Grahams Law of Diffusion (Molar Mass)

The Graham's Law of Diffusion (Molar Mass) calculator computes the molar mass (2₂) of a gas based on the effusion rate of the first gas (r₁), the molar mass of the first gas (m₁) and the effusion rate the second gas (m₂).

INSTRUCTIONS: Choose units and enter the following:

• (m₁) This is the molar mass of gas 1.
• (r₁) This is the effusion rate of gas 1.
• (r₂) This is the effusion rate of gas 2.

Molar Mass(m₂):  The calculator returns the molar mass in grams per mole.  However this can be automatically converted to compatible units via the pull-down menu.

Related Calculators

• Compute the effusion rate of a gas based on Graham's Law of Diffusion

The Math / Science

Graham's law of effusion (also called Graham's law of diffusion) was formulated by Scottish physical chemist Thomas Graham in 1848. Graham found experimentally that the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles. This formula can be written as:

`\frac{Rate_1}{Rate_2} = \sqrt(\frac{M1}{M2}`

where:

• Rate1 is the rate of effusion of the first gas (volume or number of moles per unit time).
• Rate2 is the rate of effusion for the second gas.
• M1 is the molar mass of gas 1
• M2 is the molar mass of gas 2.

Graham's law states that the rate of diffusion or of effusion of a gas is inversely proportional to the square root of its molecular weight. Thus, if the molecular weight of one gas is four times that of another, it would diffuse through a porous plug or escape through a small pinhole in a vessel at half the rate of the other (heavier gases diffuse more slowly). A complete theoretical explanation of Graham's law was provided years later by the kinetic theory of gases. 

Graham's law is most accurate for molecular effusion which involves the movement of one gas at a time through a hole. It is only approximate for diffusion of one gas in another or in air, as these processes involve the movement of more than one gas.

Effusion is the process in which a gas escapes through a hole of diameter considerably smaller than the free path of molecules.

References

• The above description of the Graham's Law is in-part derived from Wikipedia (en.wikipedia.org/wiki/Graham%27s_law)