# Grahams law of diffusion

### Graham’s Law of Diffusion:

Let's begin with this instance; when a perfume is sprayed in a room, the particles of the perfume will move from a region of higher concentration (region where the perfume was sprayed) to a region of lower concentration (other regions in the room where the perfume wasn’t sprayed). As a result, anyone present in this region of lower concentration will also perceive the scent of the perfume.

This movement of particles from a region of higher concentration to a region of lower concentration is known as diffusion.

The particles undergoing diffusion can be gaseous, liquid or solid. Diffusion is fastest in gaseous particles (because gaseous particles are able to freely move since the cohesive or binding forces between these particles are extremely small or negligible. Read our article on particles of matter HERE).

Note: Diffusion can also occur in liquid particles and solid particles but it is slowest in solid particles. Diffusion always involves the movement of particles from a region of higher concentration to the region of lower concentration. Effusion is the movement of gaseous particles through a very small opening and is always accompained by diffusion. For instance when an inflated balloon is pierced with a needle, both effusion and diffusion will occur.

When diffusion occurs, it continues until equilibrium is attained. This will imply that; from our previous instance, the scent of the perfume will continue to move from the region of higher concentration to the region of lower concentration until every part of the room is equally filled with its gaseous mixture (assuming all external openings have been shut).

Note: When a gas has a high rate of diffusion, it will take a shorter time for diffusion to occur in such gas. Diffusion will take a longer time for gases with lower rate of diffusion.

The Scottish chemist Thomas Graham (1805-1869) studied the rate at which gases diffuse. A law of diffusion (called Graham’s law of diffusion was established).

Graham’s law of diffusion states that the rate (r) of diffusion in a gas at a given temperature is inversely proportional to the square root of its density or molecular mass (m).

Image Credit: 3.bp.blogspot

Also Note that "The vapour density (v.d.) of a gas is equal to half its relative molecular mass(r.m.m.)".
⦁    Therefore...    r.m.m. = 2 x v. d.

#### Worked Example

30cm3 of a gas with an empirical formula of CH3 diffuses through a porous partition in 45.2s. If 30 cm3 of hydrogen diffused in 11.7s under the same conditions. Calculate

1. The vapour density of the CH3 gas
2. The molecular formula of the gas CH3?

(Mass of H2 = 2)

Solution:

(i)

tx/tH = √mx /√mH
t = time, m = molar mass , x = CH3  and H = hydrogen
Time taken for CH3 to diffuse = 45.2s
Time taken for H2  to diffuse = 11.7s
Mass of H2 = 2
Mass of CH3 = ?
Substituting these values into the above formula
45.2/11.7 = √(mx/2)
2(45.2/11.7)2 = mx
mx = 2 x 14.92
mx   = 29.84g
Mass of CH3 = 29.84g
r.m.m. = 2 x v.d.
v.d. = r.m.m./2
v.d. = 29.84/2
v.d = 14.92

(ii)
xCH3 = 30
15x = 30
x = 2
Therefore, molecular formula = C2H6 which is Ethane

### Usefulness of Graham's law:

• To separate gases with different densities.
• To separate certain elements with the same atomic number but different mass number (Isotopes).
• To determine the densities and molecular masses of unknown gases by comparing their rates of diffusion with known gases.