Graham's Law of Diffusion: Diffusion, Formula & Solved Examples

Graham’s law of diffusion states that the rate of diffusion of a gas or its effusion is inversely proportional to the square root of its molecular weight. The principle of the law of diffusion states that at any given temperature and pressure the rate of diffusion of any given gas is inversely proportional to the square root of its density.

• Diffusion is the process through which particles from one gas move to another.
• It is caused when the particles of a material are in low concentration and they move to areas with high area of concentration.
• An example of diffusion in the spreading of scent of perfume in the entire room when it’s sprayed in one part.
• Effusion is the process through which a gas escapes the container’s wall through a very small hole on the surface. 
• The rate of diffusion refers to the change in diffusing molecules over time.

Read More: Difference between Effusion and Diffusion

Key terms: Effusion, Square root, Temperature, Density, Pressure, Collision, temperature, Molecule, Law of Diffusion

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Rate of Diffusion

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Diffusion of a gas is the random motion of a particle involved in the net movement of the substance from the higher concentration area to the lower concentration area.

• Each of the particles inside the gas starts colliding with each other.
• The rate of diffusion of a gas is directly proportional to the square root of the density of a gas molecule.
• The density of a gas molecule is equal to the mass of a gas that is divided by the volume of the gas molecule.
• If the volume of the gas molecule is held constant one gas can be compared with another gas.

• Graham's Law of Diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of its molecular weight.

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Rate of Effusion

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The effusion of a gas is the process in which the air particles escape or leak through a hole whose diameter is considerably smaller than the mean free path of the molecules.

• In this process, all the particles and the molecules that reach the hole will pass through, as due to the collisions between the molecules in these places are negligible in number.
• The rate of effusion of a gas can be defined as the process by which particles of a material from the closed space start escaping with time.
• Suppose when we make an opening in the balloon, the gas present inside it starts escaping into the atmosphere and the balloon starts deflating from inside.
• This is called the effusion of a gas into the atmosphere.
• Hence, we can say that the rate of effusion of a gas is inversely proportional to the density of a gas and its molar mass.

Rate of Effusion ∝ 1/√density ∝ 1/√M

• Here M is the molar mass of a gas molecule.

Read More: Difference between Diffusion and Osmosis

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Graham's Law of Diffusion

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Graham's Law was first discovered by a scientist named Thomas Graham in the year 1848. He experimented with the effusion process of a gas and formulated an important aspect that the gas molecules are lighter in weight and will travel faster in air than the heavier gas molecule. This law is popularly known as Graham's law of Effusion.

According to Graham’s law of diffusion and effusion, the atoms and molecules with lower molecular mass will diffuse faster in air than the molecules and atoms that are heavier, at constant temperature and pressure of a gas. It states that the rate of effusion of a gas molecule is inversely proportional to the square root of the density of a gas or its molecular mass.

Graham's law of Diffusion Formula and Examples

Graham’s Law Formula = \({Rate_1 \over Rate_2} = {\sqrt {M2 \over M1}}\)

• Here, Rate 1 = rate of effusion of the first gas
• Rate 2 = rate of effusion of the second gas.
• M1 = Molar mass of first gas
• M2 = Molar mass of second gas.

It states that the rate of diffusion or effusion is inversely proportional to its molecular mass. Graham's law of diffusion, also known as Graham's law of effusion, states that the rate of diffusion or effusion of a gas is inversely proportional to the square root of its molecular weight. 

According to Graham's law, lighter gases diffuse or effuse quickly than heavier gases at the same temperature and pressure.

Applications of Graham’s law of diffusion

Graham's law has several applications such as –

• The separation of gases in industries such as petrochemicals, air separation, and natural gas processing.
• It is also used in fields such as atmospheric science, where it is used to understand the mixing of gases in the atmosphere.

Importance of Graham's law of diffusion

Graham's law of diffusion is important as:

• It provides a basis for separating gases of different molecular weights. So, the lighter gases can be separated from heavier gases using gas chromatography.
• Graham's law of diffusion helps to understand the mixing of gases in the atmosphere. It explains why lighter gases rise to the upper atmosphere while heavier gases remain closer to the surface.
• The law of diffusion is also used in chemical processes such as distillation.
• Graham's law of diffusion is a fundamental law of physics to understand the behavior of gases and how they interact with their environment.

Read More: Bulk Modulus

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Things to Remember

• Diffusion is a phenomenon in which gas moves from higher concentration to lower concentrations.
• In effusion, the gas moves from lower to higher concentrations.
• The diffusion of a gas leads to a significant disorder in the entire system of the gas. It acts at slower rates in liquid as well as solid gasses. 
• Graham's law of diffusion is used in determining the molecular masses and the vapor density of a gas molecule.
• Mathematically, Graham’s law can be expressed as Rate of diffusion/effusion ∝ 1/√(molecular weight)
• This is also used in separation of different gasses from the mixture of gasses and in separating the isotopes of same elements.

Read More: Young's Modulus

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