Question

i need help
A gas whose molar mass you wish to know effuses through an opening at a rate one fourth as fast as that of helium gas. What is the molar mass of the unknown gas?

Answer 1

Use Graham's Law of diffusion: \(\sf \large \dfrac{rate_{1}}{rate_{2}}=\sqrt{\dfrac{M_2}{M_1}}\)

\(\sf \large \dfrac{rate_{He}}{rate_{x}}=\sqrt{\dfrac{M_x}{4~g/mol}}\)


\(\sf \large rate_{x}=\dfrac{1}{4}rate_{He}\)

\(\sf \large \dfrac{rate_{He}}{\dfrac{1}{4}rate_{He}}=\sqrt{\dfrac{M_x}{4~g/mol}}\)

\(\sf \large 4=\sqrt{\dfrac{M_x}{4~g/mol}}\rightarrow M_x=4^2*4=64~g/mol\)