# 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:
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.

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?
$\frac{{\mathrm{Rate}}_{1}}{{\mathrm{Rate}}_{2}}=\sqrt{\frac{{M}_{2}}{{M}_{1}}}$
$\frac{{\mathrm{Rate}}_{2}}{{\mathrm{Rate}}_{1}}=\sqrt{\frac{{M}_{1}}{{M}_{2}}}\mathrm{or}{\left(\frac{{\mathrm{Rate}}_{2}}{{\mathrm{Rate}}_{1}}\right)}^{2}=\frac{Mx}{MO2}$
${\left(\frac{10\mathrm{mL per second}}{20\mathrm{mL per second}}\right)}^{2}=\frac{Mx}{32\mathrm{amu}}$
${M}_{x}={\left(\frac{10}{20}\right)}^{2}x32=8\mathrm{amu}$