Graham's Law

Graham's law establishes that the rates of diffusion and effusion of gases are inversely proportional to the square roots of their respective molar masses.

Etymology

Graham's law was formulated in 1829 by British chemist Thomas Graham.

Symbols

Symbolology

Symbol	Name	Unit
M{displaystyle M}	Molar masses	kg / mol
m{displaystyle m}	Masa	kg
u{displaystyle u}	Rapidez	m/s

Description

Deduction

	1
Equations	12m1(u1)2=12m2(u2)2{displaystyle {frac {1}{2}}m_{1}(u_{1})^{2}={frac {1}{2}}m_{2}(u_{2}){2}}}}{2}}}}
Simplifying	m1(u1)2=m2(u2)2{displaystyle m_{1}(u_{1})^{2}=m_{2}(u_{2})^{2}}}
Clearing	u1u2=m2m1{displaystyle {frac {u_{1}}{u_{2}}}}}{{sqrt {frac {m_{2}}{m_{1}}}}}}}}}}}}}}
Replacement	u1u2=M2M1{displaystyle {frac {u_{1}}{u_{2}}}}}{{sqrt {frac {M_{2}}{M_{1}}}}}}}}}}}}}

u1u2=M2M1{displaystyle {frac {u_{1}}{u_{2}}}}}{{sqrt {frac {M_{2}}{M_{1}}}}}}}}}}}}}

Effusion is the flow of gas particles through narrow holes or pores.

Use is made of this principle in the effusion method of isotope separation.

The phenomenon of effusion is related to the kinetic energy of the molecules. Thanks to their constant motion, the particles of a substance are evenly distributed in free space. If there is a greater agglomeration of particles at a point, there will be more collisions with each other, which will cause them to move towards the regions with fewer numbers: substances diffuse from a region of greater agglomeration to a region of lesser agglomeration.

Speed of diffusion of gases.

Of the 4 states of matter, gases present the greatest ease of diffusion of their respective particles, as occurs in air, since their molecules have higher speeds. Molecules of different gases have different speeds, at different temperatures, depending only on pressure...

Graham's law of diffusion.

Diffusion is the process by which a substance is distributed uniformly in the space that encloses it or in the medium in which it is found. For example: if two tanks containing the same gas at different pressures are connected, in a short time the pressure is the same in both tanks. Also if a small amount of gas A is introduced into one end of a closed tank containing another gas B, the gas A will quickly spread evenly throughout the tank.

Diffusion is a consequence of the continuous and elastic movement of gaseous molecules. Different gases have different rates of diffusion. To obtain quantitative information on diffusion rates, many determinations have been made. In one technique the gas is allowed to pass through small holes into a totally empty space; the distribution under these conditions is called effusion and the speed of the molecules is the same as in diffusion. The results are expressed by Graham's law. "The rate of diffusion of a gas is inversely proportional to the square root of its density."

Whereu1{displaystyle u_{1}}) and (u2{displaystyle u_{2}}) are the rate of diffusion of the gases that are compared and (ρ ρ 1{displaystyle rho _{1}}) and (ρ ρ 2{displaystyle rho _{2}}) are the densities. Densities can be related to mass and volume because (ρ ρ =m/V{displaystyle rho =m/V}when (M{displaystyle M}) be equal to the molecular mass (weight) and (V{displaystyle V}) to the molecular volume, the following relationship can be established between the rate of diffusion of two gases and their molecular weight:

and as the molecular volumes of gases in equal temperature and pressure conditions are identical, that is (V1=V2{displaystyle V_{1}=V_{2}}}), in the previous equation its square roots are canceled, remaining:

That is: the rate of diffusion of a gas is inversely proportional to the square root of its molecular weight.

Example 1

Which gas has the faster diffusion rate, neon or nitrogen?

• Response

First you need to know the densities of the gases involved. Since a mole of gas occupies 22.4 L at T.P.E., their densities will be (molecular weight/volume).

• neon = 20.18/22.4 = 0.9 g/l
• nitrogen (in normal conditions it forms a diatronomic gas) = 28.01/22.4 = 1.25 g/l
• be v1 = nitrogen and v2 diffusion speed = neon diffusion rate.

Because the speed of diffusion is inversely proportional to the densities, the less dense one will have a greater speed of diffusion.

Example 2

What is the diffusion rate of oxygen relative to hydrogen?

If the molar mass of oxygen is 32 and that of hydrogen is 2 (diatomic gases):

uH2uO2=322=41{displaystyle {frac {u_{rm {H_{2}}}}}{u_{rm {O_{2}}}}}}}}}{frac {sqrt {32}}{sqrt {2}}}}{{{{sqrt {2}}}}}}}{{{s}}}{s}}{

The diffusion rate of hydrogen is 4 times that of oxygen.