# Graham's law

Graham's law, known as Graham's law of effusion, was formulated by Scottish physical chemist Thomas Graham in 1846.

Graham's Law of Effusion states that the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles.

Graham's gas law is expressed as:

$\mathrm{rate\; of\; effusion}\propto \frac{1}{\sqrt{\mathrm{molar\; mass}}}\mathrm{at\; constant\; P\; and\; T}$

The ratio of effusion of two gases relates to the ratio of their densities (molar masses) and expressed as:

$\frac{{\mathrm{Rate}}_{1}}{{\mathrm{Rate}}_{2}}=\sqrt{\frac{{M}_{2}}{{M}_{1}}}$

where:

Rate_{1} is the rate of effusion of the first gas (volume or number of moles per unit time).

Rate_{2} is the rate of effusion for the second gas.

M_{1} is the molar mass of gas 1.

M_{2} is the molar mass of gas 2.

Example 1:

Oxygen has an effusion tate of 10 milliliters per second and weight of 32 amu. What is the molecular weight of a gas which diffuses twice as fast as oxygen?

$\frac{{\mathrm{Rate}}_{1}}{{\mathrm{Rate}}_{2}}=\sqrt{\frac{{M}_{2}}{{M}_{1}}}$

$\frac{{\mathrm{Rate}}_{2}}{{\mathrm{Rate}}_{1}}=\sqrt{\frac{{M}_{1}}{{M}_{2}}}\mathrm{or}{\left(\frac{{\mathrm{Rate}}_{2}}{{\mathrm{Rate}}_{1}}\right)}^{2}=\frac{Mx}{MO2}$

${\left(\frac{10\mathrm{mL\; per\; second}}{20\mathrm{mL\; per\; second}}\right)}^{2}=\frac{Mx}{32\mathrm{amu}}$

${M}_{x}={\left(\frac{10}{20}\right)}^{2}x32=8\mathrm{amu}$