# Are the effusion rates of carbon dioxide and propane the same?

##### 1 Answer

Apr 20, 2017

They are close... not quite the same.

From the root-mean-square speeds, one could derive the rate of effusion.

#v_(RMS) = sqrt((3RT)/M)#

The rate of effusion **Graham's law of effusion**:

#bb(z_A/z_B) = sqrt((3RT)/M_A)/sqrt((3RT)/M_B)#

#= bb(sqrt(M_B/M_A))#

Hence, if we choose

#z_(CO_2)/z_(C_3H_8) = sqrt(M_(CO_2)/M_(C_3H_8))#

#= sqrt("44.01 g/mol"/"44.1 g/mol")#

#= 0.9979#

So they're *almost* the same, but propane effuses slightly faster.

#z_(CO_2) = 0.9979z_(C_3H_8)#