t}}_1}}}{{~{{\text{V}}_2}/{{\text{t}}_2}}} = \sqrt {\frac{{{{\text{d}}_2}}}{{~{{\text{d}}_1}}}} = \sqrt {\frac{{{{\text{M}}_2}}}{{{{\text{M}}_1}}}} \)

If \({{\text{V}}_1} = {{\text{V}}_2},\) we have-

\(\frac{{{{\text{t}}_2}}}{{{{\text{t}}_1}}} = \sqrt {\frac{{{{\text{d}}_2}}}{{~{{\text{d}}_1}}}} = \sqrt {\frac{{{{\text{M}}_2}}}{{{{\text{M}}_1}}}} \)

Similarly, if \({{\text{t}}_1} = {{\text{t}}_2},\) then-

\(\frac{{{{\text{V}}_1}}}{{~{{\text{V}}_2}}} = \sqrt {\frac{{{{\text{d}}_2}}}{{~{{\text{d}}_1}}}} = \sqrt {\frac{{{{\text{M}}_2}}}{{{{\text{M}}_1}}}} \)

Effusion

It is a particular case of diffusion. When gas is allowed to escape through a fine orifice or a pinhole, the phenomenon is termed effusion.

Applications of Gaseous Diffusion

Diffusion is a remarkable property of gases and finds several applications, which are as follows-

i) Separation of the constituents of a gaseous mixture

The rate of diffusion of a gas depends upon its density. If the constituents of a gaseous mixture have different densities, their rates of diffusion will be different, and this property can be utilised for their separation. If a mixture of two gases is subjected to diffusion, the gas with a higher density will diffuse less as compared to the lighter gas. Hence, the diffused mixture will be richer in the lighter gas. Thus by repeating the process, the two gases can be separated almost completely. This process of separation of gases is known as fractional diffusion and has been utilised in the separation of isotopes present as a gaseous mixture.

ii) Determination of molecular masses and densities

According to Graham’s law of diffusion,

\(\frac{{{{\text{r}}_1}}}{{{{\text{r}}_2}}} = \sqrt {\frac{{{{\text{d}}_2}}}{{{{\text{d}}_1}}}} = \sqrt {\frac{{{{\text{M}}_2}}}{{{{\text{M}}_1}}}} \)

Thus, by comparing the rate of diffusion of an unknown gas with that of a gas known density or known molecular mass, the density or molecular mass of the unknown gas can be determined with the above equation.

iii) Dispersal of poisonous and foul-smelling gases

Diffusion serves as a natural process for the dispersal of foul-smelling and poisonous gases into the atmospheric air. This dilutes their bad effects on our environment. It is because of this property that atmospheric air always remains homogeneous.

Diffusion of Gases in Liquids

This can be understood with the help of an example-

Gases like carbon dioxide and oxygen are essential for the survival of aquatic life.  The oxygen and carbon dioxide present in the air diffuse into the water and dissolve in it. Thus, aquatic plants use dissolved carbon dioxide for preparing their food by photosynthesis, and aquatic animals use dissolved oxygen for respiration.

Summary

In this article, we studied that particles move from a higher concentration to a lower concentration. We studied in detail the Diffusion of gases and the various factors that can affect the rate of diffusion of the gas. Now we also know the applications of diffusion of gas and how the process of diffusion of gases in liquids is helpful.

FAQs

Q.1. What is an example of gas diffusion?
Ans: The burning of incense sticks is an example of the diffusion of a gas. We can smell the burning incense stick because it diffuses in the air and makes its way to our noses.

Q.2. What is the diffusion of gas?
Ans: The spontaneous intermixing of two or more gases even against gravity is called diffusion.

Q.3. Can diffusion happen in gases?
Ans: Yes, diffusion occurs in gas and liquids due to the random movement of their particles and the intermolecular space available.

Q.4. What are the three types of diffusion?
Ans: The three types of diffusion are as follows-
(i) Simple diffusion
(ii) Osmosis
(iii) Facilitated diffusion

Q.5. What tissue is specialized for the rapid diffusion of gases?
Ans: Simple squamous epithelia tissue, which is present as the lining of alveoli, the lining of blood vessels is a specialised tissue that allows diffusion.

Q.6. What factors affect the rate of diffusion of gases?
Ans: Several factors affect the rate of diffusion. Some of the factors are-
Mass of the gases
The density of the gases
Concentration gradient
Temperature

We hope this detailed article on the diffusion of gases will be helpful to you. If you have any questions regarding the article or, in general, about the diffusion of gases, please ping us through the comments section, and we will get back to you as soon as possible.