# If oxygen effuses through an opening at a rate of 67 particles per second, how fast would effuses Hydrogen gas effuse through the same opening?

May 1, 2016

$268$ particles per second.

#### Explanation:

Graham's law of effusion says that

${R}_{1} / {R}_{2} = \sqrt{{M}_{2} / {M}_{1}}$,

where $R$ is the rate of effusion and $M$ is the mass. The subscript number refers to either oxygen or hydrogen - it's a relative equation.

If we say that substance $1$ is hydrogen and $2$ is oxygen, then

R_1=?
${R}_{2} = 67$

${M}_{1} = 1$
${M}_{2} = 16$

($M$ values from the periodic table).

Putting these values into a rearranged equation,

${R}_{1} = {R}_{2} \cdot \sqrt{{M}_{2} / {M}_{1}}$
${R}_{1} = 67 \cdot \sqrt{\frac{16}{1}} = 67 \cdot 4 = 268$